WMAP constraints on scalar-tensor cosmology and the variation of the gravitational constant

We present observational constraints on a scalar-tensor gravity theory by ${\chi }^2$ test for the CMB anisotropy spectrum. We compare the WMAP temperature power spectrum with the harmonic attractor model, in which the scalar field has its harmonic effective potential with a curvature $\beta$ in the Einstein conformal frame and the theory relaxes toward Einstein gravity with time. We find that the present value of the scalar coupling, i.e., the present level of deviation from Einstein gravity $\left({\alpha }_0^2\right),$ is bounded to be smaller than $5\times {10}^{-4-7\beta }\left(2\mathrm{}\sigma \right),$ and ${10}^{-2-7\beta }\left(4\mathrm{}\sigma \right)$ for $0<\mathrm{}\beta <\mathrm{0.45.}\mathrm{}$ This constraint is much stronger than the bound from the solar system experiments for large $\beta$ models, i.e., $\beta >0.2\mathrm{}$ and 0.3 in $2\sigma$ and $4\sigma$ limits, respectively. Furthermore, within the framework of this model, the variation of the gravitational constant at the recombination epoch is constrained as $|{G(z=z}_{\mathrm{rec}})-G_0|{/G}_0<0.05(2\mathrm{}\sigma ),$ and $0.23\left(4\sigma \right).\mathrm{}$