Summary:
In this thesis we study cosmological inflation in modified gravity theories. Inflation solves some of the fundamental problems arising in the standard Big Bang Cosmology and in the simplest models is driven by a single scalar field. A popular model, which is in excellent agreement with the latest cosmological observations, after the launch of the Planck satellite, is the Starobinsky model. This arises from an f(R) gravity theory, with f(R) = R/2 + (k/2)R2, which is equivalent to a standard Einstein theory and a scalar field moving under the influence of a potential, which exhibits an extended plateau and is characterized by one mass parameter. The success of this model motivates us to study more general f(R)-theories, which are known to be conformally equivalent to an Einstein theory including a scalar field moving in a scalar potential whose form is dictated by the choice of f(R). It is shown that generalizing the Starobinsky model by the addition of extra terms it demands that they are unnaturally small in order to continue to have successful inflation. For this reason we study higher order gravity theories which involve derivatives of the Ricci scalar R too. In the simplest version, we focus on f(R) + R \Box R -theories, which are equivalent to an Einstein theory containing two scalar fields. In this class of theories, the case f(R) = R/2 + (k/2)R2 leads to an unstable potential and thus we consider more general forms of f(R) having all desired properties curing the aforementioned pathologies. The results of this study show that although the arising potentials can be stable, their minima correspond to anti de Sitter vacua. In order to describe successful inflation, an uplift of the potential is necessary, so that the Universe, after a period of de-Sitter accelerated expansion, falls to a Minkowski vacuum. An option towards reaching this goal is to encompass these models within the so-called no-scale Supergravity theories, which feature positive defined potentials having stable Minkowski vacua.
Keywords:
inflation, modified gravity, f(R) theory, supergravity
