Tensor-scalar cosmological models and their relaxation toward general relativity

Cosmological models within general tensor-multiscalar theories of gravity are studied. By isolating an autonomous evolution equation for the scalar fields, one shows that the expansion of the Universe during the matter-dominated era tends to drive the scalar fields toward a minimum of the function $a\left(\varphi \right)$ describing their coupling to matter, i.e., toward a state where the tensor-scalar theory becomes indistinguishable from general relativity. The two main parameters determining the efficiency of this natural attractor mechanism toward general relativity are the redshift at the beginning of the matter era (or equivalently the present cosmological matter density) and the curvature of the coupling function $a\left(\varphi \right)$. Quantitative estimates for the present level of deviation from general relativity, as measured by the post-Newtonian parameters $\gamma -1\mathrm{}$, $\beta -1\mathrm{}$, and $\frac{\dot{G}}{G}$, are derived, which give greater significance to future improvements of solar-system gravitational tests. Another prediction of many tensor-scalar scenarios (whose consequences, particularly for the formation of structure in the Universe, remain to be studied in detail) is the existence of strong oscillations of the effective Newtonian coupling strength during the first few Hubble time scales of the matter era.