Abstract
A study of the slow-roll inflation for an exponential potential in the frame of the scalar-tensor theory is performed, where non-minimal kinetic coupling to curvature and non-minimal coupling of the scalar field to the Gauss-Bonnet invariant are considered. Different models were considered with couplings given by exponential functions of the scalar field, that lead to graceful exit from inflation and give values of the scalar spectral index and the tensor-to-scalar ratio in the region bounded by the current observational data. Special cases were found, where the coupling functions are inverse of the potential, that lead to inflation with constant slow-roll parameters, and it was possible to reconstruct the model parameters for given ns and r. In first-order approximation the standard consistency relation maintains its validity in the model with non-minimal coupling, but it modifies in presence of Gauss–Bonnet coupling. The obtained Hubble parameter during inflation, Hsim 10^{-5} M_p and the energy scale of inflation V^{1/4}sim 10^{-3} M_p, are consistent with the upper bounds set by latest observations.
Highlights
The theory of cosmic inflation [1,2,3] that has been favored by the latest observational data [4,5,6,7], is the most likely scenario for the early universe, since it provides the explanation to flatness, horizon and monopole problems, among others, for the standard hot Bing Bang cosmology [8,9,10,11,12,13,14]
In the present paper we address the above shortcomings of the exponential potential, this time in the frame of scalar-tensor theories, taking into account non-minimal kinetic an GB couplings, which could play relevant role in the high curvature regime typical for inflation
We have analyzed the slow-roll dynamics for the scalartensor model with non-minimal kinetic and GB couplings, where the potential and the functional form of the couplings are given by exponential functions of the scalar field
Summary
The theory of cosmic inflation [1,2,3] that has been favored by the latest observational data [4,5,6,7], is the most likely scenario for the early universe, since it provides the explanation to flatness, horizon and monopole problems, among others, for the standard hot Bing Bang cosmology [8,9,10,11,12,13,14]. An important feature of the exponential potential (in the framework of minimally coupled scalar field model) is that under its dominance the universe expands following a power-law, which describes the asymptotic behavior of the background spacetime in different epochs. This is the case of the late time dark energy dominated universe, where the exponential potential can give rise to accelerated expansion [94,95]. Applied to the study of the early universe, the exponential potential in the minimally coupled scalar field model, gives rise to power-law inflation [96–100] with constant slow-roll parameters.
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