Abstract
An extension of the Starobinsky model is proposed. Besides the usual Starobinsky Lagrangian, a term proportional to the derivative of the scalar curvature, ∇μR∇μR, is considered. The analyzis is done in the Einstein frame with the introduction of a scalar field and a vector field. We show that inflation is attainable in our model, allowing for a graceful exit. We also build the cosmological perturbations and obtain the leading-order curvature power spectrum, scalar and tensor tilts and tensor-to-scalar ratio. The tensor and curvature power spectrums are compared to the most recent observations from BICEP2/Keck collaboration. We verify that the scalar-to-tensor rate r can be expected to be up to three times the values predicted by Starobinsky model.
Highlights
As is well known, the Starobinsky model is currently the most promising one for describing the cosmological inflation [1]
In order to generalize the f (R) models in the inflationary context other categories of modified gravity theories are taken into account, for instance those with Lagrangians containing the Gauss-Bonnet invariant and/or the Weyl tensor [34,35,36,37,38,39,40]. Some applications considering both inflationary scalar field and modified theory of gravity can be found in the literature [41,42,43,44] with some interesting results, e.g. vector fields contribution should no longer be ignored in the presence of a Weyl term in the Lagrangian [45]
Among the class of minimalist inflationary models, i.e. those composed of a single parameter [73], Starobinsky inflation is the one that best fits the observations of the CMB anisotropies [32]
Summary
The Starobinsky model is currently the most promising one for describing the cosmological inflation [1]. In order to generalize the f (R) models in the inflationary context other categories of modified gravity theories are taken into account, for instance those with Lagrangians containing the Gauss-Bonnet invariant and/or the Weyl tensor [34,35,36,37,38,39,40] Some applications considering both inflationary scalar field and modified theory of gravity can be found in the literature [41,42,43,44] with some interesting results, e.g. vector fields contribution should no longer be ignored in the presence of a (square) Weyl term in the Lagrangian [45].
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