Non-minimal coupling in fractional action cosmology

In this work, we reformulate the problem of chaotic inflation studied recently in the framework of non-minimal coupling to gravity within the context of Fractional Action Cosmology which belongs to the class of nonlocal theories of gravity and primarily for large value of the non-minimal coupling parameter xi. We analyze during the slow-roll inflation the field equations and we confront them with observations. It has been observed that the inflation field is described by the potential V(phi) approximate to xi(2)(phi(2) - v(2))(2), where v - root 4 vertical bar xi vertical bar/lambda + 4 xi(2)) approximate to root 1/vertical bar xi vertical bar and that for large value of the non-minimal coupling parameter vertical bar xi vertical bar, the scale factor and the scalar field are finite at the origin of time and besides successful inflation is achieved. The predicted values for the spectral index and tensor-to scalar ratio are in concurrence within 1 sigma of the current Wilkinson Microwave Anisotropy Probe measurements.