In this paper , we fully investigate the cosmological effects of the moduli-dependent one-loop corrections to the gravitational couplings of the string effective action to explain the cosmic acceleration problem in early ( and/or late ) universe .
These corrections comprise a Gauss-Bonnet ( GB ) invariant multiplied by universal non-trivial functions of the common modulus \sigma and the dilaton \phi .
The model exhibits several features of cosmological interest , including the transition between deceleration and acceleration phases .
By considering some phenomenologically motivated ansatzs for one of the scalars and/or the scale factor ( of the universe ) , we also construct a number of interesting inflationary potentials .
In all examples under consideration , we find that the model leads only to a standard inflation ( w \geq - 1 ) when the numerical coefficient \delta associated with modulus-GB coupling is positive , while the model can lead also to a non-standard inflation ( w < -1 ) , if \delta is negative .
In the absence of ( or trivial ) coupling between the GB term and the scalars , there is no crossing between the w < -1 and w > -1 phases , while this is possible with non-trivial GB couplings , even for constant dilaton phase of the standard picture .
Within our model , after a sufficient amount of e-folds of expansion , the rolling of both fields \phi and \sigma can be small .
In turn , any possible violation of equivalence principle or deviations from the standard general relativity may be small enough to easily satisfy all astrophysical and cosmological constraints .