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Concordance model

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Critical Tests of the Standard Model of Cosmology George F R Ellis University of Cape Town Unity of the Universe Meeting ICG,Portsmouth June 2009

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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

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The canonical picture … (WMAP) Visible Invisible

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OBSERVABLE UNIVERSE 1: Baryons (4%) and structure formation Radiation emitted and absorbed Major part of observational cosmology/astronomy 2: Dark matter (23%) and structure formation No radiation emitted or absorbed Indirectly observed: major part of what is 3: Dark energy (73%) and cosmology No radiation emitted and absorbed Existence inferred: dominant energy form PRE-OBSERVABLE UNIVERSE Interactions and geometry inferred Tested through relics (matter, radiation)

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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

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The Acceleration of the universe

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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?

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Without lab tests: rely on theoretical explorations and explanations for its nature Cosmological constant: but then10 120 too small! Theoretical disaster! Quintessence: unknown nature (arbitrary equation of state) Modified gravitational theories: higher curvature terms Effects of higher dimensions ????

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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 proposal Unity of universe is missing! Needs some other independent experimental or observational test – but we don’t have another viable context for applying such tests So how do we justify our proposed theoretical explanations? - Why this form of quintessence? - Why a cosmological constant?

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3: A Multiverse? Data is consistent with cosmological constant The 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]

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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

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Our Cosmic Habitat Martin 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.

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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”

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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.

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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)

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

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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, 10 1000 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

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?? 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.

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??: 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

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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.

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?? : 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.

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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.

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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.

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. 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

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Metric: In comoving coordinates, ds 2 = -dt 2 + B 2 (r,t) + A 2 (r,t)(dΘ 2 +sin 2 Θ dΦ 2 ) where B 2 (r,t) = A’(r,t) 2 (1-k(r)) -1 and the evolution equation is (Å/A) 2 = F(r)/A 3 + 8πGρ Λ /3 - k(r)/A 2 with F’ (A’A 2 ) -1 = 8πGρ M. Two arbitrary functions: k(r) (curvature) and F(r) (matter). LTB (Lemaitre-Tolman Bondi models

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Mustapha, Hellaby, & Ellis Alnes, Amarzguioui, and Gron astro-ph/0512006 We can fit the supernova data …that’s a theorem!

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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 analysis Quadrupole? Perhaps also (and alignment) Nucleosynthesis: OK Baryon acoustic oscillations? Maybe – more tricky

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scales probed by different observations: different distances The Tegmark representation of power spectrum data (2006)

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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.”

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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

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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

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“It is improbable we are near the centre” But there is always improbability in cosmology Can shift it: FRW geometry Inflationary potential Inflationary initial conditions Position 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

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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

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There is only one universe Concept 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 assumption and 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

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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

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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]

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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)q 0 z 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

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Distance Measurements two effects on distance measurements: expansion curvature bends null geodesics eg, positive curvature increases angular sizes These are coupled in FLRW, decoupled in LTB

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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?

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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 Lu Phys.Rev.Lett.101:011301,2008 arXiv:0712.3457

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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

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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]

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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

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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

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Consistency tests of the standard model CBR temperature with z: T = 2.75 (1+z) Ages, including for objects at high redshift: T 0(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

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Expand the spatial distances to see the causal structure (light cones at ±45 o ) He 4 at early times

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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 He 4 (talk by Andrew Pontzen) Key Observational tests

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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

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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

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Multiverse claims Unobservable universe domains, Untested claimed physics Theory 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?

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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

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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!

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?? 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) ?

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. 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

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Multiple scales of representation Implicit averaging scale 1: Local inhomogeneity: description Density Distance

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Averaging and calculating the field equations do not commute G. 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 electromagnetism P Szekeres: “Linearised gravitational theory in macroscopic media” Ann Phys 64: 599 (1971) Local inhomogeneity: dynamic effects

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Averaging and calculating the field equations do not commute g 1ab R 1ab G 1ab = T 1ab Scale 1 Averaging g 3ab R 3ab G 3ab = T 3ab Scale 3 averaging process averaging gives different answer Local inhomogeneity: dynamic effects

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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 equation T 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 - = - Local inhomogeneity: the averaging problem

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Buchert equations The Raychaudhuri equation for irrotational dust ∂ t Θ = Λ - 4πGρ – (1/3)Θ 2 - 2σ 2 averages to give ∂ t D = Λ - 4πG D + (2/3) D ) 2 > D – (1/3) D 2 – 2 D with correlations acting as a kinetic pressure. The Friedmann equation becomes 3(å D /a D ) 2 - 8πG D - Λ = - D /2 – Q D /2 where D is the averaged curvature and Q D = (2/3) D ) 2 > D – 2 D is the kinematical backreaction term resulting from expansion and shear fluctuations,

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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 adequate You 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

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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

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Ricci focusing and Weyl focusing B. Bertotti “The Luminosity of Distant Galaxies” Proc Royal Soc London. A294, 195 (1966). dθ/dv = -R ab K a K b - 2σ 2 – θ 2 dσ mn /dv = - E mn Θ = expansion σ = shear R ab = Ricci tensor, determined pointwise by matter E ab = Weyl tensor, determined non-locally by matter 2: Local inhomogeneity: observational effects

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Robertson-Walker observations: zero Weyl tensor and non-zero Ricci tensor. dθ/dv = -R ab K a K b – θ 2 dσ mn /dv = 0 Actual observations are best described by zero Ricci tensor and non-zero Weyl tensor dθ/dv = - 2σ 2 – θ 2 dσ mn /dv = - E mn This averages out to FRW equations when averaged over whole sky But supernova observations are preferentially where there is no matter

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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

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“Determination of Ω m 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 Ω m 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

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