Testing homogeneity with galaxy number counts : light-cone metric and general low-redshift expansion for a central observer in a matter dominated isotropic universe without cosmological constant

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 this hypothesis we calculate the general analytical formula to fifth order for the redshift spherical shell mass. Using the same analytical method we write the metric in the light-cone by introducing a gauge invariant quantity $G(z)$ which together with the luminosity distance $D_L(z)$ completely determine the light-cone geometry of a LTB model.

13 pages

References in corpus (9)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Mimicking Dark Energy with Lemaitre-Tolman-Bondi Models: Weak Central Singularities and Critical Points
• Mapping Luminosity-Redshift Relationship to LTB Cosmology
• Local Void vs Dark Energy: Confrontation with WMAP and Type Ia Supernovae
• Can inhomogeneties accelerate the cosmic volume expansion?
• Solving the Inverse Problem with Inhomogeneous Universes
• LTB universes as alternatives to dark energy: does positive averaged acceleration imply positive cosmic acceleration?
• Redshift spherical shell energy in isotropic Universes
• Accelerating Universe via Spatial Averaging

Cited by in corpus (18)

• Dark Energy
• Inhomogeneity and the foundations of concordance cosmology
• Establishing homogeneity of the universe in the shadow of dark energy
• 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?
• 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
• Can the cosmological constant be mimicked by smooth large-scale inhomogeneities for more than one observable?
• Thermodynamics of Lemaitre-Tolman-Bondi Model
• Emergent scenario and different anisotropic models
• Non perturbative effects of primordial curvature perturbations on the apparent value of a cosmological constant
• Spectral Distortion in a Radially Inhomogeneous Cosmology
• Thermodynamics of the inhomogeneous perfect fluid LTB model: Modified Bekenstein-Hawking system
• Low red-shift effects of local structure on the Hubble parameter in presence of a cosmological constant
• Reconstructing the metric of the local Universe from number counts observations
• Coordinate independent approach to the calculation of the effects of local structure on the luminosity distance