A Test of the Copernican Principle

The blackbody nature of the cosmic microwave background (CMB) radiation spectrum is used in a modern test of the Copernican Principle. The reionized universe serves as a mirror to reflect CMB photons, thereby permitting a view of ourselves and the local gravitational potential. By comparing with measurements of the CMB spectrum, a limit is placed on the possibility that we occupy a privileged location, residing at the center of a large void. The Hubble diagram inferred from lines-of-sight originating at the center of the void may be misinterpreted to indicate cosmic acceleration. Current limits on spectral distortions are shown to exclude the largest voids which mimic cosmic acceleration. More sensitive measurements of the CMB spectrum could prove the existence of such a void or confirm the validity of the Copernican Principle.Comment: 4 pages, 3 figure

Redshift Drift in LTB Void Universes

We study the redshift drift, i.e., the time derivative of the cosmological redshift in the Lema\^itre-Tolman-Bondi (LTB) solution in which the observer is assumed to be located at the symmetry center. This solution has often been studied as an anti-Copernican universe model to explain the acceleration of cosmic volume expansion without introducing the concept of dark energy. One of decisive differences between LTB universe models and Copernican universe models with dark energy is believed to be the redshift drift. The redshift drift is negative in all known LTB universe models, whereas it is positive in the redshift domain $z \lesssim 2$ in Copernican models with dark energy. However, there have been no detailed studies on this subject. In the present paper, we prove that the redshift drift of an off-center source is always negative in the case of LTB void models. We also show that the redshift drift can be positive with an extremely large hump-type inhomogeneity. Our results suggest that we can determine whether we live near the center of a large void without dark energy by observing the redshift drift.Comment: 16 pages, 2 figure

Precision cosmology defeats void models for acceleration

The suggestion that we occupy a privileged position near the centre of a large, nonlinear, and nearly spherical void has recently attracted much attention as an alternative to dark energy. Putting aside the philosophical problems with this scenario, we perform the most complete and up-to-date comparison with cosmological data. We use supernovae and the full cosmic microwave background spectrum as the basis of our analysis. We also include constraints from radial baryonic acoustic oscillations, the local Hubble rate, age, big bang nucleosynthesis, the Compton y-distortion, and for the first time include the local amplitude of matter fluctuations, \sigma_8. These all paint a consistent picture in which voids are in severe tension with the data. In particular, void models predict a very low local Hubble rate, suffer from an "old age problem", and predict much less local structure than is observed.Comment: 22 pages, 12 figures; v2 adds models in closed backgrounds; conclusions strengthened; version accepted to Phys. Rev.

Can decaying modes save void models for acceleration?

The unexpected dimness of Type Ia supernovae (SNe), apparently due to accelerated expansion driven by some form of dark energy or modified gravity, has led to attempts to explain the observations using only general relativity with baryonic and cold dark matter, but by dropping the standard assumption of homogeneity on Hubble scales. In particular, the SN data can be explained if we live near the centre of a Hubble-scale void. However, such void models have been shown to be inconsistent with various observations, assuming the void consists of a pure growing mode. Here it is shown that models with significant decaying mode contribution today can be ruled out on the basis of the expected cosmic microwave background spectral distortion. This essentially closes one of the very few remaining loopholes in attempts to rule out void models, and strengthens the evidence for Hubble-scale homogeneity.Comment: 11 pages, 3 figures; discussion expanded, appendix added; version accepted to Phys. Rev.

Late time solutions for inhomogeneous Lambda-CDM cosmology, their characterization and observation

Assuming homogeneous isotropic Lambda-CDM cosmology allows Lambda, spatial curvature and dark matter density to be inferred from large scale structure observations such as supernovae. The purpose of this paper is to extend this to allow observations to measure or constrain inhomogeneity and anisotropy. We obtain the general inhomogeneous anisotropic Lambda-CDM solution which is locally asymptotic to an expanding de Sitter solution as a late time expansion using Starobinsky's method (analogous to the `holographic renormalization' technique in AdS/CFT) together with a resummation of the series. The dark matter is modeled as perfect dust fluid. The terms in the expansion systematically describe inhomogeneous and anisotropic deformations of an expanding FLRW solution, and are given as a spatial derivative expansion in terms of data characterizing the solution - a 3-metric and a perturbation of that 3-metric. Leading terms describe inhomogeneity and anisotropy on the scale set by the cosmological constant, approximately the horizon scale today. Higher terms in the expansion describe shorter scale variations. We compute the luminosity distance-redshift relation and argue that comparison with current and future observation would allow a partial reconstruction of the characterizing data. We also comment on smoothing these solutions noting that geometric flows (such as Ricci flow) applied to the characterizing data provide a canonical averaging method.Comment: 15 pages, 2 figures; v2: minor corrections and improvements, references adde

Reconciling the local void with the CMB

In the standard cosmological model, the dimming of distant Type Ia supernovae is explained by invoking the existence of repulsive `dark energy' which is causing the Hubble expansion to accelerate. However this may be an artifact of interpreting the data in an (oversimplified) homogeneous model universe. In the simplest inhomogeneous model which fits the SNe Ia Hubble diagram without dark energy, we are located close to the centre of a void modelled by a Lema\'itre-Tolman-Bondi metric. It has been claimed that such models cannot fit the CMB and other cosmological data. This is however based on the assumption of a scale-free spectrum for the primordial density perturbation. An alternative physically motivated form for the spectrum enables a good fit to both SNe Ia (Constitution/Union2) and CMB (WMAP 7-yr) data, and to the locally measured Hubble parameter. Constraints from baryon acoustic oscillations and primordial nucleosynthesis are also satisfied.Comment: 13 pages, 4 figures. Typos corrected and missing references added. Matches the published version in PR

Direct Measurement of the Positive Acceleration of the Universe and Testing Inhomogeneous Models under Gravitational Wave Cosmology

One possibility for explaining the apparent accelerating expansion of the universe is that we live in the center of a spherically inhomogeneous universe. Although current observations cannot fully distinguish $\Lambda$CDM and these inhomogeneous models, direct measurement of the acceleration of the universe can be a powerful tool in probing them. We have shown that, if $\Lambda$CDM is the correct model, DECIGO/BBO would be able to detect the positive redshift drift (which is the time evolution of the source redshift $z$) in 3--5 year gravitational wave (GW) observations from neutron-star binaries, which enables us to rule out any Lema\^itre-Tolman-Bondi (LTB) void model with monotonically increasing density profile. We may even be able to rule out any LTB model unless we allow unrealistically steep density profile at $z\sim 0$. This test can be performed with GW observations alone, without any reference to electromagnetic observations, and is more powerful than the redshift drift measurement using Lyman $\alpha$ forest.Comment: 5 pages, 2 figure

Role of initial data in spherical collapse

We bring out here the role of initial data in causing the black hole and naked singularity phases as the final end state of a continual gravitational collapse. The collapse of a type I general matter field is considered, which includes most of the known physical forms of matter. It is shown that given the distribution of the density and pressure profiles at the initial surface from which the collapse evolves, there is a freedom in choosing rest of the free functions, such as the velocities of the collapsing shells, so that the end state could be either a black hole or a naked singularity depending on this choice. It is thus seen that it is the initial data that determines the end state of spherical collapse in terms of these outcomes, and we get a good picture of how these phases come about.Comment: 5 pages, Revtex4, Revised version, To appear in Physical Review

The growth of structure in the Szekeres inhomogeneous cosmological models and the matter-dominated era

This study belongs to a series devoted to using Szekeres inhomogeneous models to develop a theoretical framework where observations can be investigated with a wider range of possible interpretations. We look here into the growth of large-scale structure in the models. The Szekeres models are exact solutions to Einstein's equations that were originally derived with no symmetries. We use a formulation of the models that is due to Goode and Wainwright, who considered the models as exact perturbations of an FLRW background. Using the Raychaudhuri equation, we write for the two classes of the models, exact growth equations in terms of the under/overdensity and measurable cosmological parameters. The new equations in the overdensity split into two informative parts. The first part, while exact, is identical to the growth equation in the usual linearly perturbed FLRW models, while the second part constitutes exact non-linear perturbations. We integrate numerically the full exact growth rate equations for the flat and curved cases. We find that for the matter-dominated era, the Szekeres growth rate is up to a factor of three to five stronger than the usual linearly perturbed FLRW cases, reflecting the effect of exact Szekeres non-linear perturbations. The growth is also stronger than that of the non-linear spherical collapse model, and the difference between the two increases with time. This highlights the distinction when we use general inhomogeneous models where shear and a tidal gravitational field are present and contribute to the gravitational clustering. Additionally, it is worth observing that the enhancement of the growth found in the Szekeres models during the matter-dominated era could suggest a substitute to the argument that dark matter is needed when using FLRW models to explain the enhanced growth and resulting large-scale structures that we observe today (abridged)Comment: 18 pages, 4 figures, matches PRD accepted versio

Can the Copernican principle be tested by cosmic neutrino background?

The Copernican principle, stating that we do not occupy any special place in our universe, is usually taken for granted in modern cosmology. However recent observational data of supernova indicate that we may live in the under-dense center of our universe, which makes the Copernican principle challenged. It thus becomes urgent and important to test the Copernican principle via cosmological observations. Taking into account that unlike the cosmic photons, the cosmic neutrinos of different energies come from the different places to us along the different worldlines, we here propose cosmic neutrino background as a test of the Copernican principle. It is shown that from the theoretical perspective cosmic neutrino background can allow one to determine whether the Copernican principle is valid or not, but to implement such an observation the larger neutrino detectors are called for.Comment: JHEP style, 10 pages, 4 figures, version to appear in JCA