CMB with Quintessence: Analytic Approach and CMBFAST

A particular kind of quintessence is considered, with equation of motion pQ/ρQ = −1, corresponding to a cosmological term with time-dependence Λ(t) = Λ(t0)(R(t0)/R(t)) which we examine initially for 0 ≤ 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 ≤ 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 Ωm and ΩΛ depend on P . Some comparison is made to the CMBFAST public code.