Mimicking Dark Energy with Lemaitre-Tolman-Bondi Models: Weak Central Singularities and Critical Points

Abstract

There has been much debate over whether or not one could explain the observed acceleration of the Universe with inhomogeneous cosmological models, such as the spherically-symmetric Lemaitre-Tolman-Bondi (LTB) models. It has been claimed that the central observer in these models can observe a local acceleration, which would contradict general theorems. We resolve the contradiction by noting that many of the models that have been explored contain a weak singularity at the location of the observer which makes them unphysical. In the absence of this singularity, we show that LTB models must have a positive central deceleration parameter $q_0$, in agreement with the general theorems. We also show that it is possible to achieve a negative apparent deceleration parameter at nonzero redshifts in LTB models that do not contain this singularity. However, we find other singularities that tend to arise in LTB models when attempting to match luminosity distance data, and these generally limit the range of redshifts for which these models can mimic observations of an accelerating Universe. Exceptional models do exist that can extend to arbitrarily large redshift without encountering these pathologies, and we show how these may be constructed. These special models exhibit regions with negative effective equation of state parameter, which may fall below negative one, but we have failed to find any singularity-free models that agree with observations. Moreover, models based on dust-filled LTB metrics probably fail to reproduce observed properties of large scale structure.

arXiv comment18 pages, 4 figures, revtex4; very minor revisions

References in corpus (22)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• The Cosmological Constant and Dark Energy
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results
• Is Cosmic Speed-Up Due to New Gravitational Physics?
• An inhomogeneous alternative to dark energy?
• Dark energy from backreaction
• Can the Acceleration of Our Universe Be Explained by the Effects of Inhomogeneities?
• Do we really see a cosmological constant in the supernovae data ?
• Effect of inhomogeneities on the expansion rate of the Universe
• Large Scale Inhomogeneity Versus Source Evolution -- Can We Distinguish Them Observationally?
• Is dark energy the only solution to the apparent acceleration of the present universe?
• The Effect of Inhomogeneities on the Luminosity Distance-Redshift Relation: is Dark Energy Necessary in a Perturbed Universe?
• Can superhorizon cosmological perturbations explain the acceleration of the universe?
• Constraints on backreaction in dust universes
• Late-time Inhomogeneity and Acceleration Without Dark Energy
• Can superhorizon perturbations drive the acceleration of the Universe?
• Peculiar Velocity Limits from Measurements of the Spectrum of the Sunyaev-Zel'dovich Effect in Six Clusters of Galaxies
• Do Large-Scale Inhomogeneities Explain Away Dark Energy?
• Effects of Inhomogeneities on Cosmic Expansion
• Distance-redshift relation in an isotropic inhomogeneous universe II: Spherically symmetric dust-shell universe
• Models of Universe with an inhomogeneous Big Bang singularity. II. CMBR dipole anisotropy as a byproduct of a conic Big Bang singularity

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