10 research outputs found

### Hojman Symmetry Approach for Scalar-Tensor Cosmology

Scalar-tensor Cosmologies can be dealt under the standard of the Hojman
conservation theorem that allows to fix the form of the coupling $F(\phi)$, of
the potential $V(\phi)$ and to find out exact solutions for related
cosmological models. Specifically, the existence of a symmetry transformation
vector for the equations of motion gives rise to a Hojman conserved quantity on
the corresponding minisuperpace and exact solutions for the cosmic scale factor
$a$ and the scalar field $\phi$ can be achieved. In particular, we take
advantage of the fact that minimally coupled solutions, previously obtained in
the Einstein frame, can be conformally transformed in non-minimally coupled
solutions in the Jordan frame. Some physically relevant examples are worked
out.Comment: 6 pages, 4 figures, to appear in Phys. Lett.

### Cosmological inflation in $F(R,\mathcal{G})$ gravity

Cosmological inflation is discussed in the framework of $F(R,{\cal G})$
gravity where $F$ is a generic function of the curvature scalar $R$ and the
Gauss-Bonnet topological invariant $\cal G$. The main feature that emerges in
this analysis is the fact that this kind of theory can exhaust all the
curvature budget related to curvature invariants without considering
derivatives of $R,$ $R_{\mu\nu}$, $R^{\lambda}_{\sigma\mu\nu}$ etc. in the
action. Cosmological dynamics results driven by two effective masses (lenghts)
related to the $R$ scalaron and the $\cal G$ scalaron working respectively at
early and very early epochs of cosmic evolution. In this sense, a double
inflationary scenario naturally emerges.Comment: 9 pages, 5 figures, to be published in Phys. Rev.

### Cosmological Applications of Extended Theories of Gravity

This work investigates the cosmological applications of higher-order theories of gravity in four dimensions. In particular, we begin dealing with the possibility to obtain massive modes in the framework of effective field theories recovered by extending General Relativity and taking into account generic functions of the curvature invariants. In particular, adopting the minimal extension of f(R) gravity, an effective field theory with massive modes is straightforwardly recovered. This approach allows to evade shortcomings like ghosts and discontinuities if a suitable choice of expansion parameters is performed. Next, we stress one of the most important problem related to Extended Theories of Gravity that is the lack of a definitive, unique theory able to address the different shortcomings of General Relativity. In fact, several models have been proposed in order to address the dark side problem in cosmology and these models should be constrained also at ultraviolet scales in order to achieve a correct fundamental interpretation. We proceed analyzing the possibility to constrain f(R) theories at UV scales comparing quantum vacuum states in given cosmological back- grounds. Specifically, we compare Bogolubov transformations associated to different vacuum states for some f(R) models. The procedure consists in fixing the f(R) free parameters by requiring that the Bogolubov coefficients can be correspondingly mini- mized to be in agreement with both high redshift observations and quantum field theory predictions. In such a way, the particle production is related to the value of the Hubble parameter and then to the given f (R) model. The approach is developed in both metric and Palatini formalism.
The second part of this thesis is devoted to the search for exact solutions for Ex- tended Theories of Gravity that is very useful in order to control the physical meaning of these theories. To this goal, useful tools are Noether and Hojman approaches. The application of Hojman conservation theorem is presented in the framework of scalar-tensor cosmologies allowing to fix the form of the coupling F (Ï†), of the potential V (Ï†)
and to find out exact solutions for related cosmological models. Afterwards, Noether point symmetries are applied to metric-Palatini hybrid gravity in order to select the f(R) functional form, to find analytical solutions for the field equations and for the related Wheeler-DeWitt equation and finally to Gauss-Bonnet cosmological models,
where F is a generic function of the curvature scalar R and the Gauss-Bonnet topological invariant G, showing that the functional form of the F(R,G) function can be determined by the presence of symmetries. Exact solutions for some specific cosmological models are found out. Finally, cosmological inflation is discussed in the framework of F(R,G) gravity. In principle, this theory can exhaust all the curvature
budget related to curvature invariants. Cosmological dynamics is analysed resulting driven by two effective scalar fields, specifically a R scalaron and a G scalaron, working respectively at early and very early epochs of cosmic evolution. In this sense, a double inflationary scenario naturally emerges

### Effective field theory from modified gravity with massive modes

Massive gravitational modes in effective field theories can be recovered by
extending General Relativity and taking into account generic functions of the
curvature invariants, not necessarily linear in the Ricci scalar R. In
particular, adopting the minimal extension of f(R) gravity, an effective field
theory with massive modes is straightforwardly recovered. This approach allows
to evade shortcomings like ghosts and discontinuities if a suitable choice of
expansion parameters is performed.Comment: 11 pages, no figures; title and text match published versio

### Invariant solutions and Noether symmetries in Hybrid Gravity

Symmetries play a crucial role in physics and, in particular, the Noether
symmetries are a useful tool both to select models motivated at a fundamental
level, and to find exact solutions for specific Lagrangians. In this work, we
consider the application of point symmetries in the recently proposed
metric-Palatini Hybrid Gravity in order to select the $f({\cal R})$ functional
form and to find analytical solutions for the field equations and for the
related Wheeler-DeWitt (WDW) equation. We show that, in order to find out
integrable $f({\cal R})$ models, conformal transformations in the Lagrangians
are extremely useful. In this context, we explore two conformal transformations
of the forms $d\tau=N(a) dt$ and $d\tau=N(\phi) dt$. For the former conformal
transformation, we found two cases of $f({\cal R})$ functions where the field
equations admit Noether symmetries. In the second case, the Lagrangian reduces
to a Brans-Dicke-like theory with a general coupling function. For each case,
it is possible to transform the field equations by using normal coordinates to
simplify the dynamical system and to obtain exact solutions. Furthermore, we
perform quantization and derive the WDW equation for the minisuperspace model.
The Lie point symmetries for the WDW equation are determined and used to find
invariant solutions.Comment: 12 pages, 1 figur