In this thesis we briefly expose the shortcomings of the Hot BigBang model, thereby explaining the inflationary solution. Then, we describe a scalar singlefield slowroll model of Inflation, and introduce the topic of cosmological perturbation theory. After having summarized the standard ways to deal with cosmological perturbations, we introduce the gauge invariant scalar curvature perturbation field ζ, and explain why it is necessary to seek for its correlation functions of order higher than two in order to discriminate between inflationary models. We thus expose two important formalisms that allow us to treat cosmological correlation functions. The first one is the inin formalism, which enables one to compute correlation functions in a similar way to what its done in the Smatrix approach. The second one is the ADM formalism, with which it turns out easier to take into account perturbations of the involved fields, in the context of General Relativity. We then apply these formalisms to two, three, and fourpoints correlation functions in the framework of singlefield slowroll Inflation, and of the I2(φ) ̃F F model, where the kinetic term of a gauge field is coupled to the inflaton. Finally, we introduce the f (φ) ̃W W model, which induces parityviolating signatures from the gravity sector. This model goes under the name of gravitional ChernSimons term, coupling the inflaton with the Weyl tensor W . We then compute several two, and threepoints functions to highlight possible sources of parity violation. In the end, we compute the ⟨ζζζζ⟩ trispectrum mediated by tensor fields in the ChernSimons model. This is indeed one of the main goals of this thesis: to see whether such a gravitonmediated trispectrum carries a paritybreaking signature. We investigate this possibility in details under several assumptions, discussing under which conditions ⟨ζζζζ⟩ turns out to be parityviolating.
In this thesis we briefly expose the shortcomings of the Hot BigBang model, thereby explaining the inflationary solution. Then, we describe a scalar singlefield slowroll model of Inflation, and introduce the topic of cosmological perturbation theory. After having summarized the standard ways to deal with cosmological perturbations, we introduce the gauge invariant scalar curvature perturbation field ζ, and explain why it is necessary to seek for its correlation functions of order higher than two in order to discriminate between inflationary models. We thus expose two important formalisms that allow us to treat cosmological correlation functions. The first one is the inin formalism, which enables one to compute correlation functions in a similar way to what its done in the Smatrix approach. The second one is the ADM formalism, with which it turns out easier to take into account perturbations of the involved fields, in the context of General Relativity. We then apply these formalisms to two, three, and fourpoints correlation functions in the framework of singlefield slowroll Inflation, and of the I2(φ) ̃F F model, where the kinetic term of a gauge field is coupled to the inflaton. Finally, we introduce the f (φ) ̃W W model, which induces parityviolating signatures from the gravity sector. This model goes under the name of gravitional ChernSimons term, coupling the inflaton with the Weyl tensor W . We then compute several two, and threepoints functions to highlight possible sources of parity violation. In the end, we compute the ⟨ζζζζ⟩ trispectrum mediated by tensor fields in the ChernSimons model. This is indeed one of the main goals of this thesis: to see whether such a gravitonmediated trispectrum carries a paritybreaking signature. We investigate this possibility in details under several assumptions, discussing under which conditions ⟨ζζζζ⟩ turns out to be parityviolating.
Probing parity violation in the Early Universe
SALVARESE, ALBERTO
2021/2022
Abstract
In this thesis we briefly expose the shortcomings of the Hot BigBang model, thereby explaining the inflationary solution. Then, we describe a scalar singlefield slowroll model of Inflation, and introduce the topic of cosmological perturbation theory. After having summarized the standard ways to deal with cosmological perturbations, we introduce the gauge invariant scalar curvature perturbation field ζ, and explain why it is necessary to seek for its correlation functions of order higher than two in order to discriminate between inflationary models. We thus expose two important formalisms that allow us to treat cosmological correlation functions. The first one is the inin formalism, which enables one to compute correlation functions in a similar way to what its done in the Smatrix approach. The second one is the ADM formalism, with which it turns out easier to take into account perturbations of the involved fields, in the context of General Relativity. We then apply these formalisms to two, three, and fourpoints correlation functions in the framework of singlefield slowroll Inflation, and of the I2(φ) ̃F F model, where the kinetic term of a gauge field is coupled to the inflaton. Finally, we introduce the f (φ) ̃W W model, which induces parityviolating signatures from the gravity sector. This model goes under the name of gravitional ChernSimons term, coupling the inflaton with the Weyl tensor W . We then compute several two, and threepoints functions to highlight possible sources of parity violation. In the end, we compute the ⟨ζζζζ⟩ trispectrum mediated by tensor fields in the ChernSimons model. This is indeed one of the main goals of this thesis: to see whether such a gravitonmediated trispectrum carries a paritybreaking signature. We investigate this possibility in details under several assumptions, discussing under which conditions ⟨ζζζζ⟩ turns out to be parityviolating.File  Dimensione  Formato  

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https://hdl.handle.net/20.500.12608/11976