asymptotic observables and the swampland

ACFI-T20-08

Asymptotic Observables and the Swampland

Tom Rudelius∗

Physics Department, University of California, Berkeley CA 94720 USA(Dated: June 18, 2021)

We show that constraints on scalar field potentials and towers of light massive states in asymp-totic limits of scalar field space (as posited by the de Sitter Conjecture and the Swampland DistanceConjecture, respectively) are correlated with the prospects for defining asymptotic observables inexpanding FRW cosmologies. The observations of a “census taker” in an eternally inflating cos-mology are further related to the question of whether certain domain walls satisfy a version of theWeak Gravity Conjecture. This suggests that answers to fundamental questions about asymptoticobservables in cosmology could help shed light on the Swampland program, and vice versa.

I. INTRODUCTION

The past few years have seen significant advances inour understanding of the physics of black holes. Recentcomputations of the Page curve [1–3] have shed lighton the black hole information paradox [4] and led to aconcrete realization of black hole complementarity [5–7].Meanwhile, strong evidence has been provided for the ab-sence of global symmetries in quantum gravity [8–14] andthe Weak Gravity Conjecture (WGC) [15–19]—two con-jectures motivated by demanding consistent black holedecay—as well as the Swampland Distance Conjecture(SDC) [20–26]. The consequences of these conjectureshave been studied extensively.

At the same time, there has been a revival of interest inquestions about de Sitter space and inflation, though asof yet these questions have not been clearly answered.Various works have considered bounds on scalar fieldpotentials in quantum gravity [27–32], called into ques-tion the existence of de Sitter vacua in quantum gravity[27, 33, 34], and advocated for alternative models of darkenergy [35–38]. Yet at the same time, other works havemade progress in putting claimed de Sitter constructionsin string theory on more solid footing [39–42]. Similarly,various works have proposed constraints on inflation inquantum gravity [35, 43–47], while other works have at-tempted to evade these constraints [48–50].

The goal of this paper is to draw parallels between thephysics of black holes and the physics of de Sitter cos-mologies, which ideally may allow us to translate some ofthe recent lessons learned in the former area into progressin the latter. At the same time, we will also highlight con-nections between semiclassical analyses of black holes andcosmology and recent developments in the “Swamplandprogram.” In particular, we will argue that older studieson the difficulties of defining asymptotic observables inan expanding universe may shed light on recent studiesof scalar field potentials in string theory, and in turn, re-cent progress on the Weak Gravity Conjecture and blackhole complementarity may shed light on asymptotic ob-servables in de Sitter space.

∗ [email protected]

The remainder of this paper is structured as follows.In Section II, we review the difficulties of defining asymp-totic observables in expanding spacetimes. In Section III,we review the difficulties of defining asymptotic observ-ables, and making predictions, in an eternally inflatingcosmology. In Section IV, we connect the problem ofdefining asymptotic observables to the de Sitter Conjec-ture [27]. We advocate for a particular “strong form” ofthe de Sitter Conjecture, recently proposed by the au-thor in [51], and we explain why this Strong de SitterConjecture may be thought of as a sort of Weak Grav-ity Conjecture [15]. In Section V, we connect the ther-mal fluctuations that occur in quintessence models to theSwampland Distance Conjecture [20]. In Section VI, weemphasize that the experiences of observers in an eter-nally inflating cosmology are dictated by whether or notdomain walls satisfy a version of the Weak Gravity Con-jecture, which suggests a parallel between black hole de-cay (which involves the ordinary Weak Gravity Conjec-ture for charged particles) and de Sitter vacuum decay(which involves this version of the Weak Gravity Conjec-ture for domain walls). We conclude with a discussion ofour results and remaining questions in Section VII.

II. ASYMPTOTIC OBSERVABLES IN ANEXPANDING UNIVERSE

To date, all precise formulations of quantum gravityinvolve either Anti-de Sitter (AdS) spacetimes or asymp-totically flat spacetimes. This is related to the fact thatsuch spacetimes allow us to define asymptotic observ-ables: in the former, such observables are represented bycorrelation functions of a conformal field theory livingat the boundary of AdS, though the AdS/CFT corre-spondence. In the latter, observables are represented byS-matrix elements.

In cosmology, on the other hand, it is not nearly sosimple to define asymptotic observables. In many cos-mologies, the presence of an initial singularity precludesthe existence of an S-matrix, though this issue may per-haps be sidestepped by assuming a unique initial stateand writing down an S-vector that describes only the fi-nal state amplitudes [52, 53]. However, an even largerissue looms: as emphasized in e.g. [54, 55], FRW cos-

arX

iv:2

106.

0902

6v1

[he

p-th

] 1

6 Ju

n 20

21

mailto:[email protected]

2

mologies do not have a property known as “asymptoticcoldness”: the energy density of these spacetimes doesnot tend to zero at spatial infinity on a fixed Cauchyslice, and relatedly fluctuations of the geometry extendindefinitely. Any observer looking into the past at finitetime can only access a finite portion of such a universe,whereas the unobserved region of space contains an infi-nite amount of energy and (perhaps) an infinite amountof information. This prevents the observer from access-ing the global state of the universe no matter how longthey wait, and it precludes an S-matrix or S-vector de-scription.

It is possible that exact asymptotic observables simplydo not exist in cosmology, and trying to define them isnothing but a fool’s errand. But on the other hand, it ispossible that the above issues could be partially circum-vented, and some sort of asymptotic observables could bedefined even in the absence of asymptotic coldness. Theprospects for this depend strongly on the type of cosmol-ogy under consideration. Following [54], we review threesuch possibilities: de Sitter space (with equation of stateparameter w = −1), Q-space (−1 < w < −1/3), and adecelerating universe (w > −1/3).

For future reference, let us write down the metric of a(spatially flat) 4d FRW cosmology:

ds2 = −dt2 + a(t)2(dr2 + r2dΩ2

2

), (1)

where a(t) is the scale factor, which we assume evolvesaccording to

a(t) =

t

23(w+1) w > −1eHt w = −1

. (2)

Here we define the Hubble parameter H := a/a, which isconstant for w = −1 but vanishes in the t→∞ limit forw > −1. The energy density is then given by ρ = H2/3,and the pressure is given by p = wρ. Throughout thispaper we set 8πG = 1.

A. De Sitter

De Sitter space (dS) has equation of state parameterw = −1: the scale factor a(t) expands exponentially at aconstant rate for all time. The maximal extension of deSitter has the metric

ds2 =1

H2 sin2 η

(−dη2 + dχ2 + sin2 χdΩ2

2

). (3)

and its Penrose diagram is shown in Figure 1. The spatialsections at constant η are 3-spheres, so there is no notionof spatial infinity or null infinity: the only asymptoticregions are I±. A comoving observer has both past andfuture horizons of radius H−1. The region limited bythese respective horizons is called the causal diamond.

Several factors preclude the existence of asymptoticobservables in de Sitter space. To begin, de Sitter space

I+

<latexit sha1_base64="sV/uQbHPnYArqvlHGS9Oqulb2DQ=">AAAB6nicbVDLSgNBEOz1GeMr6tHLYBAEIexKRI8BQfQW0TwgWcPspDcZMju7zMwKYcknePGgiFe/yJt/4+Rx0MSChqKqm+6uIBFcG9f9dpaWV1bX1nMb+c2t7Z3dwt5+XcepYlhjsYhVM6AaBZdYM9wIbCYKaRQIbASDq7HfeEKleSwfzDBBP6I9yUPOqLHS/e3jaadQdEvuBGSReDNShBmqncJXuxuzNEJpmKBatzw3MX5GleFM4CjfTjUmlA1oD1uWShqh9rPJqSNybJUuCWNlSxoyUX9PZDTSehgFtjOipq/nvbH4n9dKTXjpZ1wmqUHJpovCVBATk/HfpMsVMiOGllCmuL2VsD5VlBmbTt6G4M2/vEjqZyWvXDq/Kxcr17M4cnAIR3ACHlxABW6gCjVg0INneIU3RzgvzrvzMW1dcmYzB/AHzucPvTaNdg==</latexit>

I+


I

<latexit sha1_base64="0zZjP0GMebGNLuNwB5LAxe2pMI0=">AAAB6nicbVDLSgNBEOz1GeMr6tHLYBC8GHYloseAIHqLaB6QrGF20psMmZ1dZmaFsOQTvHhQxKtf5M2/cfI4aGJBQ1HVTXdXkAiujet+O0vLK6tr67mN/ObW9s5uYW+/ruNUMayxWMSqGVCNgkusGW4ENhOFNAoENoLB1dhvPKHSPJYPZpigH9Ge5CFn1Fjp/vbxtFMouiV3ArJIvBkpwgzVTuGr3Y1ZGqE0TFCtW56bGD+jynAmcJRvpxoTyga0hy1LJY1Q+9nk1BE5tkqXhLGyJQ2ZqL8nMhppPYwC2xlR09fz3lj8z2ulJrz0My6T1KBk00VhKoiJyfhv0uUKmRFDSyhT3N5KWJ8qyoxNJ29D8OZfXiT1s5JXLp3flYuV61kcOTiEIzgBDy6gAjdQhRow6MEzvMKbI5wX5935mLYuObOZA/gD5/MHwD6NeA==</latexit>

Futurehorizon

<latexit sha1_base64="fKcSLlKUIsKGKOQPLJfnHPsCuHI=">AAAB9XicbVDLSgNBEJz1GeMr6tHLYBA8hd2gKJ4CgniMYB6QrGF20kmGzM4s81Dikv/w4kERr/6LN//GSbIHTSxoKKq66e6KEs608f1vb2l5ZXVtPbeR39za3tkt7O3XtbSKQo1KLlUzIho4E1AzzHBoJgpIHHFoRMOrid94AKWZFHdmlEAYk75gPUaJcdL9tTVWAR5IxZ6k6BSKfsmfAi+SICNFlKHaKXy1u5LaGIShnGjdCvzEhClRhlEO43zbakgIHZI+tBwVJAYdptOrx/jYKV3ck8qVMHiq/p5ISaz1KI5cZ0zMQM97E/E/r2VN7yJMmUisAUFni3qWYyPxJALcZQqo4SNHCFXM3YrpgChCjQsq70II5l9eJPVyKTgtnd2Wi5XLLI4cOkRH6AQF6BxV0A2qohqiSKFn9IrevEfvxXv3PmatS142c4D+wPv8AcDikqg=</latexit>

Past

horiz

on

<latexit sha1_base64="pIA5mkCEn57CK+wxd18t2AYqkzA=">AAAB83icbVDLSgNBEOyNrxhfUY9eBoPgKewGRfEU8OIxgnlAEsLsZDYZMjuzzPQKcclvePGgiFd/xpt/4+Rx0MSChqKqm+6uMJHCou9/e7m19Y3Nrfx2YWd3b/+geHjUsDo1jNeZltq0Qmq5FIrXUaDkrcRwGoeSN8PR7dRvPnJjhVYPOE54N6YDJSLBKDqpU6MWyVAb8aRVr1jyy/4MZJUEC1KCBWq94lenr1kac4VMUmvbgZ9gN6MGBZN8UuiklieUjeiAtx1VNOa2m81unpAzp/RJpI0rhWSm/p7IaGztOA5dZ0xxaJe9qfif104xuu5mQiUpcsXmi6JUEtRkGgDpC8MZyrEjlBnhbiVsSA1l6GIquBCC5ZdXSaNSDi7Kl/eVUvVmEUceTuAUziGAK6jCHdSgDgwSeIZXePNS78V79z7mrTlvMXMMf+B9/gAT9JGx</latexit>

Big bang

<latexit sha1_base64="JTaCW8By/k1JqppBsNQpiQWHbDo=">AAAB73icbVBNS8NAEJ34WetX1aOXxSJ4KklRFE9FLx4r2A9oQ5lsN+nSzSbuboRS+ie8eFDEq3/Hm//GbZuDtj4YeLw3w8y8IBVcG9f9dlZW19Y3Ngtbxe2d3b390sFhUyeZoqxBE5GodoCaCS5Zw3AjWDtVDONAsFYwvJ36rSemNE/kgxmlzI8xkjzkFI2V2jc8IgHKqFcquxV3BrJMvJyUIUe9V/rq9hOaxUwaKlDrjuemxh+jMpwKNil2M81SpEOMWMdSiTHT/nh274ScWqVPwkTZkobM1N8TY4y1HsWB7YzRDPSiNxX/8zqZCa/8MZdpZpik80VhJohJyPR50ueKUSNGliBV3N5K6AAVUmMjKtoQvMWXl0mzWvHOKxf31XLtOo+jAMdwAmfgwSXU4A7q0AAKAp7hFd6cR+fFeXc+5q0rTj5zBH/gfP4Add+Pkg==</latexit>

i0

<latexit sha1_base64="buzno7+CRTU17rMr5tqTJH6z0pg=">AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mkoseCIB4r2g9oQ9lsJ+3SzSbsboQS+hO8eFDEq7/Im//GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCopeNUMWyyWMSqE1CNgktsGm4EdhKFNAoEtoPxzcxvP6HSPJaPZpKgH9Gh5CFn1FjpgffdfrniVt05yCrxclKBHI1++as3iFkaoTRMUK27npsYP6PKcCZwWuqlGhPKxnSIXUsljVD72fzUKTmzyoCEsbIlDZmrvycyGmk9iQLbGVEz0sveTPzP66YmvPYzLpPUoGSLRWEqiInJ7G8y4AqZERNLKFPc3krYiCrKjE2nZEPwll9eJa2LqlerXt7XKvXbPI4inMApnIMHV1CHO2hAExgM4Rle4c0Rzovz7nwsWgtOPnMMf+B8/gD3D42c</latexit>

Big

bang


Horizon

<latexit sha1_base64="sh8yYtpShLAbprOAYFDc5TMJQio=">AAAB7nicbVDLSgNBEOz1GeMr6tHLYBA8hd2gKJ4CXnKMYB6QLGF2MpsMmccyMyvEJR/hxYMiXv0eb/6Nk2QPmljQUFR1090VJZwZ6/vf3tr6xubWdmGnuLu3f3BYOjpuGZVqQptEcaU7ETaUM0mblllOO4mmWESctqPx3cxvP1JtmJIPdpLQUOChZDEj2DqpXVeaPSnZL5X9ij8HWiVBTsqQo9EvffUGiqSCSks4NqYb+IkNM6wtI5xOi73U0ASTMR7SrqMSC2rCbH7uFJ07ZYBipV1Ji+bq74kMC2MmInKdAtuRWfZm4n9eN7XxTZgxmaSWSrJYFKccWYVmv6MB05RYPnEEE83crYiMsMbEuoSKLoRg+eVV0qpWgsvK1X21XLvN4yjAKZzBBQRwDTWoQwOaQGAMz/AKb17ivXjv3seidc3LZ07gD7zPH38Pj6c=</latexit>

I+


FIG. 1. The Penrose diagram of de Sitter space.

has a future horizon: there are regions of spacetime thatare forever out of contact of a comoving observer, so noobserver can ever witness the final state of the entireuniverse. Second, de Sitter has a finite entropy,

SdS =8π2

H2, (4)

and the Hilbert space of quantum gravity in de Sitteris (likely) finite-dimensional, which puts a limit on thecomplexity of any sort of measurement apparatus thatcould exist in de Sitter space [52]. Finally, as noted in[54], de Sitter has a constant temperature

TdS =H

2π, (5)

and the resulting thermal fluctuations, if sufficiently en-ergetic, may destroy any observers. Such high-energythermal fluctuations are Boltzmann-suppressed by a fac-tor of exp(−E/TdS), but if one waits long enough suchfluctuations are bound to occur, and thus no observerscan exist eternally in de Sitter space.

For practical purposes in our own universe, these issuesare not so important: the de Sitter entropy is enormous,of order 10123, and the temperature is minuscule, of order10−61, so observables can be defined to very good approx-imation. In addition, one might also entertain the possi-bility of “meta-observables” [52], which are exact quanti-ties that could be determined by a “meta-observer” whohas access to the entirety of I+ and I− (see Figure 1).However, neither of these approaches quite addresses theconceptual problem at hand: no observer living in deSitter space can perform a measurement with arbitraryprecision, so exact observables do not exist in de Sitter.

B. Q-space

Q-space (−1 < w < −1/3) describes a quintessence-dominated universe, which accelerates indefinitely intothe future but with decreasing Hubble parameter H =a/a. Its associated Penrose diagram is shown in Figure

3

I+


I+


I


Futurehorizon


Past

horiz

on


Big bang


i0


Big

bang


Horizon


I+


FIG. 2. The Penrose diagram of Q-space.

2. An observer’s causal diamond is bounded by a light-like big bang singularity and a future event horizon ofradius

RE = −3(w + 1)

3w + 1t = − 2

3w + 1H−1 . (6)

There is also an apparent horizon of radius

RA = H−1 =3

2(w + 1)t . (7)

Note that the size of these horizons grows without boundin the limit t → ∞, and correspondingly there is nobound on the amount of entropy that can exist withina comoving observer’s causal diamond. Indeed, such anobserver will experience a thermal heat bath with tem-perature

TQ =H

2π=

3

π(w + 1)t, (8)

and although this temperature decreases indefinitely withtime, arbitrarily high-entropy fluctuations will occur evenat late times. However, unlike in de Sitter, the Boltz-mann suppression of high-energy fluctuations increaseswith time, and shortly after the Hubble scale H dropsbelow a given energy E, the probability of ever again ob-serving a thermal fluctuation of energy E drops quicklyto zero [54].

Thus, life is not quite as bad for an observer in Q-space as it is for an observer in de Sitter: although thereis still a future cosmic horizon, there is no limit on theentropy contained within such a horizon, and correspond-ingly there is no inherent limit on the precision of a mea-surement. Furthermore, observers in Q-space are rarelydestroyed by high-energy thermal fluctuations, whereasin de Sitter this will eventually occur with probability 1.

Nonetheless, an important problem faces any observerin Q-space who wants to measure some observable withever-greater precision: although the maximal entropy al-lowed within the horizon may increase indefinitely, theonly source of such entropy is the thermal fluctuationsof massless (or nearly massless—see Section V) particlesfrom the horizon. Even in a more realistic cosmology

I+


I+


I


Futurehorizon


Past

horiz

on


Big bang


i0


Big

bang


Horizon


I+


FIG. 3. The Penrose diagram of a decelerating FRW cosmol-ogy.

with a period of matter/radiation domination precedingaccelerated expansion, the entropy of conventional mat-ter/radiation that enters the causal diamond of the ob-server by classical evolution is finite: eventually, a pairof comoving objects will exit one another’s horizons andcease to interact. Thus, constructing an experimentalapparatus of arbitrarily large complexity would requirethe observer to somehow harness the entropy of thermalradiation from the horizon, and it is not clear that thisis possible [54].

In summary, while the prospects for defining asymp-totic observables are more promising in Q-space than inde Sitter, there are nonetheless some important difficul-ties that must be overcome. We will now see that someof these difficulties are avoided in a decelerating universe.

C. Decelerating Universes

The Penrose diagram of a decelerating universe w >−1/3 is shown in Figure 3: essentially, it is obtained byturning the Penrose diagram of Q-space upside down.A decelerating universe does not have a future horizon:eventually, any two coming objects will enter one an-other’s past light cones, and correspondingly the entropyaccessible to a given observer diverges in the asymptoticfuture. There is therefore no limitation on the complex-ity of a possible experimental apparatus, and there isno limit on the size of space visible to a late-time ob-server. The theory at late times approaches that of par-ticles interacting in flat space: in short, the conditionsfor observers are as ideal as they could be in a universewithout asymptotic coldness.

III. ASYMPTOTIC OBSERVABLES INETERNAL INFLATION

Our universe is experiencing accelerated expansion,and thus far dark energy has no observed departure fromw = −1. This is difficult to square with the aforemen-tioned difficulties facing de Sitter space (among otherdifficulties [56–58]), but string theory may point us inthe right direction: in string theory, de Sitter vacua are

4

generally expected to be metastable, decaying via bubblenucleation to other vacua in the string Landscape [59].These vacua may in turn decay via bubble nucleation,and this process continues until a terminal vacuum isreached [60, 61]: presumably either a Λ < 0 AdS vacuum(which promptly crunches) or a Λ = 0 vacuum. In thelatter case, the vacuum in question may lie in an asymp-totic limit of scalar field space, in which case bubble nu-cleation may produce either an accelerating or decelerat-ing universe, depending on the shape of the potential—we will elaborate on the details of this point in the nextsection.

The upshot of this is that the difficult task of defin-ing asymptotic observables in de Sitter space has beenexchanged for the difficult task of defining asymptoticobservables in an eternally inflating cosmology.1 In sucha cosmology, anything that can happen does happen aninfinite number of times, raising the difficult question ofhow to define a measure on the Landscape of all possibleuniverses. For a nice review of the measure problem ineternal inflation, see [67].

One approach to the measure problem, notably advo-cated by Susskind [55], is to introduce a comoving ob-server who looks back into the past and collects data.The expected observations of this observer then define ameasure on the Landscape: namely, the probability pi ofoutcome i is given in terms of the number of measure-ments N(t) in the past light cone of the observer at timet and the number of times Ni(t) the observer measures iby [68]

pi := limt→∞

Ni(t)

N(t). (9)

Such an observer is called a “census taker.”Of course, there are different possible census takers one

could choose, i.e., different locations where the “censusbureau” could be located. Some census takers will endtheir lives in an AdS vacuum, which ends with a sin-gular crunch. Such a census taker only has access toa finite amount of entropy before meeting their demise,so they cannot measure any observable to arbitrary pre-cision. Other census takers may end up in a bubble ofQ-space, in which the acceleration of the universe asymp-totes to zero. This is a much more promising location fora census bureau, but the challenges of defining asymp-totic observables here are just as thorny here as theywere in Q-space: in particular, a pair of comoving ob-jects will eventually exit one another’s horizons, and noobserver can see all the way to spatial infinity.

The most promising location for a census bureau isin a “hat region”: a bubble containing a deceleratinguniverse, so named because of the hat-like feature it in-troduces to the Penrose diagram (see Figure 4). Such a

1 A number of works have questioned the plausibility of eternalinflation [31, 33, 62–66], though at present there is no sharp no-go result which forbids it.

<latexit sha1_base64="Wim2HL6twfrMcILLa+kiXxV0HQU=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKoseAIB4jmgckS5idzCZj5rHMzAphyT948aCIV//Hm3/jJNmDJhY0FFXddHdFCWfG+v63V1hZXVvfKG6WtrZ3dvfK+wdNo1JNaIMornQ7woZyJmnDMstpO9EUi4jTVjS6nvqtJ6oNU/LBjhMaCjyQLGYEWyc1u/dsIHCvXPGr/gxomQQ5qUCOeq/81e0rkgoqLeHYmE7gJzbMsLaMcDopdVNDE0xGeEA7jkosqAmz2bUTdOKUPoqVdiUtmqm/JzIsjBmLyHUKbIdm0ZuK/3md1MZXYcZkkloqyXxRnHJkFZq+jvpMU2L52BFMNHO3IjLEGhPrAiq5EILFl5dJ86wanFcv7s4rtZs8jiIcwTGcQgCXUINbqEMDCDzCM7zCm6e8F+/d+5i3Frx85hD+wPv8AW8rjw8=</latexit>

<latexit sha1_base64="Wim2HL6twfrMcILLa+kiXxV0HQU=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKoseAIB4jmgckS5idzCZj5rHMzAphyT948aCIV//Hm3/jJNmDJhY0FFXddHdFCWfG+v63V1hZXVvfKG6WtrZ3dvfK+wdNo1JNaIMornQ7woZyJmnDMstpO9EUi4jTVjS6nvqtJ6oNU/LBjhMaCjyQLGYEWyc1u/dsIHCvXPGr/gxomQQ5qUCOeq/81e0rkgoqLeHYmE7gJzbMsLaMcDopdVNDE0xGeEA7jkosqAmz2bUTdOKUPoqVdiUtmqm/JzIsjBmLyHUKbIdm0ZuK/3md1MZXYcZkkloqyXxRnHJkFZq+jvpMU2L52BFMNHO3IjLEGhPrAiq5EILFl5dJ86wanFcv7s4rtZs8jiIcwTGcQgCXUINbqEMDCDzCM7zCm6e8F+/d+5i3Frx85hD+wPv8AW8rjw8=</latexit>

I+


I+


Horizon


Horizon


FIG. 4. A hat region of an eternally inflating cosmology.

region has many of the nice features of a decelerating uni-verse: a census taker in the hat region region will observean infinite amount of entropy if she waits long enough,any two comoving objects in the hat region will eventu-ally come into causal contact, and physics at late timescan be described by an effective field theory in flat space.

Some preliminary but noteworthy progress has beenmade in understanding the physics in such regions. Inparticular, [69] proposed that the physics in a hat re-gion has a dual description in terms of a CFT coupled toLiouville gravity living at spatial infinity Σ (see Figure4). In [70], Harlow and Susskind further conjectured thatthe maximum precision of a dual description of a cosmo-logical geometry is determined by the maximal entropybound on the past light cone of a census taker, and theyargued that this description can be exact, i.e., ultravioletcomplete, only if there exists a census taker with an in-finite entropy bound (also known as a “maximal” censustaker). In principle, a census taker in a bubble of Q-spacefits this description as well, since they too have an infi-nite entropy bound, but to date there has been little tono work in understanding the dual descriptions of suchuniverses.

One issue facing a census taker in hat region, which isabsent in the case of a decelerating FRW universe, is theexistence of a cosmic horizon: as shown in Figure 4, sucha census taker can see all the way to spatial infinity Σ inher own bubble, but there are other parts of spacetimehidden beyond the cosmic horizon. This issue, however,is probably not devastating from the perspective of defin-ing asymptotic observables: indeed, black hole horizonsexist in asymptotically AdS spacetimes. Here, a crucialrole is played by the notion of black hole complementar-ity [5–7]: the physics of the black hole interior is encodedin the radiation emitted by the black hole horizon. It isplausible that a similar notion of cosmic horizon comple-mentarity is relevant here, so that the global structure ofthe eternally inflating spacetime is encoded in the radia-tion emitted from the cosmic horizon [55, 71], ostensiblyallowing the census taker to define a global measure onthe spacetime beyond her horizon [68]. Similarities be-tween de Sitter cosmic horizons and black hole horizonshave recently been investigated in [72–74].

5

IV. ASYMPTOTIC OBSERVABLES AND THEDE SITTER CONJECTURE

While the difficulties of constructing de Sitter vacuain string theory are not new, they have drawn renewedinterest since the publication of what is now referred toas the “de Sitter Conjecture (dSC)” [27]. In this work,the authors proposed a bound on the gradient of scalarfield potentials V in quantum gravity in d spacetime di-mensions of the form

|∇V | ≥ cdV , (10)

where cd is an O(1) constant in d-dimensional Planckunits to be determined later. This bound is almost surelyviolated at the maximum of the standard model Higgspotential, so it is very unlikely that it applies universallyin quantum gravity [75]. However, it is quite plausiblethat a bound of this form applies in asymptotic regionsof scalar field space [29, 76], and indeed many examplesin string theory satisfy this criterion [27, 77, 78]. In thefollowing section, we will review one general argument forthe validity of this bound in asymptotic regions of scalarfield space, originally given in [79].

In order to determine the domain of validity of thedSC bound (10), it is crucial to fix the precise value ofthe O(1) constant cd, and relatedly to understand thephysical principle underlying this bound. As an analogy,the precise O(1) coefficient γd appearing in the WGCbound |q|/m ≥ γd is fixed by the physical principle thatnon-supersymmetric black holes must be able to decay.We would like a similar statement here to fix the valueof cd.

In [51], it was noted that the dSC is exactly preservedunder dimensional reduction if we set

cd = cstrongd :=2√d− 2

. (11)

In other words, a theory which saturates the bound (10)with this value of cd will still saturate the bound af-ter dimensional reduction. Of course, it is not obviousthat every valid Swampland conjecture must be exactlypreserved under dimensional reduction, but it is worthnoting that some of the most well-supported Swamplandconjectures are, including the Weak Gravity Conjectureand the absence of global symmetries [80, 81]. The value

cd = cstrongd is also special from the perspective of thelate-time expansion of the universe: a scalar field rollingin a potential of the form

V ∝ exp(−λφ) (12)

will drive expansion of the universe with equation of state

w = −1 +1

2

d− 2

d− 1λ2 , (13)

which for λ > cstrongd implies

w ≥ −d− 3

d− 1. (14)

This is precisely the strong energy condition in d dimen-sions, which is precisely the condition that forbids accel-erated expansion of the universe. Consequently, we definethe “Strong de Sitter Conjecture” as the statement thatthe strong energy condition should be satisfied in asymp-totic limits of scalar field space, which is equivalent tothe de Sitter bound (10) with cd = cstrongd := 2/

√d− 2 if

we suppose that the energy density is dominated by thescalar field condensate. Note that we do not expect thiscondition to hold outside of such asymptotic regions ofscalar field space: indeed, the strong energy condition isviolated even in our own universe.

String vacua with vanishing vacuum energy V = 0 areexpected to be supersymmetric, except in certain asymp-totic limits of scalar field space [70] such as the weak cou-pling limit of non-supersymmetric, SO(16)×SO(16) het-erotic string theory [82].2 Many string vacua in asymp-totic limits of scalar field space are supersymmetric, how-ever, and in this context compelling evidence for theStrong dSC was given in [53]: the authors of that pa-per argued that within an accelerating cosmology in fourdimensions, a scalar field cannot asymptote to a zero-energy supersymmetric minimum, and their argumentcan be extended trivially to general spacetime dimen-sions. In particular, the potential around a stable super-symmetric minimum in d dimensions must take the form[83, 84]:

V (φi) = 2(d− 2)((d− 2)(∇W )2 − (d− 1)W 2

), (15)

where W is the superpotential. If we then assume thatthe potential takes the asymptotic form V ∝ exp(−λφ)as φ→∞, we must impose W ≈W0 exp(−λφ/2), whichleads to

V (φ) ≈ 2(d− 2)W 20 e−λφ

((d− 2)

λ2

4− (d− 1)

). (16)

This is positive only if

λ > 2

√d− 1

d− 2, (17)

which immediately implies λ > 2/√d− 2, thereby satis-

fying the Strong dSC.From the discussion in the previous section, we see that

the Strong dSC may also be motivated by a more physicalprinciple: the existence of asymptotic hat regions, whichmay be necessary for the existence of well-defined observ-ables in spacetimes with positive vacuum energy, requiresnot only that V → 0 limits exist in scalar field space, butalso that these limits occur in regions with decelerat-ing expansion. Conversely, the difficulty of defining ex-act observables in asymptotic Q-space may signal an in-consistency with such spacetimes, implying that a scalar

2 We thank Irene Valenzuela for explaining this example to us.

6

field potential which violates the Strong dSC bound inasymptotic regions of scalar field space must reside inthe Swampland.

In a decelerating universe (in contrast to Q-space),physics at late times is governed by an effective theory ofinteracting particles in flat space. In a sense, the StrongdSC should therefore be thought of as a type of WeakGravity Conjecture: just as the ordinary WGC holds thatgravity can be decoupled from electromagnetism at lowenergies and the scalar WGC [85] holds that gravity canbe decoupled from interactions mediated by a scalar fieldat low energies, the Strong dSC holds that gravitationalexpansion of the universe can be decoupled from otherinteractions at late times.

V. THERMAL FLUCTUATIONS AND THESWAMPLAND DISTANCE CONJECTURE

We have argued that the Strong dSC value cstrongd =

2/√d− 2 is a particularly natural choice for the O(1)

constant cd appearing in the dSC bound, motivated bothby dimensional reduction and by the improved prospectsfor defining asymptotic observables in a decelerating uni-verse. Nonetheless, it is worthwhile to consider the alter-native possibility of an observer who ends their life inQ-space.

Recall from our discussion above that the prospectsfor asymptotic observables in Q-space are not completelyhopeless: perhaps the greatest difference between a cen-sus taker in Q-space and a census taker in a hat region isthat the Q-space observer cannot access arbitrarily largeamounts of information through classical evolution: theonly way to build a measuring device of arbitrary com-plexity is through low-energy, high-entropy thermal fluc-tuations coming from the cosmic horizon. To assess thepossibility of asymptotic observables in Q-space, we musttherefore investigate the thermal fluctuations that occurin such cosmologies.

At late times, the temperature of the future horizonin Q-space tends to zero, so the thermal fluctuations be-come softer and softer. Eventually, one expects that onlymassless modes will be emitted unless there are stateswhose energy decreases appropriately with time. Indeed,the existence of such states is a stipulation of anotherwell-tested Swampland conjecture called the SwamplandDistance Conjecture (SDC) [20],3 which holds that inany asymptotic limit φ → ∞ in scalar field space, there

3 Strictly speaking, the Swampland Distance Conjecture appliesonly to massless scalar field moduli in supersymmetric theo-ries, whereas we are concerned here with a “refined version” ofthe conjecture, which holds that this conjecture should applyin asymptotic limits of scalar field space in non-supersymmetrictheories as well [86]. Compelling, general arguments for both theSDC and its refinement have been given in [21, 22], and we willnot distinguish the two conjectures in this work.

must exist a tower of particles, each labeled by a positiveinteger n, whose masses scale with φ and n as

mn ∼ nm0e−αφ , (18)

for m0 an arbitrary mass scale and α some O(1) constantin Planck units. Like the value of cd appearing in the dSCbound (10), the question of what values of α are allowedin quantum gravity is a topic of ongoing research.

Motivated by the SDC, let us now consider thermalemission from the Q-space horizon in four dimensions.As discussed in [54], the probability of thermal emissionper unit time of a state of energy E is given roughly by

PE ∼1

RAexp [S(E)− 2πERA] , (19)

where RA = H−1, exp(S(E)) is the number of statesof energy E, and we are assuming that there are onlyO(1) states of energy below the Q-space temperatureTQ = H/(2π). According to Bousso’s D-bound [87],which generalizes the Bekenstein bound [88, 89] to deSitter space, the term in the exponent in (19) is neces-sarily negative.

Integrating this result over all time t > t0, we findthe probability of a thermal fluctuation of energy E aftertime t0:

P(E) =

∫ ∞t0

dtPE(t)

=

∫ ∞t0

dt1

RA(t)exp [S(E)− 2πERA] . (20)

For constant E R−1A (t0), the Boltzmann suppressionexp(−2πERA(t0)) dominates, and the total probabilityP(E) is small. However, in a theory satisfying the SDC,the energy of a single-particle state in the tower itselfchanges with time, E = E(t). In particular, if we have

mn ∼ nm0e−αφ , V (φ) ∼ V0e−λφ , (21)

for φ a canonically normalized scalar field, then the en-ergy of such a state behaves as E ∼ E(t0) exp(−αφ),whereas the radius RA scales as RA ∼ RA(t0) exp(λφ/2).This means that if

α =λ

2, (22)

then the Boltzmann suppression factor exp(−2πERA) re-mains roughly constant over time, and the total proba-bility is bounded from below by

P(E) ≥∫ ∞t0

dt1

RA(t)exp [−2πE(t)RA(t)]

&2

3(w + 1)exp [−2πE(t0)RA(t0)]

∫ ∞RA(t0)

dRARA

,

(23)

where we have used the fact that RA = 3(w+1)2 t. This

integral diverges logarithmically, so we see that thermal

7

emission of particles in the SDC tower continues indefi-nitely when α ≥ λ/2.

Let us make a few remarks on how this result fits withexisting literature. Reference [90] proposed precisely therelationship α ≥ cd/2 between the exponent of the SDCtower α and the coefficient of the dSC bound (10), basedon the fact that many examples in string theory seem tosatisfy or saturate this bound [21, 90] if one sets

cd = cTCCd :=

2√(d− 1)(d− 2)

, (24)

which is the value of cd specified by the “TransplanckianCensorship Conjecture (TCC)” [32]. We see here thatthe bound α ≥ λ/2 follows from the requirement thatstates in the SDC tower are thermally produced at latetimes, which together with the dSC bound λ ≥ cd impliesα ≥ cd/2. Whether or not such a requirement shouldhold—and whether or not asymptotic Q-space can evenoccur in quantum gravity—is a topic for future research.

Under the assumption of the SDC, [79] presenteda compelling argument for the validity of the dSC inasymptotic regions of scalar field space: in the limitφ→∞, the SDC implies the existence of a large numberof light species N , which in turn lead to a UV cutoff oneffective field theory that is parametrically below the 4dPlanck scale [91–94]:

ΛUV ∼MPl√N(ΛUV)

. (25)

According to the SDC, the number of light species isgiven by

N(ΛUV) &ΛUV

m0e−αφ, (26)

so

ΛUV ∼ e−αφ/3 . (27)

On the other hand, the Hubble scale H acts as an IRcutoff on effective field theory, and this scales with φ as

H ∼ V 1/2 ∼ e−λφ/2 . (28)

Requiring that the UV cutoff ΛUV is larger than the IRcutoff H as φ→∞ therefore implies

α ≤ 3

2λ , (29)

which is consistent with the condition α ≥ λ/2.It is worth emphasizing that the relationship α ≥ λ/2

we have found here assumes that we are in Q-space, sothe universe is accelerating at late times, i.e., 0 < λ <2/√d− 2. Our calculation tells us nothing about the

coefficient α of an SDC tower in a decelerating universe(λ > 2/

√d− 2) or a supersymmetric theory in flat space

(V ≡ 0), so in particular the bound α ≥ cd/2 is notapplicable if one assumes the Strong dSC.

VI. VACUUM DECAY AND THE WEAKGRAVITY CONJECTURE

So far, we have seen how the experiences of differentobservers in an expanding universe point towards theStrong de Sitter Conjecture and perhaps the SwamplandDistance Conjecture: census takers have helped shedlight on the Swampland. We now present an instanceof the opposite: the Weak Gravity Conjecture (WGC)may help shed light on the observations of census takersin a hat region.

Consider a maximal census taker, i.e., a census takerwho begins her life in a de Sitter phase and ends her life ina hat region. Such a census taker is maximal in the sensethat she will eventually have access to infinite entropy.However, in the standard description of eternal inflation,her past light cone will not contain the entirety of theexpanding universe (see Figure 4): her observations arelimited by a cosmic horizon. As discussed in SectionIII above, this issue could be circumvented by a suitablenotion of cosmic horizon complementarity, in which theregion behind the observer’s horizon is somehow encodedin the radiation she receives from this horizon.4

Nonetheless, there is a somewhat surprising aspect ofthis picture: not all decays from de Sitter space intothe Λ = 0 vacuum can occur in the past light cone ofa maximal census taker [67]. This is due to the counter-intuitive fact that the domain wall separating a Λi > 0vacuum from a Λf = 0 vacuum may appear to recedefrom the perspective of both the inside observer and theoutside observer. (This fact can be visualized by analogywith stereographic projection of the 2-sphere, as shownin Figure 5.) The radius of curvature of concentric shellsinside/outside a spherical bubble at constant time de-creases away from the bubble wall on both sides. In thiscase, observers on both sides of the bubble believe thatthey are actually on the inside of an expanding bubble,and the Λf = 0 bubble never grows to encompass theobserver in the Λi > 0 region. As a result, the observerin the Λi > 0 region never enters the past horizon of theΛf = 0 census taker, so he will never be counted in hercensus.

The question of whether the observer in the Λi > 0region sees the domain wall approaching or receding de-pends on the relative sizes of Λi and the tension T of thedomain wall. In particular, the qualification requirementfor the census is given in 4d reduced Planck units by [96]

T ≤ 2√3

(√Λi −

√Λf

), (30)

4 Some support of this idea may come from recent work [95], whichfound islands in a dS2 spacetime with a hat region, indicatingthat an observer in the hat region has access to information aboutthe inflating region, analogous to the way islands in black holespacetimes indicate that an asymptotic observer has access toinformation about the black hole interior [1–3]. It is unclear atpresent if this story can be extended to de Sitter spacetimes inmore than two dimensions, however.

8

d d d d d d d d

FIG. 5. Stereographic projection of the 2-sphere. Latitudes inthe southern hemisphere map to circles in the interior of theunit disk, and their radius of curvature on the 2-sphere growswith increasing size in the stereographic plane. Latitudes inthe northern hemisphere, on the other hand, map to circlesoutside the unit disk, and the radius of curvature of theselatitudes on the 2-sphere actually decreases while the size ofthe associated circles in the plane increases.

where in the case at hand, Λf = 0. If this bound is sat-isfied, the Λi > 0 observer will eventually enter the pastlight cone of the maximal census taker. If it is violated,the Λi > 0 observer will remain forever beyond her hori-zon, and information about the Λi > 0 observer can reachthe maximal census taker only in a highly scrambled formthrough the radiation she receives from her horizon [68].

This bound is familiar from the classic paper on vac-uum decay by Coleman and de Luccia [59]: when (30) issatisfied comfortably, gravitational effects are weak andcan be largely neglected from the computation of the de-cay rate. When it is violated, gravitational effects arestrong. Indeed, for a decay from a Λi = 0 vacuum toa Λf < 0 vacuum, these gravitational effects become sostrong that bubble nucleation shuts off entirely. BPSdomain walls in the supersymmetric Λi = 0 vacuum sat-urate this bound [97], and their decay rate vanishes, sothe supersymmetric vacuum is (marginally) stable.

An upper bound on the tension of a brane which is sat-urated by a BPS brane smells an awful lot like a WeakGravity Conjecture, and indeed this connection was dis-cussed at length by Freivogel and Kleban in [98], whoconjectured that for every vacuum in the Landscape withvacuum energy Λi, there should exist another vacuum ofenergy Λf < Λi and a domain wall between them whosetension satisfies (30). If true, this conjecture would im-ply that the lifetime of any de Sitter vacuum must beshorter than its Poincare recurrence time, and it wouldimply that any non-supersymmetric Anti-de Sitter vac-uum will decay in finite time (see also [99]).

The relationship between this conjecture and the usualWeak Gravity Conjecture for p-form gauge fields can bemade more concrete in the case of domain walls separat-ing vacua distinguished by different values of flux [98, 99].In particular, consider the 4d description of axion mon-odromy inflation [100, 101] pioneered in [102], which hasa Lagrangian of the form

L =1

2(∂µφ)2 − 1

2|F4|2 + gφF4 , (31)

with F4 = dC3. The 3-form field has no propagating

degrees of freedom in 4d, so it can be integrated outto produce a quadratic, multi-branched potential for theaxion φ,

V =1

2(nf0 + gφ)2 . (32)

Here, n ∈ Z, and f0 is the coupling constant of C3. Thepotential is preserved under shifts φ → φ + 2πf , n →n − 1 after imposing the consistency condition 2πfg =f0. The difference of vacuum energies between a pair ofneighboring flux vacua is given roughly by nf20 , so for nof order 1, (30) becomes

T . f0 . (33)

Up to an unspecified O(1) prefactor, this is simply theWGC bound for a domain wall charged under a 3-formgauge field.

Why is this significant? In past discussions, the factthat the observations of a census taker in a hat regioncould depend on “arcane details” such as the tensionof a particular domain wall was viewed as an unwel-come surprise, and potentially even as an indication thatsuch a census taker is not well-suited to making predic-tions in eternal inflation [67]. However, recent work onthe WGC suggests a very different perspective: we haveseen in many contexts that the violation/observation ofa WGC bound is not an arcane detail, but rather a cru-cial consistency condition of quantum gravity. In a the-ory which violates the ordinary WGC bound q/m ≥ γd,non-supersymmetric extremal black holes cannot decay.Analogously, we see here that a Λi > 0 vacuum decayto a Λf = 0 vacuum cannot occur in the past light coneof a census taker in the latter vacuum if no domain wallbetween them satisfies the WGC-like bound (30).

Perhaps, like the ordinary WGC, this should be inter-preted as a consistency condition on the effective fieldtheory of the Λi > 0 vacuum: given a Λi > 0 vacuum,there necessarily exists a Λf = 0 vacuum and a domainwall separating the two vacua whose tension satisfies (30).Such a condition would represent a strengthening of theconjecture of [98], which demands the existence of a do-main wall with tension satisfying (30) for every Λi > 0,but does not demand Λf = 0. This is also related to theconjecture of McNamara and Vafa that there should beno nontrivial cobordisms in quantum gravity [103], whichimplies that there must exist a domain wall between anytwo vacua but does not impose a constraint on the ten-sion of this domain wall.

On the other hand, it is quite hard to imagine thatsuch a decay channel should exist for any Λi > 0 vac-uum: it seems very unlikely, for instance, that our stan-dard model vacuum can decay to a Λf = 0 vacuum via adomain wall whose tension satisfies (30), though it is dif-ficult to rule out this possibility without a better under-standing of the quantum gravity Landscape. In addition,it is worth noting that that the condition (30) is not satis-fied by the domain wall interpolating between the Λi > 0vacuum and the asymptotic region of scalar field space

9

in the KKLT proposal [104] (though the Strong dSC issatisfied in the asymptotic regime of scalar field space inthat example). Whether this is due to an inconsistencyin the KKLT proposal, indicates the existence of somedomain wall not considered in the original KKLT paper,or represents a counterexample to the supposal of thepreceding paragraph remains to be seen.

VII. DISCUSSION

In this paper, we have established a connection be-tween various Swampland conjectures and the difficultyof defining asymptotic observables in expanding andeternally inflating cosmologies. We have seen that astrong version of the dSC in asymptotic regions ofscalar field space—previously distinguished by dimen-sional reduction—would offer the best prospects fordefining asymptotic observables in eternal inflation, asit implies the existence of hat regions (i.e., deceleratingbubble universes). We have seen that the observations ofa census taker in a hat region depends on whether or not aWGC-like bound is satisfied, and we have considered thepossibility that this may be a consistency condition ondS vacuum decay in quantum gravity, similar to how theordinary WGC is a consistency condition on black holedecay. We also saw, however, that a recently-proposed,sharpened version of the SDC implies that a tower of lightstates are thermally produced at late times in Q-space.This may be related to the definition of precise asymp-totic observables in such spacetimes, which necessarilydepend on thermal fluctuations.

On the other hand, we have not tackled the most im-portant questions: do asymptotic observables exist in ex-panding spacetimes? If so, what are they, and how arethey computed? Can census takers in an eternally inflat-

ing universe be used to define a measure on the stringLandscape, and if so, what is it? It is very possible thatthese questions will ultimately lead us in directions or-thogonal to the the ones we have pursued in this paper:as discussed, even a decelerating cosmology suffers fromasymptotic warmness, and in light of this it is not clearthat even the Strong dSC is sufficient to guarantee the ex-istence of well-defined observables. Another possibility isthat our semiclassical description of expanding cosmolo-gies must be modified significantly in the full quantumgravity, so that distant regions of space contain little newinformation, and asymptotic coldness is restored. Thispossibility is worth exploring further, especially in lightof the recent realization of black hole complementarityin terms of islands [1–3]. Ultimately, our current car-toon picture of de Sitter and/or eternal inflation may besubject to serious revision.

Clearly, the correct picture of quantum gravity in cos-mology is still coming into focus, and the ground rulesare not yet clear. Nonetheless, it is heartening to thinkthat progress in the Swampland program may shed lighton the problem of asymptotic observables in cosmology,and vice versa. Certainly, these are beautiful times toponder the mysteries of quantum gravity.

Acknowledgments. We thank Lars Aalsma, RaphaelBousso, Juan Carlos Carrasco Martınez, Hugo Mar-rochio, Liam McAllister, Jacob McNamara, MatthewReece, Gary Shiu, and Irene Valenzuela for useful discus-sions. We further thank Lars Aalsma, Raphael Bousso,Hugo Marrochio, Liam McAllister, Matthew Reece, andGary Shiu for comments on a draft. The work of TR wassupported by NSF grant PHY1820912, the Simons Foun-dation, and the Berkeley Center for Theoretical Physics.

[1] G. Penington, Entanglement Wedge Reconstructionand the Information Paradox, JHEP 09, 002,arXiv:1905.08255 [hep-th].

[2] A. Almheiri, N. Engelhardt, D. Marolf, and H. Maxfield,The entropy of bulk quantum fields and the entangle-ment wedge of an evaporating black hole, JHEP 12, 063,arXiv:1905.08762 [hep-th].

[3] A. Almheiri, R. Mahajan, J. Maldacena, and Y. Zhao,The Page curve of Hawking radiation from semiclassicalgeometry, JHEP 03, 149, arXiv:1908.10996 [hep-th].

[4] J. Polchinski, The Black Hole Information Problem,in Theoretical Advanced Study Institute in ElementaryParticle Physics: New Frontiers in Fields and Strings(2016) arXiv:1609.04036 [hep-th].

[5] L. Susskind, L. Thorlacius, and J. Uglum, The Stretchedhorizon and black hole complementarity, Phys. Rev. D48, 3743 (1993), arXiv:hep-th/9306069.

[6] Y. Kiem, H. L. Verlinde, and E. P. Verlinde, Black holehorizons and complementarity, Phys. Rev. D 52, 7053(1995), arXiv:hep-th/9502074.

[7] T. Banks and W. Fischler, M theory observables for cos-mological space-times, (2001), arXiv:hep-th/0102077.

[8] T. Banks and N. Seiberg, Symmetries and Strings inField Theory and Gravity, Phys. Rev. D83, 084019(2011), arXiv:1011.5120 [hep-th].

[9] D. Harlow and H. Ooguri, Symmetries in quantum fieldtheory and quantum gravity, (2018), arXiv:1810.05338[hep-th].

[10] D. Harlow and E. Shaghoulian, Global symmetry, Eu-clidean gravity, and the black hole information problem,(2020), arXiv:2010.10539 [hep-th].

[11] Y. Chen and H. W. Lin, Signatures of global symmetryviolation in relative entropies and replica wormholes,(2020), arXiv:2011.06005 [hep-th].

[12] K. Yonekura, Topological violation of global symmetriesin quantum gravity, (2020), arXiv:2011.11868 [hep-th].

[13] B. Heidenreich, J. McNamara, M. Montero, M. Reece,T. Rudelius, and I. Valenzuela, Chern-Weil GlobalSymmetries and How Quantum Gravity Avoids Them,(2020), arXiv:2012.00009 [hep-th].

https://doi.org/10.1007/JHEP09(2020)002

https://arxiv.org/abs/1905.08255





https://doi.org/10.1142/9789813149441_0006

https://doi.org/10.1142/9789813149441_0006


https://doi.org/10.1103/PhysRevD.48.3743


https://arxiv.org/abs/hep-th/9306069














10

[14] P.-S. Hsin, L. V. Iliesiu, and Z. Yang, A violation ofglobal symmetries from replica wormholes and the fateof black hole remnants, (2020), arXiv:2011.09444 [hep-th].

[15] N. Arkani-Hamed, L. Motl, A. Nicolis, and C. Vafa, TheString landscape, black holes and gravity as the weakestforce, JHEP 0706, 060, arXiv:hep-th/0601001 [hep-th].

[16] B. Heidenreich, M. Reece, and T. Rudelius, Evidencefor a sublattice weak gravity conjecture, JHEP 08, 025,arXiv:1606.08437 [hep-th].

[17] M. Montero, G. Shiu, and P. Soler, The Weak Grav-ity Conjecture in three dimensions, JHEP 10, 159,arXiv:1606.08438 [hep-th].

[18] S.-J. Lee, W. Lerche, and T. Weigand, Modular Fluxes,Elliptic Genera, and Weak Gravity Conjectures in FourDimensions, (2019), arXiv:1901.08065 [hep-th].

[19] S.-J. Lee, W. Lerche, and T. Weigand, TensionlessStrings and the Weak Gravity Conjecture, JHEP 10,164, arXiv:1808.05958 [hep-th].

[20] H. Ooguri and C. Vafa, On the Geometry of the StringLandscape and the Swampland, Nucl. Phys. B 766, 21(2007), arXiv:hep-th/0605264.

[21] T. W. Grimm, E. Palti, and I. Valenzuela, Infinite Dis-tances in Field Space and Massless Towers of States,JHEP 08, 143, arXiv:1802.08264 [hep-th].

[22] B. Heidenreich, M. Reece, and T. Rudelius, Emer-gence of Weak Coupling at Large Distance in Quan-tum Gravity, Phys. Rev. Lett. 121, 051601 (2018),arXiv:1802.08698 [hep-th].

[23] R. Blumenhagen, D. Klawer, L. Schlechter, and F. Wolf,The Refined Swampland Distance Conjecture in Calabi-Yau Moduli Spaces, JHEP 06, 052, arXiv:1803.04989[hep-th].

[24] P. Corvilain, T. W. Grimm, and I. Valenzuela, TheSwampland Distance Conjecture for Kahler moduli,JHEP 08, 075, arXiv:1812.07548 [hep-th].

[25] T. W. Grimm, C. Li, and E. Palti, Infinite DistanceNetworks in Field Space and Charge Orbits, JHEP 03,016, arXiv:1811.02571 [hep-th].

[26] N. Gendler and I. Valenzuela, Merging the Weak Grav-ity and Distance Conjectures Using BPS ExtremalBlack Holes, (2020), arXiv:2004.10768 [hep-th].

[27] G. Obied, H. Ooguri, L. Spodyneiko, and C. Vafa,De Sitter Space and the Swampland, (2018),arXiv:1806.08362 [hep-th].

[28] S. K. Garg and C. Krishnan, Bounds on Slow Rolland the de Sitter Swampland, (2018), arXiv:1807.05193[hep-th].

[29] H. Ooguri, E. Palti, G. Shiu, and C. Vafa,Distance and de Sitter Conjectures on theSwampland 10.1016/j.physletb.2018.11.018 (2018),arXiv:1810.05506 [hep-th].

[30] D. Andriot and C. Roupec, Further refining the de Sit-ter swampland conjecture, Fortsch. Phys. 67, 1800105(2019), arXiv:1811.08889 [hep-th].

[31] T. Rudelius, Conditions for (No) Eternal Inflation,JCAP 08, 009, arXiv:1905.05198 [hep-th].

[32] A. Bedroya and C. Vafa, Trans-Planckian Censorshipand the Swampland, JHEP 09, 123, arXiv:1909.11063[hep-th].

[33] G. Dvali, C. Gomez, and S. Zell, Quantum Break-Timeof de Sitter, JCAP 1706, 028, arXiv:1701.08776 [hep-th].

[34] U. H. Danielsson and T. Van Riet, What if string the-

ory has no de Sitter vacua?, Int. J. Mod. Phys. D27,1830007 (2018), arXiv:1804.01120 [hep-th].

[35] P. Agrawal, G. Obied, P. J. Steinhardt, and C. Vafa, Onthe Cosmological Implications of the String Swampland,Phys. Lett. B784, 271 (2018), arXiv:1806.09718 [hep-th].

[36] R. Brandenberger, R. R. Cuzinatto, J. Frohlich, andR. Namba, New Scalar Field Quartessence, JCAP 02,043, arXiv:1809.07409 [gr-qc].

[37] P. Agrawal, G. Obied, and C. Vafa, H0 tension, swamp-land conjectures, and the epoch of fading dark mat-ter, Phys. Rev. D 103, 043523 (2021), arXiv:1906.08261[astro-ph.CO].

[38] L. A. Anchordoqui, I. Antoniadis, D. Lust, J. F. Soriano,and T. R. Taylor, H0 tension and the String Swampland,Phys. Rev. D 101, 083532 (2020), arXiv:1912.00242[hep-th].

[39] J. Moritz, A. Retolaza, and A. Westphal, Toward de Sit-ter space from ten dimensions, Phys. Rev. D97, 046010(2018), arXiv:1707.08678 [hep-th].

[40] Y. Akrami, R. Kallosh, A. Linde, and V. Vardanyan,The Landscape, the Swampland and the Era of Pre-cision Cosmology, Fortsch. Phys. 67, 1800075 (2019),arXiv:1808.09440 [hep-th].

[41] Y. Hamada, A. Hebecker, G. Shiu, and P. Soler, Under-standing KKLT from a 10d perspective, JHEP 06, 019,arXiv:1902.01410 [hep-th].

[42] S. Kachru, M. Kim, L. Mcallister, and M. Zimet,de Sitter Vacua from Ten Dimensions, (2019),arXiv:1908.04788 [hep-th].

[43] T. Rudelius, Constraints on Axion Inflation fromthe Weak Gravity Conjecture, JCAP 09, 020,arXiv:1503.00795 [hep-th].

[44] M. Montero, A. M. Uranga, and I. Valenzuela, Trans-planckian axions!?, JHEP 08, 032, arXiv:1503.03886[hep-th].

[45] J. Brown, W. Cottrell, G. Shiu, and P. Soler, Fencingin the Swampland: Quantum Gravity Constraints onLarge Field Inflation, JHEP 10, 023, arXiv:1503.04783[hep-th].

[46] B. Heidenreich, M. Reece, and T. Rudelius, Weak Grav-ity Strongly Constrains Large-Field Axion Inflation,JHEP 12, 108, arXiv:1506.03447 [hep-th].

[47] G. Buratti, J. Calderon, and A. M. Uranga,Transplanckian Axion Monodromy !?, (2018),arXiv:1812.05016 [hep-th].

[48] T. C. Bachlechner, C. Long, and L. McAllister, Planck-ian Axions and the Weak Gravity Conjecture, JHEP 01,091, arXiv:1503.07853 [hep-th].

[49] A. Hebecker, P. Mangat, F. Rompineve, and L. T.Witkowski, Winding out of the Swamp: Evading theWeak Gravity Conjecture with F-term Winding Infla-tion?, Phys. Lett. B 748, 455 (2015), arXiv:1503.07912[hep-th].

[50] A. Achucarro and G. A. Palma, The string swamplandconstraints require multi-field inflation, JCAP 02, 041,arXiv:1807.04390 [hep-th].

[51] T. Rudelius, Dimensional Reduction and (Anti) de Sit-ter Bounds, (2021), arXiv:2101.11617 [hep-th].

[52] E. Witten, Quantum gravity in de Sitter space, inStrings 2001: International Conference Mumbai, India,January 5-10, 2001 (2001) arXiv:hep-th/0106109 [hep-th].

[53] S. Hellerman, N. Kaloper, and L. Susskind, String



https://doi.org/10.1088/1126-6708/2007/06/060










https://doi.org/10.1016/j.nuclphysb.2006.10.033

https://doi.org/10.1016/j.nuclphysb.2006.10.033




https://doi.org/10.1103/PhysRevLett.121.051601














https://doi.org/10.1016/j.physletb.2018.11.018


https://doi.org/10.1002/prop.201800105



https://doi.org/10.1088/1475-7516/2019/08/009





https://doi.org/10.1088/1475-7516/2017/06/028



https://doi.org/10.1142/S0218271818300070

https://doi.org/10.1142/S0218271818300070





https://doi.org/10.1088/1475-7516/2019/02/043

https://doi.org/10.1088/1475-7516/2019/02/043
















https://doi.org/10.1088/1475-7516/2015/9/020

















https://doi.org/10.1088/1475-7516/2019/02/041





11

theory and quintessence, JHEP 06, 003, arXiv:hep-th/0104180 [hep-th].

[54] R. Bousso, Cosmology and the S-matrix, Phys. Rev. D71, 064024 (2005), arXiv:hep-th/0412197.

[55] L. Susskind, The Census taker’s hat, (2007),arXiv:0710.1129 [hep-th].

[56] L. Dyson, M. Kleban, and L. Susskind, Disturbing im-plications of a cosmological constant, JHEP 10, 011,arXiv:hep-th/0208013.

[57] N. Goheer, M. Kleban, and L. Susskind, The Trou-ble with de Sitter space, JHEP 07, 056, arXiv:hep-th/0212209.

[58] D. N. Page, Is our universe decaying at an astronom-ical rate?, Phys. Lett. B669, 197 (2008), arXiv:hep-th/0612137 [hep-th].

[59] S. R. Coleman and F. De Luccia, Gravitational Effectson and of Vacuum Decay, Phys. Rev. D21, 3305 (1980).

[60] L. Susskind, Fractal-Flows and Time’s Arrow, (2012),arXiv:1203.6440 [hep-th].

[61] D. Harlow, S. H. Shenker, D. Stanford, and L. Susskind,Tree-like structure of eternal inflation: A solv-able model, Phys. Rev. D 85, 063516 (2012),arXiv:1110.0496 [hep-th].

[62] T. Banks and W. Fischler, An Upper bound on thenumber of e-foldings, (2003), arXiv:astro-ph/0307459[astro-ph].

[63] N. Arkani-Hamed, S. Dubovsky, A. Nicolis,E. Trincherini, and G. Villadoro, A Measure of deSitter entropy and eternal inflation, JHEP 05, 055,arXiv:0704.1814 [hep-th].

[64] N. Arkani-Hamed, S. Dubovsky, L. Senatore, andG. Villadoro, (No) Eternal Inflation and Precision HiggsPhysics, JHEP 03, 075, arXiv:0801.2399 [hep-ph].

[65] K. D. Olum, Is there any coherent measure foreternal inflation?, Phys. Rev. D 86, 063509 (2012),arXiv:1202.3376 [hep-th].

[66] A. Bedroya, M. Montero, C. Vafa, and I. Valen-zuela, de Sitter Bubbles and the Swampland, (2020),arXiv:2008.07555 [hep-th].

[67] B. Freivogel, Making predictions in the multiverse,Class. Quant. Grav. 28, 204007 (2011), arXiv:1105.0244[hep-th].

[68] R. Bousso and L. Susskind, The Multiverse Interpreta-tion of Quantum Mechanics, Phys. Rev. D 85, 045007(2012), arXiv:1105.3796 [hep-th].

[69] B. Freivogel, Y. Sekino, L. Susskind, and C.-P. Yeh, AHolographic framework for eternal inflation, Phys. Rev.D 74, 086003 (2006), arXiv:hep-th/0606204.

[70] D. Harlow and L. Susskind, Crunches, Hats, and a Con-jecture, (2010), arXiv:1012.5302 [hep-th].

[71] Y. Sekino and L. Susskind, Census Taking in the Hat:FRW/CFT Duality, Phys. Rev. D 80, 083531 (2009),arXiv:0908.3844 [hep-th].

[72] L. Aalsma and G. Shiu, Chaos and complementarity inde Sitter space, JHEP 05, 152, arXiv:2002.01326 [hep-th].

[73] L. Aalsma and W. Sybesma, The Price of Curios-ity: Information Recovery in de Sitter Space, (2021),arXiv:2104.00006 [hep-th].

[74] L. Aalsma, A. Cole, E. Morvan, J. P. van der Schaar,and G. Shiu, Shocks and Information Exchange in deSitter Space, (2021), arXiv:2105.12737 [hep-th].

[75] F. Denef, A. Hebecker, and T. Wrase, de Sitter swamp-land conjecture and the Higgs potential, Phys. Rev.

D98, 086004 (2018), arXiv:1807.06581 [hep-th].[76] M. Dine and N. Seiberg, Is the Superstring Weakly Cou-

pled?, Phys. Lett. 162B, 299 (1985).[77] T. Wrase and M. Zagermann, On Classical de Sitter

Vacua in String Theory, Fortsch. Phys. 58, 906 (2010),arXiv:1003.0029 [hep-th].

[78] D. Andriot, Open problems on classical de Sit-ter solutions, Fortsch. Phys. 67, 1900026 (2019),arXiv:1902.10093 [hep-th].

[79] A. Hebecker and T. Wrase, The Asymptotic dS Swamp-land Conjecture ? a Simplified Derivation and a Po-tential Loophole, Fortsch. Phys. 67, 1800097 (2019),arXiv:1810.08182 [hep-th].

[80] B. Heidenreich, M. Reece, and T. Rudelius, Sharpeningthe Weak Gravity Conjecture with Dimensional Reduc-tion, JHEP 02, 140, arXiv:1509.06374 [hep-th].

[81] B. Heidenreich, M. Reece, and T. Rudelius, RepulsiveForces and the Weak Gravity Conjecture, JHEP 10,055, arXiv:1906.02206 [hep-th].

[82] L. Alvarez-Gaume, P. H. Ginsparg, G. W. Moore, andC. Vafa, An O(16) x O(16) Heterotic String, Phys. Lett.B 171, 155 (1986).

[83] P. K. Townsend, Positive Energy and the Scalar Po-tential in Higher Dimensional (Super)gravity Theories,Phys. Lett. B 148, 55 (1984).

[84] K. Skenderis and P. K. Townsend, Gravitational stabil-ity and renormalization group flow, Phys. Lett. B 468,46 (1999), arXiv:hep-th/9909070.

[85] E. Palti, The Weak Gravity Conjecture and ScalarFields, JHEP 08, 034, arXiv:1705.04328 [hep-th].

[86] D. Klaewer and E. Palti, Super-Planckian SpatialField Variations and Quantum Gravity, JHEP 01, 088,arXiv:1610.00010 [hep-th].

[87] R. Bousso, Bekenstein bounds in de Sitter and flatspace, JHEP 04, 035, arXiv:hep-th/0012052.

[88] J. D. Bekenstein, Black holes and the second law, Lett.Nuovo Cim. 4, 737 (1972).

[89] J. D. Bekenstein, A Universal Upper Bound on the En-tropy to Energy Ratio for Bounded Systems, Phys.Rev.D23, 287 (1981).

[90] D. Andriot, N. Cribiori, and D. Erkinger, The web ofswampland conjectures and the TCC bound, JHEP 07,162, arXiv:2004.00030 [hep-th].

[91] G. Veneziano, Large N bounds on, and compositenesslimit of, gauge and gravitational interactions, JHEP 06,051, arXiv:hep-th/0110129.

[92] N. Arkani-Hamed, S. Dimopoulos, and S. Kachru, Pre-dictive landscapes and new physics at a TeV, (2005),arXiv:hep-th/0501082.

[93] G. Dvali and M. Redi, Black Hole Bound on the Numberof Species and Quantum Gravity at LHC, Phys. Rev. D77, 045027 (2008), arXiv:0710.4344 [hep-th].

[94] G. Dvali, Black Holes and Large N Species Solution tothe Hierarchy Problem, Fortsch. Phys. 58, 528 (2010),arXiv:0706.2050 [hep-th].

[95] T. Hartman, Y. Jiang, and E. Shaghoulian, Islands incosmology, JHEP 11, 111, arXiv:2008.01022 [hep-th].

[96] H. Sato, Motion of a Shell at Metric Junc-tion, Progress of Theoretical Physics 76, 1250(1986), https://academic.oup.com/ptp/article-pdf/76/6/1250/5344949/76-6-1250.pdf.

[97] M. Cvetic, S. Griffies, and H. H. Soleng, Local andglobal gravitational aspects of domain wall space-times,Phys. Rev. D 48, 2613 (1993), arXiv:gr-qc/9306005.

https://doi.org/10.1088/1126-6708/2001/06/003







https://doi.org/10.1088/1126-6708/2002/10/011


https://doi.org/10.1088/1126-6708/2003/07/056










https://arxiv.org/abs/astro-ph/0307459

https://arxiv.org/abs/astro-ph/0307459

https://doi.org/10.1088/1126-6708/2007/05/055


https://doi.org/10.1088/1126-6708/2008/03/075





https://doi.org/10.1088/0264-9381/28/20/204007




















https://doi.org/10.1016/0370-2693(85)90927-X












https://doi.org/10.1016/0370-2693(86)91524-8

https://doi.org/10.1016/0370-2693(86)91524-8

https://doi.org/10.1016/0370-2693(84)91610-1

https://doi.org/10.1016/S0370-2693(99)01212-5

https://doi.org/10.1016/S0370-2693(99)01212-5






https://doi.org/10.1088/1126-6708/2001/04/035


https://doi.org/10.1007/BF02757029

https://doi.org/10.1007/BF02757029






https://doi.org/10.1088/1126-6708/2002/06/051

https://doi.org/10.1088/1126-6708/2002/06/051










https://doi.org/10.1143/PTP.76.1250

https://doi.org/10.1143/PTP.76.1250

https://arxiv.org/abs/https://academic.oup.com/ptp/article-pdf/76/6/1250/5344949/76-6-1250.pdf

https://arxiv.org/abs/https://academic.oup.com/ptp/article-pdf/76/6/1250/5344949/76-6-1250.pdf


https://arxiv.org/abs/gr-qc/9306005

12

[98] B. Freivogel and M. Kleban, Vacua Morghulis, (2016),arXiv:1610.04564 [hep-th].

[99] H. Ooguri and C. Vafa, Non-supersymmetric AdS andthe Swampland, Adv. Theor. Math. Phys. 21, 1787(2017), arXiv:1610.01533 [hep-th].

[100] L. McAllister, E. Silverstein, and A. Westphal, Grav-ity Waves and Linear Inflation from Axion Monodromy,Phys. Rev. D82, 046003 (2010), arXiv:0808.0706 [hep-th].

[101] E. Silverstein and A. Westphal, Monodromy in the

CMB: Gravity Waves and String Inflation, Phys. Rev.D 78, 106003 (2008), arXiv:0803.3085 [hep-th].

[102] N. Kaloper, A. Lawrence, and L. Sorbo, An Igno-ble Approach to Large Field Inflation, JCAP 03, 023,arXiv:1101.0026 [hep-th].

[103] J. McNamara and C. Vafa, Cobordism Classes and theSwampland, (2019), arXiv:1909.10355 [hep-th].

[104] S. Kachru, R. Kallosh, A. D. Linde, and S. P. Trivedi, DeSitter vacua in string theory, Phys. Rev. D68, 046005(2003), arXiv:hep-th/0301240 [hep-th].


https://doi.org/10.4310/ATMP.2017.v21.n7.a8

https://doi.org/10.4310/ATMP.2017.v21.n7.a8








https://doi.org/10.1088/1475-7516/2011/03/023






asymptotic observables and the swampland

Documents