Paolella, Mariacristina (2016) Cosmological Applications of Extended Theories of Gravity. [Tesi di dottorato]


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Item Type: Tesi di dottorato
Lingua: English
Title: Cosmological Applications of Extended Theories of Gravity
Date: 29 June 2016
Number of Pages: 162
Institution: Università degli Studi di Napoli Federico II
Department: Fisica
Scuola di dottorato: Scienze fisiche
Dottorato: Fisica fondamentale ed applicata
Ciclo di dottorato: 28
Coordinatore del Corso di dottorato:
Capozziello, SalvatoreUNSPECIFIED
De Laurentis, MariafeliciaUNSPECIFIED
Date: 29 June 2016
Number of Pages: 162
Uncontrolled Keywords: Extended Theories of Gravity; Cosmology; Dark Energy; Dark Matter; Exact solutions; Inflation
Settori scientifico-disciplinari del MIUR: Area 02 - Scienze fisiche > FIS/02 - Fisica teorica, modelli e metodi matematici
Area 02 - Scienze fisiche > FIS/05 - Astronomia e astrofisica
Date Deposited: 04 Jul 2016 08:37
Last Modified: 31 Oct 2016 09:49


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 (φ), of the potential V (φ) 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.


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