Blueshifts in the Lema\^{\i}tre -- Tolman models

TL;DR

This paper investigates blueshifts in Lemaître--Tolman models, showing how they can be hidden before recombination and analyzing their implications for cosmological observations and model viability.

Contribution

It demonstrates how the blueshift-generating regions in L--T models can be concealed prior to recombination and assesses the observational constraints on these models.

Findings

Blueshift regions can be hidden before recombination in general L--T models.

The specific L--T(t_B) model can replicate ΛCDM luminosity distance but faces astrophysical constraints.

In composite models, blueshifts are generally incompatible with early universe conditions.

Abstract

In the Lema\^{\i}tre -- Tolman (L--T) models that have nonconstant bang-time function $t_B(r)$, light emitted close to those points of the Big Bang where $\dril {t_B} r \neq 0$ is blueshifted at the receiver position. The blueshifted rays are expected to perturb the temperature of the cosmic microwave background (CMB) radiation along the lines of sight of the present central observer. It is shown here that, in a general L--T model, the $t_B(r)$ can be chosen so that the blueshift-generating region is hidden before the recombination time, where the L--T model does not apply. The rest of the paper is devoted to investigating blueshifts in one specific L--T model, called L--T$(t_B)$ -- the one that duplicates the luminosity distance vs. redshift relation of the $\Lambda$CDM model using nonconstant $t_B(r)$ alone. The location of the blueshift-generating region in the L--T$(t_B)$ spacetime is determined. Profiles of redshift/blueshift along several rays intersecting the past light cone of the present central observer are calculated. The L--T$(t_B)$ model matched to Friedmann is considered, and profiles of redshift/blueshift in such a composite model are calculated. The requirement of invisibility of blueshifts makes the L--T$(t_B)$ model astrophysically unacceptable if it should apply back to the recombination time, but does not "rule out" a general L--T model -- it only puts limits on $\dril {t_B} r$.