Mapping luminosity-redshift relationship to Lemaitre-Tolman-Bondi cosmology

Abstract

We derive a direct general map from the luminosity distance D L z to the inhomogeneous matter distribution Mr in the Lemaitre-Tolman-Bondi (LTB) cosmology and compute several examples. One of our examples explicitly demonstrates that it is possible to tune the LTB cosmological solution to approximately reproduce the luminosity distance curve of a flat Friedmann-Robertson-Walker universe with a cosmological constant. We also discuss how smooth matter distributions can evolve into naked singularities due to shell crossing when the inhomogeneous ''curvature'' Er is a function which changes sign.

The effect of inhomogeneous expansion on the supernova observations

“…The LTB model has been used for the supernova data fitting several times before [23,24,[26][27][28][29][30]. However, there is a crucial physical difference between these models and ours.…”

“…This model works best in describing smooth inhomogeneities at scales of 100 Mpc and larger; the spherical symmetry prevents to use it as a model for the random small scale lumpiness caused by galaxies, as noted in [23]. Indeed, the LTB model has been used to study the effect of the smooth inhomogeneities on the cosmological observations by several authors [23][24][25][26][27][28][29][30][31][32]; a common conception is that these models inevitably contradict the observed homogeneity of the large scale galaxy distribution.…”

Supernova Hubble diagram for off-center observers in a spherically symmetric inhomogeneous universe

“…More recently, the interest in such models has grown increasingly as an alternative way to explain the appararent acceleration without introducing dark energy. A non-exhaustive list of references investigating this possibility is [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27].…”

Redshift spherical shell energy in isotropic universes

“…(2) that there is a clear distinction between ρ SS (z) F RW and ρ SS (z) LT B , which could be used to exclude one of the two models even at relatively low redshift. For an LTB model ρ SS (z) would be another observable such as D L (z) which could be used to find M(r), E(r), t b (r) with a differential method similar to the one used in [19], allowing to reduce the degeneracy of the mapping. In fact as shown in [19] , given E(r), D L (z), t b (r) we can always find the corresponding M(r), making the relation between D L (z) and LTB models not one-toone.…”

“…Despite of this intrinsic observational difficulty in testing spatial homogeneity, we can still try to use available data to test different cosmological models, and in the same way high redshift luminosity distance observation D L (z) have been shown [12,19] to be consistent with both a FRW model with cosmological constant and LTB models without dark energy, we could find an appropriate inhomogeneous LTB model in agreement with the observed "radial spherical shell energy" (RSSE) ρ SS (z) .…”