The Starobinsky model, considered in the framework of the Palatini formalism, in contrast to the metric formulation, does not provide us with a model for inflation, due to the absence of a propagating scalar degree of freedom that can play the role of the inflaton. In the present article we study the Palatini formulation of the Starobinsky model coupled, in general nonminimally, to scalar fields and analyze its inflationary behavior. We consider scalars, minimally or nonminimally coupled to the Starobinsky model, such as a quadratic model, the induced gravity model or the standard Higgs-like inflation model and analyze the corresponding modifications favorable to inflation. In addition we examine the case of a classically scale-invariant model driven by the Coleman-Weinberg mechanism. In the slow-roll approximation, we analyze the inflationary predictions of these models and compare them to the latest constraints from the Planck collaboration. In all cases, we find that the effect of the R 2 term is to lower the value of the tensor-to-scalar ratio.
When considered in the Palatini formalism, the Starobinsky model does not provide us with a mechanism for inflation due to the absence of a propagating scalar degree of freedom. By (non)-minimally coupling scalar fields to the Starobinsky model in the Palatini formalism we can in principle describe the inflationary epoch. In this article, we focus on the minimally coupled quartic and natural inflation models. Both theories are excluded in their simplest realization since they predict values for the inflationary observables that are outside the limits set by the Planck data. However, with the addition of the R 2 term and the use of the Palatini formalism, we show that these models can be rendered viable.
The recent interest in modified theories of gravity, involving some type of non-minimal coupling to the Ricci scalar, and the calculation of cosmological observables in the Einstein or the Jordan frame, motivate the formulation of these theories in terms of quantities that are invariant under frame transformations. Furthermore, in view of the description of gravity and its geometry motivated by string theory, such a formulation could be extended to include theories of extra spatial dimensions. In the present article, we generalize the construction of frame-invariant quantities, concerning a general, Ddimensional scalar-tensor theory. Then, we limit our scope to the 5D braneworld scenario, where we study thick brane solutions that are localized on the 3-brane and extend the invariant formulation to the case of multiple scalar fields (non-)minimally coupled to gravity.
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