Costa, Francesco (2020) Heavy field Radiative Corrections to the Primordial Power Spectrum during Inflation. [Magistrali biennali]
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Nearly scale-invariant primordial power spectrum is one of the key features of cosmic inflation. The amplitude of the power spectrum as well as its spectral tilt are constrained by modern experiments. To date no sign of deviations from the simplest single-field inflation models has been observed. On the other hand, realistic models of inflation, meaning particle physics-based models, contain multiple fields other than the inflaton. The presence of heavy fields coupled to the inflaton may alter the predictions of the single-field inflation models. In this thesis we consider the effects of heavy fields on the primordial power spectrum, studying a generic model which contains massive scalar and fermion fields coupled to the inflaton. The spacetime background for the quantum fields during inflation is time-dependent due to the expansion of the Universe and the time translation symmetry is broken. Therefore we expect the radiative corrections to the inflaton power spectrum to be time-dependent. The natural theoretical framework to formulate such models is the Schwinger-Keldysh also known as the in-in formalism. We first introduce the Schwinger-Keldysh formalism. We then compute the one-loop radiative corrections to the inflaton two-point correlation function due to the heavy fields; without specifying the inflaton potential at first, keeping the inflationary scenario general. We perform the computations in a de Sitter spacetime, choosing the initial state at some initial conformal time τ_ to be the Bunch-Davies vacuum. We explicitly single-out, in both the bosonic and fermionic contributions to the one-loop inflaton two-point function, the quadratic and logarithmic divergences, in terms of a cut-off, as expected from the results on the Minkowski background. The analytical analysis is performed using the WKB approximated mode functions. We then compute numerically the same radiative corrections, using the full expressions for the solution of the mode functions. We show that the WKB approximation is a good analytical approximation for massive mode functions and we argue that it is a good tool to capture the UV divergences of massive fields. Finally we apply our results to the supersymmetric hybrid inflation model. The bosonic and fermionic divergences in the radiative corrections carry opposite sign and we show that they cancel exactly giving rise to a finite total result. The radiative corrections introduce the presence in the power spectrum of time-dependent features of two type. One arises from the evolution of the background. The other is an oscillatory feature. The scalar and fermion contributions produce a constant shift and this peculiar oscillatory effects on top of the tree-level primordial power spectrum. Future improvements of CMB measurements may refine our current understanding of the primordial power spectrum and lead to a possible detection of these effects.
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