Investigating new physics through cosmology

Throughout the years, the cosmic microwave background (CMB) has given a crucial contribution to build the standard cosmological model as we know today, becoming a privileged observational tool of modern cosmology. In particular, in the so-called era of high-precision cosmology, CMB data can put stringent constraints about the physics of the primordial Universe, when, according to the standard paradigm, the first cosmological perturbations formed. The measurements of anisotropies in the temperature of CMB and of CMB polarization are perfectly compatible with a Universe that in the past has experienced an inflationary phase of accelerated expansion (simply known as inflation), which is assumed to be driven by a scalar field, the so-called inflaton field. During inflation quantum perturbations of the inflaton field were stretched on very large (super-horizon) cosmological scales, where they got frozen. These are thought to be the seeds which later on evolved into the large scale structures that we observe today. In particular, from the precise analysis of the CMB maps, we can constrain a large variety of theoretical models aiming to describe the inflationary epoch. In fact, the CMB is for cosmologists what the colliders are for particle-physicists, allowing to test modified gravity theories, symmetries breaking, and the particle content during inflation. The CMB observations currently seem to favor the simplest inflationary models, the so-called slow-roll models, where a single slowly-rolling scalar field drives the expansion of the Universe under the effects of Einstein gravity, sourcing both scalar and tensor perturbations, which are the so-called primordial curvature perturbation and primordial gravitational waves. However, our understanding of inflation is far away to be complete both for theoretical and observational aspects. For instance, we still do not know the precise mechanism realizing inflation. In fact, primordial gravitational waves as predicted by slow-roll models have not been detected yet. Therefore, we do not have detailed information on their (power spectrum) statistics, which would be crucial to determine the exact inflationary model. Another example is the recent confirmation from the Planck satellite of the presence of some anomalies in the CMB map, suggesting a possible violation of some symmetries (e.g. the parity symmetry) at some point in the evolution of the Universe. Moreover, we are still facing the so-called trans-Planckian problem, i.e. the fact that the CMB physical observational scales could have been inside the Planck scale at the beginning of inflationary epoch, thus requiring an ultra-violet completion of the theory. All these aspects force us to push our research efforts further on about the physics of inflation. The physics of the CMB can be used to provide an insight into all these different issues related to the inflationary epoch. On the other hand, it also provides an observational tool to test other aspects of fundamental physics. For example, in this Thesis, we will show how modifications of the photon-fermion interactions as we know from the Standard Model of particle physics may lead to alternative theoretical predictions about the expected level of CMB polarization anisotropies generated during and after the recombination epoch. For example, they can generate non-zero circular polarization which is not allowed in the standard lore, but not completely excluded by the CMB experiments. Motivated by all these considerations, in this Thesis we will review some fundamental aspects of the standard cosmological model (regarding in particular the inflationary epoch) and investigate new scenarios that go beyond the standard paradigm, leading to predictions that could be tested with current and future CMB experiments which will focus on CMB polarization. The Thesis is organized as follows: - In part I, we will review different aspects of the standard cosmological model, focusing on the inflationary epoch and the connection between primordial perturbations and CMB anisotropies. - In part II, we will study parity breaking signatures in the gravity sector during the primordial Universe. In particular, we will consider the modifications to the statistics of primordial perturbations in presence of Chern-Simons gravity, which is the first order parity breaking modified gravity theory arising from an effective field theory modification of Einstein gravity. We will show that the expected amount of chirality in the power spectrum statistics of gravitational waves is expected to be very small, in a way that is difficult to have a detection with current and futuristic CMB experiments. Thus, we will make an analysis of the parity breaking signatures induced to the higher order (bispectra) statistics of primordial perturbations, showing interesting prospects for the 2 gravitons-1 scalar bispectrum. We will perform a Fisher-matrix forecast on the possibility to detect primordial signatures of Chern-Simons gravity from this bispectrum, with next decade CMB experiments focusing on CMB B modes. In particular, we will show that, in general, an improvement in the angular resolution of CMB experiments, together with lensing subtraction, can significantly enhance the sensitivity of CMB bispectra to parity breaking signatures in the primordial Universe. On the contrary, we will show that no significant improvements in constraining primordial parity breaking signatures are expected from the power spectra statistics of futuristic CMB experiments, even with very high angular resolution and perfect lensing subtraction. This result suggests that CMB bispectra statistics could be, in the future, a crucial observable to constrain parity breaking signatures from inflation. - In part III, we will consider how CMB can be possibly exploited to probe new physics beyond Standard Model of particle physics. We will study the generation of CMB circular polarization from the forward scattering between CMB photons and other particles. This is the same physical mechanism that also generates the neutrino flavor mixings in the Standard Model of fundamental interactions, causing the oscillation of neutrino flavors. In particular, firstly we will study the forward scattering between CMB photons and gravitons, showing a non-zero generation of V modes in case of anisotropies in the statistics of primordial gravitons. However, we will show that the final amount of V modes expected today is too low to be detected by both current and futuristic CMB experiments. Nevertheless, we will derive general equations that can be applied to a general photon-graviton interaction in contexts different from the CMB, e.g. for searching of gravitational wave events of astrophysical origin. We will then study the polarization mixing due to the forward scattering of CMB photons and generic fermions. In particular, we will provide a general parametrization of the photon-fermion forward-scattering amplitude (assuming only gauge invariance and CPT symmetry) and compute the corresponding mixing terms between the different CMB polarization states. We will consider different general extensions of Standard Model interactions which violate discrete symmetries, while preserving the combination of charge conjugation, parity and time reversal. We will show that it is possible to source CMB circular polarization by violating parity and charge conjugation symmetries. Instead, a B-mode generation (in absence of primordial gravitational waves) is associated to the violation of symmetry for time-reversal. Our final results will be expressed in terms of some free parameters characterizing different kinds of forward scattering interactions, thus offering in the future a viable and general tool to put constraints on fundamental physics properties beyond the standard paradigms using CMB data. - In part IV, we will provide our conclusions and final considerations about the research developed in this Thesis. - Finally, in part V, we will provide an Appendix, where some formulas and formalisms employed in this work are reviewed.