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

Understand

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.