Concordance model

Critical Tests of the Standard Model of Cosmology

George F R EllisUniversity of Cape Town

Unity of the Universe Meeting

ICG,Portsmouth

June 2009

We now have a consensus standard model of cosmology, based on the Robertson-Walker geometries and

standard physics.

It seems to fit the observations well.

However it has some mysteries. We need to test it to check its

foundations.

1: The consensus model

The canonical picture … (WMAP)

Visible Invisible

OBSERVABLE UNIVERSE

1: Baryons (4%) and structure formationRadiation emitted and absorbed

Major part of observational cosmology/astronomy

2: Dark matter (23%) and structure formationNo radiation emitted or absorbed

Indirectly observed: major part of what is

3: Dark energy (73%) and cosmologyNo radiation emitted and absorbed

Existence inferred: dominant energy form

PRE-OBSERVABLE UNIVERSEInteractions and geometry inferred

Tested through relics (matter, radiation)

The explanation of dark energy is a central pre-occupation of present day cosmology.

Its presence is indicated by the recent speeding up of the expansion of the universe indicated by supernova

observations

confirmed by other observations such as those of the cosmic background radiation anisotropies and

LSS/BAO studies

Its nature (whether constant, or varying) is a major problem for theoretical physics

Not uniquely related to any known field or particles

NB: discovered, not predicted!

2: The Acceleration of the universe

The Acceleration of the universe

Experimental detection of dark energy in a lab or even the solar system is not feasible, for the usual conception of DE as cosmological constant or quintessence

- CONTRAST With Dark Matter: NO LAB TESTS

But: Unified approaches to DE and DM need to be explored: they may be facets of the same problem

Towards a unifying scalar field?Then evidence for dark matter is also evidence for dark

energy

But then changing (with scale) from attraction to repulsion: why and how? Can we test that change?

NO!

Lab tests of Dark energy?

Without lab tests: rely on theoretical explorations and explanations for its nature

Cosmological constant: but then10120 too small!Theoretical disaster!

Quintessence: unknown nature (arbitrary equation of state)

Modified gravitational theories: higher curvature terms

Effects of higher dimensions????

But how do we test these theoretical proposals?Many seem very arbitrary

Just writing down a Lagrangian does not prove such matter exists!

If the explanation only explains one thing (acceleration) and has no other testable outcome, it is an ad hoc explanation for

that one thing rather than a unifying scientific proposalUnity of universe is missing!

Needs some other independent experimental or observational test – but we don’t have another viable context for applying

such testsSo how do we justify our proposed theoretical

explanations?- Why this form of quintessence? - Why a cosmological constant?

3: A Multiverse?

Data is consistent with cosmological constantThe major theoretical proposal to explain the force causing acceleration is via a multiverse

The idea of a multiverse -- an ensemble of universes or of universe domains – has received increasing attention in cosmology [Andrei Linde’s talk]

  - separate places: chaotic inflation [Vilenkin, Linde, Guth, Weinberg]    - the Everett quantum multi-universe: other branches of the wavefunction [Deutsch]

- the cosmic landscape of string theory, imbedded in a chaotic cosmology [Susskind]

Application: explaining fundamental constants

Explaining the small value of the cosmological constant by anthropic argument [Steven Weinberg: astro-ph/0005265;

Susskind, The Cosmic Landscape]

• A multiverse with varied local physical properties is one possible scientific explanation:

- an infinite set of universe domains allows all possibilities to occur, so somewhere things work out OK

- NB: it must be an actually existing multiverse - this is essential for any such anthropic argument

- too large a value for results in no structure and hence no life, so anthropic considerations mean that the value of we observe will be small [in fundamental units:

- thus justifying an actual value extremely different from the `natural’ one predicted by physics: 120 orders of magnitude

Our Cosmic HabitatMartin Rees

Rees explores the notion that our universe is just a part of a vast ''multiverse,'' or ensemble of universes, in which most of the other universes are lifeless. What we call the laws of nature would then be no more than local bylaws, imposed in the aftermath of our own Big Bang. In this scenario, our cosmic habitat would be a special, possibly unique universe where the prevailing laws of physics allowed life to emerge.

The Cosmic Landscape: String Theory and the Illusion of Intelligent Design

Leonard Susskind

Susskind concludes that questions such as "why is a certain constant of nature one number rather than another?" may well be answered by "somewhere in the megaverse the constant equals this number: somewhere else it is that number. We live in one tiny pocket where the value of the constant is consistent with our kind of life. That’s it! That’s all. There is no other answer to the question".“The anthropic principle is thus rendered respectable and intelligent design is just an illusion”

Is this science, or scientifically based philosophy?

Two central scientific virtues are testability and explanatory power. In the cosmological context, these are often in conflict with each other. The extreme case is multiverse proposals, where no direct observational tests of the hypothesis are possible, as the supposed other universes cannot be seen by any observations whatever, and the assumed underlying physics is also untested and indeed probably untestable.

In this context one must re-evaluate what the core of science is: can one maintain one has a genuine scientific theory when direct and indeed indirect tests of the theory are impossible? If one claims this, one is altering what one means by science. One should be very careful before so doing.

The key observational point is that the domains considered are beyond the particle horizon and are

therefore unobservable. See the diagrams of our past light cone by Mark Whittle (Virginia)

Expand the spatial distances to see the causal structure (light cones at ±45o)

Observable

Start of universe

Now it is clear what the observational and causal limits are:

No observational data whatever are available!

Better scale:

The assumption is we that can extrapolate to 100 Hubble radii, 101000

Hubble radii, or much much more (`infinity’) – go to Cape Town and we haven’t even started! Hubris!

Observable universe domain

Extrapolation to unobservable universe domain

Observable universe domain

Extrapolation to unobservable universe domain

?? Implied by known physics that leads to chaotic inflation

The key physics (Coleman-de Luccia tunneling, the string theory landscape) is extrapolated from known and tested physics to new contexts; the extrapolation is unverified and indeed is unverifiable; it may or may not be true. The physics is hypothetical rather than tested

Known Physics → Multiverse ?? NO!Known Physics → Hypothetical Physics → Multiverse

Major Extrapolation

It is a great extrapolation from known physics. This extrapolation is untestable: it may or may not be

correct.

??: Implied by inflation, which is justified by CBR anisotropy observations

- it is implied by some forms of inflation but not others; inflation is not yet a well defined theory (and not a single scalar field has yet been physically detected). Not all forms of inflation lead to chaotic inflation.

- For example inflation in small closed universes

However:

Chaotic inflation version can be disproved if we observe a small universe: have already seen round the universe. Therefore spatially closed:

- Can search for identical circles in the CBR sky, also CMB low anisotropy power at large angular scales (which is what is observed).

- A very important test as it would indeed disprove the chaotic inflation variety of multiverse.

- But not seeing them would not prove a multiverse exists. Their non-existence is a necessary but not sufficient condition .

??: Implied by probability argument: the universe is no more special than need be to create life.

Hence the observed value of the Cosmological constant is confirmation (Weinberg).

But the statistical argument only applies if a multiverse exists; it is simply inapplicable if there is no multiverse.

In that case we only have one object we can observe; we can do many observations of that one object, but it is still only one object (one universe), and you can’t do statistical tests if there is only one existent entity

We don’t know the measure to use; but the result depends critically on it

This is in fact a weak consistency test on multiverses, that is indicative but not conclusive (a probability argument cannot be falsified). Consistency tests must be satisfied, but they are not confirmation unless no other explanation is possible. Necessary is not sufficient.

Implication of all the above:

The multiverse idea is not provable either by observation, or as an implication of well established physics. It may be true, but cannot be shown to be true by observation or experiment.

However it does have great explanatory power: it does provide an empirically based rationalization for fine tuning, developing from known physical principles.

Here one must distinguish between explanation and prediction. Successful scientific theories make predictions, which can then be tested. The multiverse theory can’t make any predictions because it can explain anything at all. Any theory that is so flexible is not testable because almost any observation can be accommodated.

The key issue is if we choose to let theory trump observations, or insist on observational test of our theories.

Multiverse proponents essentially propose the former. Scientific conservatism chooses the latter.

The very nature of the scientific enterprise is at stake in the multiverse debate: the multiverse proponents are proposing weakening the nature of scientific proof in order to claim that multiverses provide a scientific explanation.

This is a dangerous tactic, as is proven by history. Note: we are concerned with really existing multiverses, not potential or hypothetical.

. The deduction of the existence of dark energy is based on the assumption that the universe has a Robertson-

Walker geometry- spatially homogeneous and isotropic on a large scale.

The observations can at least in principle be accounted for without the presence of any dark energy, if we

consider the possibility of inhomogeneity

We abandon the Cosmological Principle: that the universe is the same everywhere

4: Inhomogeneity and the Acceleration of the universe

Metric: In comoving coordinates,

ds2 = -dt2 + B2(r,t) + A2(r,t)(dΘ2+sin2 Θ dΦ2)

where

B2(r,t) = A’(r,t)2 (1-k(r))-1

and the evolution equation is

(Å/A)2 = F(r)/A3 + 8πGρΛ/3 - k(r)/A2

with F’ (A’A2)-1 = 8πGρM.

Two arbitrary functions: k(r) (curvature) and F(r) (matter).

LTB (Lemaitre-Tolman Bondi models

Mustapha, Hellaby, & Ellis

Alnes, Amarzguioui, and Gron astro-ph/0512006

We can fit the supernova data …that’s a theorem!

Other observations??

Can also fit cbr observations:Larger values of r

S. Alexander, T. Biswas, A. Notari, D. Vaid “Local void vs dark energy: confrontation with WMAP and Type IA

supernovae” (2007) [arXiv:0712.0370].

Nb: cbr dipole can then (partly) be because we are a bit off-centre

Re-evaluate the great attractor analysisQuadrupole? Perhaps also (and alignment)

Nucleosynthesis: OK

Baryon acoustic oscillations?Maybe – more tricky

scales probed by different observations: different distances

The Tegmark representation of power spectrum data (2006)

Ishak et al 0708.2943

“We find that such a model can easily explain the observed luminosity distance-redshift relation of supernovae without the need for dark energy, when the inhomogeneity is in the form of an underdense bubble centered near the observer. With the additional assumption that the universe outside the bubble is approximately described by a homogeneous Einstein-de Sitter model, we find that the position of the first CMB peak can be made to match the WMAP observations.”

Typical observationally viable model:

We live roughly centrally (within 10% of the central position) in a large void:

a compensated underdense region stretching to z ≈ 0.08 with δ ≈ -0.4 and size 160/h Mpc to 250/h Mpc, a jump in the Hubble constant of

about 1.20, and no dark energy or quintessence field

Solving inverse problem with inhomogenoeus universe

Can we find dynamics (inflation, HBB) that matches the observations?

Same basic dynamics (FRW evolution along individual world lines) but with distant dependent parameters

Depends on the initial data, the amount of inflation, and the details of the unknown inflaton

If we are allowed usual possibilities of arbitrarily choosing the potential, adding in multiple fields as needed, and fine-tuning initial conditions, then of

course we can!

Large scale inhomogeneity:dynamic evolution

“It is improbable we are near the centre”But there is always improbability in cosmology

Can shift it:

FRW geometryInflationary potential

Inflationary initial conditionsPosition in inhomogeneous universe

Which universe in multiverse

Competing with probability 10-120 for Λ in a FRW universe.

Also: there is no proof universe is probable. May be improbable!! Indeed, it is!!

Improbability

Do We Live in the Center of the World? Andrei Linde, Dmitri Linde, Arthur Mezhlumian

“We investigate the distribution of energy density in a stationary self-reproducing inflationary universe. We show that the main fraction of volume of the universe in a state with a given density ρ at any given moment of time t in synchronous coordinates is concentrated near the centers of deep exponentially wide spherically symmetric holes in the density distribution.”

“A possible interpretation of this result is that a typical observer should see himself living in the center of the world. Validity of this interpretation depends on the choice of measure in quantum cosmology.”

Phys.Lett.B345:203-210,1995: arXiv:hep-th/9411111

There is only one universeConcept of probability does not apply to a single object, even though we can make many measurements of that

single object

There is no physically realised ensemble to apply that probability to, unless a multiverse exists

– which is not proven: it’s a philosophical assumptionand in any case there is no well-justified measure for any

such probability proposal

Can we observationally test the inhomogeneity possibility?

Whatever theory may say, it must give way to such tests

Improbability

We have stalemate: DE in FLRW can explain, so can LTB with no DE

How to discriminate?

It follows that:direct observational tests of the Copernican (spatial

homogeneity) assumption are of considerable importance;

particularly those that are independent of field equations or matter content

5: Direct Observational tests

Observational Tests

• only previously known direct tests use scattered CMB photons - looking inside past null cone

– if CMB very anisotropic around distant observers, SZ scattered photons have distorted spectrum

– but model dependent - good for void models but misses, e.g., conformally stationary spacetimes

• ideally we need a model-independent ‘forensic’ test ... is FLRW the correct metric?

[Goodman 1995; Caldwell & Stebbins 2007]

1: Consistency test of LTB

• Must not have observational cusp at origin – implies singularity there

Vanderveld, Flangan and Wasserman astro-ph/0602476

“Living in a void: Testing the Copernican Principle with distant supernovae”, T Clifton, P G Ferreira and K Land

• Phys. Rev. Lett. 101 (2008) 131302 [arXiv:0807.1443]

• Distance modulus Δdm(z) ≈ - (5/2)q0z in ΛCDM, but if this were true in void model without Λ this implies singularity

- Observational test will be available from intermediate redshift supernovae in future

Distance Measurements• two effects on distance measurements:

expansioncurvature bends null geodesics

•eg, positive curvature increases angular sizes

•These are coupled in FLRW, decoupled in LTB

Measuring Curvature in FLRW• in FLRW we can combine Hubble rate and distance data

to find curvature

• independent of all other cosmological parameters, including dark energy model, and theory of gravity

• can be used at single redshift

• what else can we learn from this?

2: Generic Consistency Test of FLRW

• since independent of z we can differentiate to get consistency relation

•

• depends only on FLRW geometry: ‣ independent of curvature, dark energy, theory of

gravity• consistency test for homogeneity and isotropy• should expect in FLRW

A general test of the Copernican Principle Chris Clarkson, Bruce A. Bassett and Teresa Hui-Ching LuPhys.Rev.Lett.101:011301,2008 arXiv:0712.3457

Testing the Copernican Assumption

• Copernican assumption hard to test ... but in non-FLRW

‣ even at center of symmetry‣ simplest to measure H(z) from BAO

deceleration parameter measured from distance

measurements

deceleration parameter measured from Hubble

measurements

It’s only as difficult as dark energy...

• measuring w(z) from Hubble uses

– requires H’(z)

• and from distances requires second derivatives D’’(z)

• simplest to begin with via

[see Clarkson Cortes & Bassett JCAP08(2007)011; arXiv:astro-ph/0702670]

If the standard inverse analysis of the supernova data to determine the required equation of state shows

there is any redshift range where w := p/ρ < -1,

this may well be a strong indication that one of these

geometric explanations is preferable to the Copernican (Robertson-Walker) assumption,

for otherwise the matter model indicated by these observations is non-physical (it has a negative k.e.)

M.P. Lima, S. Vitenti, M.J. Reboucas “Energy conditions bounds and their confrontation with supernovae data”

(2008) [arXiv:0802.0706].

3: Indirect Observational tests

The physically most conservative approach is to assume no unusual dark energy but rather that

geometry might be responsible for the observed apparent acceleration

This could happen due to large scale inhomogeneity that can probably do the job, but may not exist

Observational tests of the latter possibility is as important as pursuing the dark energy (exotic physics) option in a homogeneous universe

Theoretical prejudices as to the universe’s geometry, and our place in it, must bow to observational tests

Consistency tests of the standard model

• CBR temperature with z: T = 2.75 (1+z)

• Ages, including for objects at high redshift:

T0(object) = T(observed) - T(lookback)

Compare with physical age estimates

• Confirming that helium abundances as a function of z are consistent with a primordial value of 25% at large distances (high redshifts) in all directions. This probes very early times at large comoving distance

6: Key Observational tests

Expand the spatial distances to see the causal structure (light cones at ±45o)

He4 at early times

Consistency tests [continued]

• Number anisotropy: Checking that there is a 2% number count dipole parallel to the CBR – independent of source nature and evolution

[G Ellis and J Baldwin, MNRAS 206, 377-381 (1984).

• Realistic equation of state – not w < -1

• Test inhomogeneous modes (LTB) on large scale – Clarkson Bassett and Lu

• Test anisotropic (Bianchi) modes, by CBR anisotropy and He4 (talk by Andrew Pontzen)

Key Observational tests

Alternative Global topology: Closed or not? k = +1 ??simply connected or not?

? Small universe?Have we seen right round the universe already,

maybe many times?• Identified images• Number counts• Circles in the CBR sky- Completely different status philosophically

Key Observational tests

Dennis Sciama was always adventurous in both physical and geometric speculation

But

He insisted on the fundamental importance of the relation between theory and observations

He always insisted on working out testable consequences, and then seeing if the test

could actually be done

This remains good advice today

7: Status of Testing in cosmology

Multiverse claims Unobservable universe domains,

Untested claimed physicsTheory takes precedence over observations

Reasonable philosophical proposal. Not proven science.

“Universe is a computer simulation”How could this function?Where is this computer?

How did it come to be there?What tests are possible of this claim?

Neither sensible nor science!

Status of Untestable models?

Critical tests of the geometry and topology of the standard model can be carried out. These will

either confirm the standard picture in a satisfactory way, or will show that one of its underlying

assumptions is incorrect, and so will imply the need for a major revision of the consensus model.

I urge the importance of carrying out these critical tests. We need to test the foundations of standard

cosmology in all possible ways –

Don’t just take them for granted!

Testing the standard model

Can be disproved if we determine there are closed spatial sections because curvature is positive: k = +1

The claim is that only negatively curved FRW models can emerge in a chaotic inflation multiverse.

a: because Coleman-de Luccia tunneling only gives k = -1; But that claim is already disputed, there are already papers

suggesting k=+1 tunneling is possible- indeed it depends on a very specific speculative mechanism,

which has not been verified to actually work, and indeed such verification is impossible.

b: because the spatial sections are then necessarily closed

and are all that is, if they extend far enough- but we could live in high density lump imbedded in a low

density universe: the extrapolation of k=+1 may not be valid

Neither conclusive!

?? It is the only physical explanation for fine tuning of parameters that lead to our existence,

- in particular the value of the cosmological constant

[n.b. theoretical explanation, not observation]

?? It results from the theory that “everything that can happen, happens” (Lewis, Sciama, Deutsch) as suggested by Feynman QFT approach

[n.b. theoretical explanation, not observation]

Which is more important in cosmology: theory (explanation) or observations (tests against

reality) ?

. The deduction of the existence of dark energy is based on the assumption that the universe has a

Robertson-Walker geometry

- spatially homogeneous and isotropic on a large scale.

The observations can at least in principle be accounted for without the presence of any dark

energy, if we consider the possibility of inhomogeneity

This can happen in two ways:local and large scale

The Acceleration of the universe

Multiple scales of representation

Implicit averaging scale

1: Local inhomogeneity:description

Density

Distance

Averaging and calculating the field

equations do not commuteG. F. R. Ellis: ``Relativistic cosmology: its nature, aims and problems". In General

Relativity and Gravitation, Ed B Bertotti et al (Reidel, 1984), 215.

Large scale effective equations include polarisation terms, as in the case of

electromagnetismP Szekeres: “Linearised gravitational theory

in macroscopic media” Ann Phys 64: 599 (1971)

Local inhomogeneity:dynamic effects

Averaging and calculating the field equations do not commute

g1ab R1ab G1ab = T1ab Scale 1

Averaging

g3ab R3ab G3ab= T3ab Scale 3

averaging process averaging gives different answer

Local inhomogeneity:dynamic effects

Problem: covariant averaging of tensors, particularly metric

Zalaletdinov approach using bitensors

R Zalaletdinov “The Averaging Problem in Cosmology and Macroscopic Gravity” Int. J. Mod. Phys. A 23: 1173 (2008)

[arXiv:0801.3256]

Buchert equations for scalars gives modified Friedmann equationT Buchert “Dark energy from structure: a status report”. GRG

Journal 40: 467 (2008) [arXiv:0707.2153].

Keypoint:Expansion and averaging do not commute:

in any domain D, for any field Ψ∂t<Ψ> - <∂tΨ> = <θΨ> - <θ><Ψ>

Local inhomogeneity:the averaging problem

Buchert equations

The Raychaudhuri equation for irrotational dust

∂tΘ = Λ - 4πGρ – (1/3)Θ2 - 2σ2

averages to give

∂t<Θ>D = Λ - 4πG<ρ>D + (2/3) < (Θ - <Θ>D)2 >D– (1/3)<Θ>D2 – 2 < σ2 >D

with correlations acting as a kinetic pressure.

The Friedmann equation becomes

3(åD/aD)2 - 8πG<ρ>D - Λ = - <R>D/2 – QD/2

where <R>D is the averaged curvature and

QD= (2/3) < (Θ - <Θ>D)2 >D – 2 < σ2 >D

is the kinematical backreaction term resulting from expansion and shear fluctuations,

Claim: weak field approximation is adequate

and shows effect is negligible (Peebles)

Counter claim: as there are major voids in the expanding universe a weak-field kind of

approximation is not adequateYou have to model (quasi-static) voids and

junction to expanding external universe

D.L. Wiltshire "Cosmic clocks, cosmic variance and cosmic averages" New J. Phys. 9, 377 (2007)

[arXiv:gr-qc/0702082].

Local inhomogeneity:dynamic effects

Fully explain it? Maybe:

B.M. Leith, S.C.C. Ng and D.L. Wiltshire "Gravitational energy as dark energy: Concordance of

cosmological tests" Astrophys. J. 672, L91 (2008) [arXiv:0709:2535].

T. Mattsson “Dark energy as a mirage” (2007) [arXiv:0711.4264]

But others disagree:S. Rasanen: “Evaluating backreaction with the peak model

of structure formation” arxiv:0801.2692 (2008).

But then it still can alter basic relations: density to curvature

Local inhomogeneity:dynamic effects

Ricci focusing and Weyl focusing

B. Bertotti “The Luminosity of Distant Galaxies” Proc Royal Soc London. A294, 195 (1966).

dθ/dv = -RabKaKb - 2σ2 – θ2

dσmn/dv = - Emn

Θ = expansionσ = shear

Rab = Ricci tensor, determined pointwise by matter

Eab = Weyl tensor, determined non-locally by matter

2: Local inhomogeneity:observational effects

Robertson-Walker observations: zero Weyl tensor and non-zero Ricci tensor.

dθ/dv = -RabKaKb – θ2

dσmn/dv = 0

Actual observations are best described by zero Ricci tensor and non-zero Weyl tensor

dθ/dv = - 2σ2 – θ2

dσmn/dv = - Emn

This averages out to FRW equations when averaged over whole sky

But supernova observations are preferentially where there is no matter

Dyer-Roeder equations are most used to represent this:

do not accurately do so: no shear, only represent reduced density along the bundle of null rays

C. C Dyer. & R C Roeder, “Observations in Locally Inhomogeneous Cosmological Models”

Astrophysical Journal, Vol. 189: 167 (1974)

Local inhomogeneity:observational effects

“Determination of Ωm made by applying the homogeneous distance-redshift relation to SN 1997ap at z=0.83 could be as much as 50%

lower than its true value” R. Kantowski “The Effects of Inhomogeneities on Evaluating the

mass parameter Ωm and the cosmological constant Λ” (1998) [astro-ph/9802208]

Swiss-Cheese models: FRW regions joined to vacuum regions

Exact inhomogeneous solutions

V. Marra, E. W. Kolb, S. Matarrese “Light-cone averages in a Swiss-Cheese universe” (2007) [arXiv:0710.5505].

Debatable if enough to account for apparent acceleration [included in Wiltshire papers]

Probably enough to significantly influence conconcordance model values

Local inhomogeneity:observational effects