Required Conditions for Late Time Acceleration and Early Time Deceleration in Generalized Scalar-Tensor Theories

Abstract

We consider a generalized scalar-tensor theory, where we let the coupling function $\omega (\varphi )$ and the effective cosmological constants $\Lambda (\varphi )$ undetermined. We obtain general expressions for $\omega (\varphi )$ and $\Lambda (\varphi )$ in terms of the scalar field and the scale factor, and show that $\omega (\varphi )$ depends on the scalar field and the scale factor in a complicated way. In order to study the conditions for an accelerated expansion at the present time and a decelerated expansion in the past, we assume a power law evolution for the scalar field and the scale factor. We analyse the required conditions that allow our model to satisfy the weak field limits on $\omega (\varphi )$, and at the same time, to obtain the correct values of cosmological parameters, as the energy density ${\Omega }_{m0}$ and cosmological constant $\Lambda (t_0)$. We also study the conditions for a decelerated expansion at an early time dominated by radiation. We find values for $\omega (\varphi )$ and $\Lambda (\varphi )$ consistent with the expectations of a theory where the cosmological constant decreases with the time and the coupling function increases until the values accepted today.

21 pages, 5 figures, to appear in Int. J. Mod. Phys. A

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