Effects on the temperatures of a variable cosmological term after recombination

The thermal evolution of the universe with a variable cosmological term λ = λ₁₀ + λ₂₀a^-m is investigated, where a is the scale factor. Energy densities of the radiation and matter are included to examine numerically the thermal evolution from the primordial nucleosynthesis to the matter-dominant era. It is found that the radiation temperature predicted from the variable λ models is lowered significantly compared with the constant λ model if λ₂₀ ≳ 0.0002 and z ≲ 10⁴, which implies that the matter temperature decreases drastically. We stress that the strong decreases in both the radiation temperature and matter temperature affect the formation of the first objects at 10 ≲ z ≲ 1000.