CMB with Quintessence: Analytic Approach and CMBFAST

Abstract

A particular kind of quintessence is considered, with equation of motion $p_Q/ρ_Q = -1$, corresponding to a cosmological term with time-dependence $Λ(t) = Λ(t_0) (R(t_0)/R(t))^{P}$ which we examine initially for $0 \leq P < 3$. Energy conservation is imposed, as is consistency with big-bang nucleosynthesis, and the range of allowed $P$ is thereby much restricted to $0 \leq P < 0.2$. The position of the first Doppler peak is computed analytically and the result combined with analysis of high-Z supernovae to find how values of $Ω_m$ and $Ω_Λ$ depend on $P$. Some comparison is made to the CMBFAST public code.