Quintessence and CMB

A particular kind of quintessence is considered, with equation of motion $p_Q\mathrm{/}{\rho }_Q=-1$, corresponding to a cosmological term with time-dependence $\mathrm{\Lambda }(t)=\mathrm{\Lambda }(t_0)(R(t_0)\mathrm{/}R(t){)}^P$ 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 ${\mathrm{\Omega }}_m$ and ${\mathrm{\Omega }}_{\mathrm{\Lambda }}$ depend on $P$.