超弦理论与宇宙学 李淼 ...
DESCRIPTION
超弦理论与宇宙学 李淼 中国科学院理论物理研究所. String Theory and Cosmology Miao Li Institute of Theoretical Physics Chinese Academy of Sciences. String theory is widely believed to be a theory of quantum gravity. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/1.jpg)
超弦理论与宇宙学
李淼
中国科学院理论物理研究所
![Page 2: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/2.jpg)
String Theory and Cosmology
Miao Li
Institute of Theoretical Physics
Chinese Academy of Sciences
![Page 3: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/3.jpg)
String theory is widely believed to be a theory of quantum gravity.
As such, it is usually formulated in a fixed background using the definition of scattering amplitudes
![Page 4: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/4.jpg)
More precisely, we can study string theory in a time-independent background that has asymptotic geometry of either
(a) Minkowski
or
(b) Anti-de Sitter
![Page 5: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/5.jpg)
String theory used to have
many different guises:
Open String, Closed String,
Heterotic String, Different
compactifications.
It is now understood
that they are manifestations
of a single grand theory,
M theory
![Page 6: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/6.jpg)
Different string theories
are connected by duality
relations, the prototype
of this transformations is
the relation between a
electric charge and a
magnetic charge:
For example, in type IIB
theory, a string is
mapped to a D-string,
the new theory is D-
strings is again a type
IIB theory:
![Page 7: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/7.jpg)
However, it has proven very difficult to study string theory in a time-varying background.
A universe with a startingpoint in time
De Sitter space with a bounce
![Page 8: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/8.jpg)
The most used approach to cosmology in string theory is to
use adiabatic approximation. In such an approach, one uses
a collection of fields {F(t)} to describe the background at any
given time t, F(t) can be a scalar field, or the geometry
parameter. By adiabaticity, we mean that the physics of {F(t)}
is simply that of a fixed background with the same values of
these fields for all times.
![Page 9: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/9.jpg)
However, this conservative, poor man’s approach
must miss some of most important ingredients of a
theory of quantum gravity.
One such ingredient is the so-called holography,
motivated by quantum physics of black holes.
![Page 10: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/10.jpg)
A quantitative statement is that the entropy in a
region is bounded by the area of the surface
surrounding this region.
Bekenstein-Hawking formula:
This formula implies that, the physics of quantum gravity can
be utterly non-local and even a-causal.
![Page 11: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/11.jpg)
In the context of cosmology, several people (Fischler,
Susskind, Bousso) proposed principle of
cosmological holography. Bousso’s covariant entropy
Bound:
![Page 12: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/12.jpg)
So far, string theorists are faced with this very challenging problems:
(a)To formulate string theory on a time-varying background.
(b) To find a formalism reflecting directly the holographic principle.
![Page 13: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/13.jpg)
![Page 14: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/14.jpg)
Two major developments in
observational cosmology.
(1)Discovery of accelerating expansion.
(2) Detailed map of primordial perturbation constructed from the power spectrum of CMB
(cosmic microwave background)
![Page 15: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/15.jpg)
(1) Dark energyReconstructed from data about supernov
ae type Ia
![Page 16: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/16.jpg)
This results implies that there is dark energy in
our universe, or simply a cosmological constant.
![Page 17: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/17.jpg)
According to these obsevations, our universe is
filled with relativistic matter and dark energy, the
latter is characterized by the equation of state
Furthermore, the dark energy density is very small
![Page 18: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/18.jpg)
It is very important to determine the nature of the dark
energy through determining parameter w. For a cosmological
constant, w=-1.
Some of the most recent results are:
From astro-ph/0204512
![Page 19: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/19.jpg)
The nonvanishing and a very small dark energy
density poses a serious challenge to string theory.
Since in string theory, as in a quantum field theory,
dark energy is understood as vacuum energy
generated by quantum fluctuations.
![Page 20: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/20.jpg)
As such, the vacuum energy is always determined by
a characteristic energy scale.
The most natural scale is the Planck scale, at which a
particle will dress itself by a gravitational horizon:
So the largest theoretical dark energy value is
The ratio of the observed value to this theoretical
value is absurdly small
![Page 21: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/21.jpg)
People have tried for several decades to understand
this problem and invented numerous ideas, by far not
a single idea is widely accepted as hopeful.
In the researcg community, one of the most popular
idea is the so-called quintessence model. In this
model, the dark energy comes from a scalar field Q,
a spatially homogeneous scalar field has the energy
density and pressure:
Thus
if
![Page 22: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/22.jpg)
The quintessence model is at best a phenomenological
model, since, it is not yet possible to realize such a
model in string theory or a quantum field.
The essential difficulty is that in string theory, one
usually has super-symmetry, a kind of symmetry
relating bosons to fermions, and usually badly broken
in nature. When it is broken, we usually have a relation
The mass difference is too small to be consistent with
experiments.
![Page 23: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/23.jpg)
Although string theory has not been able to resolve
this deep puzzle, string theory does hold the key to
understanding it. For instance, holography may imply
that dark energy related to the cosmic horizon. It has
been conjectured that in a holographic universe, dark
energy is given by
Where L is an infrared cut-off set by our universe.
More recently, it was argued that if L is the size of the
event horizon, then the present observational data
can be explained.
![Page 24: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/24.jpg)
(2) Primordial perturbations.
A series of CMB experiments, in particular, the Wilkinson Microwave Anisotropy Probe (WMAP)experiment, has collected enough data to give a verydetailed map on the primordial perturbations generatedprior Big Bang. These perturbations are seeds of the structure (galaxies, clusters of galaxies, filaments,voids). From the data, many important cosmic parameters(age of universe, densities, Hubble constant…) are inferred.
![Page 25: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/25.jpg)
The map of cosmic microwave background
fluctuations
![Page 26: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/26.jpg)
Some of the cosmic parameters
Age of the universe 13.7 billion years old
Dark energy 73%, dark matter 23%, atoms 4%.
The Hubble constant was 71 +4/-3 km/s/Mpc .
The universe is flat.
……
![Page 27: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/27.jpg)
More detailed data
![Page 28: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/28.jpg)
More detailed results
![Page 29: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/29.jpg)
Detailed results continued
![Page 30: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/30.jpg)
Consistency with other experiments
![Page 31: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/31.jpg)
![Page 32: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/32.jpg)
![Page 33: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/33.jpg)
These observations confirm the predictions of the
inflation scenario: prior big bang, there exists a very
short period during which the universe expands very
fast, and density perturbations are generated by
quantum fluctuations of the inflaton-a scalar field
driving inflation.
![Page 34: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/34.jpg)
Inflation explores fundamental physics in at least two ways.
First, the inflaton potential is supposed to be very flat,
this is often referred to as a fine-tuning problem.
There is no natural way to construct such a potential
in a fundamental theory such as string theory.
![Page 35: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/35.jpg)
Second, inflation greatly amplifies space. For
instance, the largest cosmic scale just entered our
horizon originated 60 e-foldings before the end of
inflation, thus, the ratio of amplification is
The Planck scale ended up to be about
larger than the size of atom.
Indeed, WMAP results indicate that the traditional
slow-roll inflation may not be good enough to explain
everything.
![Page 36: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/36.jpg)
For example, the unexpected suppression of power
of low multi-pole correlation (if not due to systematic
error) certainly indicates that something unusual
happened 60 e-foldings before the end of inflation.
The running of spectral index of the primordial power
spectrum can not be explained by the usual inflation
too, it may not be to crazy to speculate that this is
really due to new effects in string theory, for instance,
non-commutative space-time.
![Page 37: 超弦理论与宇宙学 李淼 中国科学院理论物理研究所](https://reader034.vdocuments.net/reader034/viewer/2022052117/56813ada550346895da31ef3/html5/thumbnails/37.jpg)
Conclusions:
(1) We are in an exciting era of precision cosmological observation. Once in a while, new flux of experimental data comes to sight.
(2) A few serious challenges are awaiting fundamental theory such as string theory to meet.
(3) Many researchers in string theory are for the first time facing experiments, not just theoretic artifice.