universe and on the effective value[^1] of $w$ [@CDS98; @HFZT01; @KCS01]. As noted by these authors, for a fixed $w$ value, a change in the physical density parameter $\omega_m=\Omega_mh^2$ that keeps the characteristic angular scale of the first acoustic peak fixed will also leave the age approximately unchanged. Thus an independent estimate of the absolute age of the universe at $z=0$ combined with a measurement of $\ell_1$ yields an estimate of $w$ largely independent of other cosmological parameters (e.g., $\Omega_m$ and $h$).

This can be better understood by considering that for a constant $w(z)$, the age of a flat universe is given by $$t_0= H_0^{-1} \int_{0}^{\infty} (1+z)^{-1}\left[\Omega_{\rm
rad}(1+z)^4+\Omega_m(1+z)^3+\Omega_{\Lambda} (1+z)^{3(1+w)}\right]^{-1/2}
dz\;.
\label{eq:ageflatwconst}$$ The position of the first acoustic peak is fixed by the quantity $$\theta_A=r_s(a_{dec})/d_A(a_{dec})\;,
\label{eq:thetaa}$$ where $a_{dec}$ is the scale factor at decoupling, $r_s(a_{dec})$ is the sound horizon at decoupling, and $d_A(a_{dec})$ is the angular diameter distance at decoupling. For a flat universe, $$r_s(a_{dec})=\frac{c}{H_0\sqrt{3}}\int_0^{a_{dec}}\left[\left(1 +
\frac{3\Omega_b} {4\Omega_{\gamma}}\right)(\Omega_{\Lambda}x^{1-3w} +
\Omega_mx + \Omega_{\rm rad})\right]^{-1/2}dx
\label{eq:rs}$$ and $$d_A(a_{dec})=\frac{c}{H_0}\int_{a_{dec}}^1\left[\Omega_{\Lambda}x^{1-3w}
+ \Omega_mx + \Omega_{\rm rad}\right]^{-1/2}dx\;.
\label{eq:dA}$$ See @VerdeWMAP03 for more details. We use equations \[eq:ageflatwconst\] to \[eq:dA\] and fix $\theta_A$ to be consistent with the [*WMAP*]{} determination [$\ell_1\simeq
220$; @PageWMAP03]. Figure 1 shows the allowed 