Inhomogeneous cosmologies George Ellis, University of Cape Town 27th Texas Symposium on Relativistic Astrophyiscs Dallas, Texas Thursday 12th December 9h00-9h45 • The universe is inhomogeneous on all scales except the largest • This conclusion has often been resisted by theorists who have said it could not be so (e.g. walls and large scale motions) • Most of the universe is almost empty space, punctuated by very small very high density objects (e.g. solar system) • Very non-linear: / = 1030 in this room. Models in cosmology • Static: Einstein (1917), de Sitter (1917) • Spatially homogeneous and isotropic, evolving: - Friedmann (1922), Lemaitre (1927), Robertson-Walker, Tolman, Guth • Spatially homogeneous anisotropic (Bianchi/ Kantowski-Sachs) models: - Gödel, Schücking, Thorne, Misner, Collins and Hawking,Wainwright, … • Perturbed FLRW: Lifschitz, Hawking, Sachs and Wolfe, Peebles, Bardeen, Ellis and Bruni: structure formation (linear), CMB anisotropies, lensing Spherically symmetric inhomogeneous: • LTB: Lemaître, Tolman, Bondi, Silk, Krasinski, Celerier , Bolejko,…, • Szekeres (no symmetries): Sussman, Hellaby, Ishak, … • Swiss cheese: Einstein and Strauss, Schücking, Kantowski, Dyer,… • Lindquist and Wheeler: Perreira, Clifton, … • Black holes: Schwarzschild, Kerr The key observational point is that we can only observe on the past light cone (Hoyle, Schücking, Sachs) See the diagrams of our past light cone by Mark Whittle (Virginia) 5 Expand the spatial distances to see the causal structure: light cones at ±45o. Observable Geo Data Start of universe Particle Horizon (Rindler) Spacelike singularity (Penrose). 6 The cosmological principle The CP is the foundational assumption that the Universe obeys a cosmological law: It is necessarily spatially homogeneous and isotropic (Milne 1935, Bondi 1960) Thus a priori: geometry is Robertson-Walker Weaker form: the Copernican Principle: We do not live in a special place (Weinberg 1973). With observed isotropy, implies Robertson-Walker. Philosophical Principle at Foundation of Standard Cosmology On this basis: dark energy exists Dark Energy Discovery Decay of supernovae in distant galaxies provides a usable standard candle (maximum brightness is correlated to decay rate) With redshifts, gives the first reliable detection of non-linearity - the assumed FLRW universe is presently accelerating Consequently there is presently an effective positive cosmological constant with ~ 0.7: Nature unknown! Concordance FLRW model: Dark energy and dark matter with an almost flat universe BUT: We can’t see spatial homogeneity! What we can see is isotropy : Here and now Past light cone Isotropic Galaxies at redshift z G F R Ellis: ``Limits to verification in cosmology". 9th Texas Symposium on Relativistic Astrophysics, 1978. Munich. Spatially homogeneous extension: Here and now Extend spaclike: homogeneous FLRW model: Standard cosmology Spatially inhomogeneous extension: Here and now Extend timelike: inhomogeneous LTB model, in pressure-free case. Is the CP True? Two major theorems 1. Isotropy everywhere in an open set U implies spatial homogeneity in U FLRW in U (Walker 1944, Ehlers 1961) 2: Isotropy of freely moving CMB everywhere about a geodesic congruence in an open set U implies spatial homogeneity in U FLRW in U (Elhers, Geren and Sachs 1967) Stability of EGS: “Almost EGS” theorem (Stoeger, Maartens, Ellis 1995) But those conditions are not directly observable (G F R Ellis: Qu Journ Roy Ast Soc 16, 245-264: 1975). Is dark energy inevitable? Large scale inhomogeneity? Perhaps there is a large scale inhomogeneity of the observable universe such as that described by the Lemaitre-Tolman-Bondi pressure-free spherically symmetric models: - With no dark energy or CC. We are near the centre of a void M-N. Célérier: “The Accelerated Expansion of the Universe Challenged by an Effect of the Inhomogeneities. A Review” New Advances in Physics 1, 29 (2007) [astro ph/0702416]. LTB (Lemaitre-Tolman Bondi) models 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 2 3 2 (Å/A) = F(r)/A + 8πGρΛ/3 - k(r)/A 2 -1 with F’(A’A ) = 8πGρM. Two arbitrary functions: k(r) (curvature) and F(r) (matter). Large scale inhomogeneity: observational properties Theorem: LTB model scan provide any m(z) and r0(z) relations with or without any dark energy, N Mustapha, C Hellaby and G F R Ellis: Large Scale Inhomogeneity vs Source Evolution: Can we Distinguish Them? Mon Not Roy Ast Soc 292: 817-830 (1999) Two arbitrary functions can match any data Number counts don’t prove spatial homogeneity because of source evolution Can’t fit radio source number count data by FRW model without source evolution. We run models backwards to find source evolution! Alnes, Amarzguioui, and Gron astro-ph/0512006 We can fit any area distance and number count observations with no dark energy in an inhomogeneous model Szekeres model: “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. We find that the position of the first CMB peak can be made to match the WMAP observations.” Ishak et al 0708.2943 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 Other observations?? Can also fit CBR observations: Larger values of r “Local void vs dark energy: confrontation with WMAP and Type IA supernovae” (2007) S. Alexander, T. Biswas, A. Notari, D. Vaid [arXiv:0712.0370] . “Testing the Void against Cosmological data: fitting CMB, BAO, SN and H0” Biswas, Notari, Valkenburg [arXiv:1007.3065] Quadrupole? Perhaps also (and alignment) Baryon acoustic oscillations? Maybe – more tricky Nucleosynthesis: OK indeed better scales probed by different observations: different distances Do large voids occur? Perhaps- CMB cold spot: Might indicate large void. If so: your inflationary model had better allow this to happen! – Indeed inflation can allow almost anything to happen (Steinhardt) Stop press: Pan-STARRS preliminary figures that appear to tell a story of a fairly large, (up to 100 Mpc radius) void at around redshift 0.1-0.11, and front of it a filament at a slightly lower redshift. From I.Szapudi, A.Kovacs, B. Granett, and Z. Frei with the Pan-STARRS1 Collaboration: 22 I.Szapudi, A.Kovacs, B. Granett, and Z. Frei with the Pan-STARRS1 Collaboration Photo-metric redshift slices showing LSS=Large Scale Structure, i.e. galaxies. They are centered on the ``infamous'' CMB Coldspot, and the main void appears to be centered slightly in the lower left from that. The photometric redshift error is estimated to be 0.033 from GAMA, so the slices are clearly not independent. Our main problem is that we are still worried about systematic errors, in particular another method gives us about 20% stretched photo-z (although qualitatively similar images), and while we tried to figure out the reason, so far we could not get them to be consistent. Therefore all of this is *very* preliminary, should be taken with a grain of salt. 23 I.Szapudi, A.Kovacs, B. Granett, and Z. Frei with the Pan-STARRS1 Collaboration • . A photo-metric redshift slice (0.12<z<0.15). The left figure shows the CMB in colors with LSS in contours, while the right figure shows LSS in colors, and CMB in contours. Fairly large void (up to 100 Mpc radius) at z ~ 0.1-0.11 24 Improbability “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!! - Test idea by making inhomogeneous models Can We Avoid Dark Energy? James P. Zibin, Adam Moss, and Douglas Scott The idea that we live near the center of a large, nonlinear void has attracted attention recently as an alternative to dark energy or modified gravity. We show that an appropriate void profile can fit both the latest cosmic microwave background and supernova data. However, this requires either a fine-tuned primordial spectrum or a Hubble rate so low as to rule these models out. We also show that measurements of the radial baryon acoustic scale can provide very strong constraints. Our results present a serious challenge to void models of acceleration. Phys. Rev. Lett. 101, 251303 (2008) 26 • “First-Year Sloan Digital Sky Survey-II (SDSS-II) Supernova Results: Constraints on Non-Standard Cosmological Models” J. Sollerman, et al Astrophysical Journal 703 (2009) 1374-1385 [arXiv:0908.4276] – We use the new SNe Ia discovered by the SDSS-II Supernova Survey together with additional supernova datasets as well as observations of the cosmic microwave background and baryon acoustic oscillations to constrain cosmological models. This complements the analysis presented by Kessler et al. in that we discuss and rank a number of the most popular non-standard cosmology scenarios. – Our investigation also includes inhomogeneous Lemaitre- Tolman-Bondi (LTB) models. While our LTB models can be made to fit the supernova data as well as any other model, the extra parameters they require are not supported by our information criteria analysis. Testing the void against cosmological data: fitting CMB, BAO, SN and H0 Tirthabir Biswas, Alessio Notari and Wessel Valkenburg JCAP November 2010 We improve on previous analyses by allowing for nonzero overall curvature, accurately computing the distance to the last-scattering surface and the observed scale of the Baryon Acoustic peaks, and investigating important effects that could arise from having nontrivial Void density profiles.