Can the cosmological constant be mimicked by smooth large-scale inhomogeneities for more than one observable?

Abstract

As an alternative to dark energy it has been suggested that we may be at the center of an inhomogeneous isotropic universe described by a Lemaitre-Tolman-Bondi (LTB) solution of Einstein's field equations. In order to test such an hypothesis we calculate the low redshift expansion of the luminosity distance $D_L(z)$ and the redshift spherical shell mass density $mn(z)$ for a central observer in a LTB space without cosmological constant and show how they cannot fit the observations implied by a $\Lambda CDM$ model if the conditions to avoid a weak central singularity are imposed, i.e. if the matter distribution is smooth everywhere. Our conclusions are valid for any value of the cosmological constant, not only for ${\Omega }_{\Lambda }>1/3$ as implied by previous proofs that $q_0^{app}$ has to be positive in a smooth LTB space, based on considering only the luminosity distance. The observational signatures of smooth LTB matter dominated models are fundamentally different from the ones of $\Lambda CDM$ models not only because it is not possible to reproduce a negative apparent central deceleration $q_0^{app}$, but because of deeper differences in their space-time geometry which make impossible the inversion problem when more than one observable is considered, and emerge at any redshift, not only for $z=0$.

18 pages, corrected a typo in the definition of the energy density which doesn't change the conclusion, references added

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• Redshift spherical shell energy in isotropic Universes
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Cited by in corpus (18)

• Dark Energy
• Establishing homogeneity of the universe in the shadow of dark energy
• Testing the Void against Cosmological data: fitting CMB, BAO, SN and H0
• The Cosmic Microwave Background in an Inhomogeneous Universe - why void models of dark energy are only weakly constrained by the CMB
• How close can an Inhomogeneous Universe mimic the Concordance Model?
• Local and non-local measures of acceleration in cosmology
• Conformally Friedmann-Lemaitre-Robertson-Walker cosmologies
• Complete solutions to the metric of spherically collapsing dust in an expanding spacetime with a cosmological constant
• CMB observations in LTB universes: Part I: Matching peak positions in the CMB spectrum
• Corrections to the apparent value of the cosmological constant due to local inhomogeneities
• Cosmic age test in inhomogeneous cosmological models mimicking $\Lambda$CDM on the light cone
• The Metric of the Cosmos from Luminosity and Age Data
• Mimicking the cosmological constant for more than one observable with large scale inhomogeneities
• Thermodynamics of Lemaitre-Tolman-Bondi Model
• Emergent scenario and different anisotropic models
• Inverse Construction of the $\Lambda$LTB Model from a Distance-redshift Relation
• Thermodynamics of the inhomogeneous perfect fluid LTB model: Modified Bekenstein-Hawking system
• How large is the contribution of cosmic web to ${\Omega }_{\Lambda }$ ? A preliminary study on a novel inhomogenous model