Inflationary attractors in F(R) gravity

In this letter we shall demonstrate that the viable F(R) gravities can be classified mainly into two classes of inflationary attractors, either the R2 attractors or the α-attractors. To show this, we shall derive the most general relation between the tensor-to-scalar ratio r and the spectral index of primordial curvature perturbations ns, namely the r−ns relation, by assuming that the slow-roll condition constrains the values of the slow-roll indices. As we show, the relation between the tensor-to-scalar ratio and the spectral index of the primordial curvature perturbations has the form r≃48(1−ns)2(4−x)2, where the dimensionless parameter x contains higher derivatives of the F(R) gravity function with respect to the Ricci scalar, and it is a function of the e-foldings number N and may also be a function of the free parameters of the various F(R) gravity models. For F(R) gravities which have a spectral index compatible with the observational data and also yield x≪1, these belong to the R2-type of attractors, with r∼3(1−ns)2, and these are viable theories. Moreover, in the case that x takes larger values in specific ranges and is constant for a given F(R) gravity, the resulting r−ns relation has the form r∼3α(1−ns)2, where α is a constant. Thus we conclude that the viable F(R) gravities may be classified into two limiting types of r−ns relations, one identical to the R2 model at leading order in x, and one similar to the α-attractors r−ns relation, for the F(R) gravity models that yield x constant. Finally, we also discuss the case that x is not constant.

Hali tarjima qilinmagan