Related papers: Inflation with $R_{(\alpha\beta)}$ terms in the Pa…
In this paper we derive the Modified Friedmann equation in the Palatini formulation of $R^2$ gravity. Then we use it to discuss the problem of whether in Palatini formulation a $R^2$ term can drive an inflation. We show that the Palatini…
We study Quadratic Inflation with the inflaton field $\phi$ coupled non-minimally to the curvature scalar $R$, so that the potential during inflation is of the form $V\propto m^2\phi^2+\xi R\phi^2$. We show that with a suitable choice of…
We perform an analysis of models of chaotic inflation where the inflaton field $\phi$ is coupled non-minimally to gravity via $\xi \phi^n g^{\mu\nu}R_{\mu\nu}(\Gamma), n>0$. We focus on the Palatini theory of gravity, i.e. the case where…
We study the possibility that inflation is driven by a scalar field together with a vector field minimally coupled to gravity. By assuming an effective potential that incorporates both fields into the action, we explore two distinct…
We explore inflationary cosmology in a theory where there are two scalar fields which non-minimally couple to the Ricci scalar and an additional $R^2$ term, which breaks the conformal invariance. Particularly, we investigate the slow-roll…
We examine the generation of primordial perturbations during an inflationary epoch in generalised theories of gravity when the equations of motion are derived using the Palatini variational principle. Both f(R) and Scalar-Tensor theories…
This thesis presents research exploring aspects of inflation and cosmology in the context of inflation models in which an inflaton is non-minimally coupled to the Ricci scalar, or is considered in conjunction with a term quadratic in the…
We compare Higgs inflation in the metric and Palatini formulations of general relativity, with loop corrections are treated in a simple approximation. We consider Higgs inflation on the plateau, at a critical point, at a hilltop and in a…
The $R^2$ inflation which is an extension of general relativity (GR) by quadratic scalar curvature introduces a quasi-de Sitter expansion of the early Universe governed by Ricci scalar being an eigenmode of d'Alembertian operator. In this…
The theory of General Relativity was established on a spacetime manifold equipped with a metric tensor, $(\mathcal{M}_4,\text{g})$, and the connection on $\mathcal{M}_4$ identified with the Levi-Civita one. Even though there are valid…
We consider the cosmology of the Ricci-tensor-squared gravity in the Palatini variational approach. The gravitational action of standard general relativity is modified by adding a function f(R^abR_ab) to the Einstein-Hilbert action, and the…
$F(R)$ Palatini gravity provides a robust framework for constructing viable inflationary potentials. In this study, we examine natural inflation and show that its consistency with observational data can be restored when the model is…
Inflationary models based on a single scalar field $\phi$ with a quadratic potential $V = \frac{1}{2} m^2 \phi^2$ are disfavoured by the recent Planck constraints on the scalar index, $n_s$, and the tensor-to-scalar ratio for cosmological…
We discuss another approach regarding the inflation from the R^2 theory of gravity originally proposed by Starobinski. A non-singular early cosmology is proposed, where, adding a nonlinear electrodynamics Lagrangian to the high-order…
We show that upon applying Palatini $f(R)$, characterized by an $\a R^2$-term, within a scenario motivated by a temporal variation of strong coupling constant, then one gets a quadratic kinetic energy. We do not drop this term, but rather…
Natural Inflation with non-minimal coupling (NMC) to gravity, embodied by a Lagrangian term $\xi \phi^2 R $, is investigated in the context of an extended gravity of the form $R+ \alpha R^2$. The treatment is performed in the Palatini…
It is natural to expect a consistent inflationary model of the very early Universe to be an effective theory of quantum gravity, at least at energies much less than the Planck one. For the moment, $R+R^2$, or shortly $R^2$, inflation is the…
We study the dynamics of inflation in a generalized scalar-torsion gravity scenario by assuming a canonical scalar field non-minimally coupled to torsion with a Galileon-type self-interaction. After obtaining the field equations for a flat…
Within the framework of metric-affine theories of gravity, where both the metric and connection are treated as independent variables, we consider actions quadratic in the Ricci scalar curvature coupled non-minimally to a scalar field…
In this paper, we explore the inflationary dynamics of the $\beta$-exponential potential model, where a scalar field couples to quadratic $(R + R^2)$ gravity. In this model, the inflaton is the field that determines the size of the extra…