Slow-roll inflation in (R+R*4) gravity

We reconsider the toy-model of topological inflation, based on the R*4-modified gravity. By using its equivalence to the certain scalar-tensor gravity model in four space-time dimensions, we compute the inflaton scalar potential and investigate a possibility of inflation. We confirm the existence of the slow-roll inflation with an exit. However, the model suffers from the eta-problem that gives rise to the unacceptable value of the spectral index n_s of scalar perturbations.Comment: 12 pages, 3 figures, LaTeX, misprints corrected and references update

Palatini versus metric formulation in higher curvature gravity

We compare the metric and the Palatini formalism to obtain the Einstein equations in the presence of higher-order curvature corrections that consist of contractions of the Riemann tensor, but not of its derivatives. We find that there is a class of theories for which the two formalisms are equivalent. This class contains the Palatini version of Lovelock theory, but also more Lagrangians that are not Lovelock, but respect certain symmetries. For the general case, we find that imposing the Levi-Civita connection as an Ansatz, the Palatini formalism is contained within the metric formalism, in the sense that any solution of the former also appears as a solution of the latter, but not necessarily the other way around. Finally we give the conditions the solutions of the metric equations should satisfy in order to solve the Palatini equations.Comment: 13 pages, latex. V2: reference added, major changes in section 3, conclusions partially correcte

Scalar potential in F(R) supergravity

We derive a scalar potential in the recently proposed N=1 supersymmetric generalization of f(R) gravity in four space-time dimensions. Any such higher-derivative supergravity is classically equivalent to the standard N=1 supergravity coupled to a chiral (matter) superfield, via a Legendre-Weyl transform in superspace. The Kaehler potential, the superpotential and the scalar potential of that theory are all governed by a single holomorphic function. We also find the conditions for the vanishing cosmological constant and spontaneous supersymmetry breaking, without fine-tuning, which define a no-scale F(R) supergravity. The F(R) supergravities are suitable for physical applications in the inflationary cosmology based on supergravity and superstrings.Comment: 10 pages, LateX, no figures; section 4 extende