Constraining physics beyond ΛCDM through the cosmic microwave background and the large scale structure of the Universe.

This thesis investigates physics beyond the standard cosmological model (ΛCDM) through three interconnected topics: third-order corrections to primordial perturbations from inflation, signals of Cosmic Birefringence in the Cosmic Microwave Background (CMB) polarization, and photon– axion interactions in galactic magnetic fields. Using a combination of cosmological observations and theoretical modeling, these studies aim to improve our understanding of early-universe pro- cesses and possible new physics breaking fundamental symmetries. Cosmic inflation amplifies quantum fluctuations that seeded the observed anisotropies in the CMB and large-scale structure. Comparing theoretical predictions with observational data re- quires precision matching the improvements in measurement sensitivity. An analytical solution at third order in slow-roll parameters has been derived for scalar and tensor primordial per- turbations by solving the Mukhanov–Sasaki equation, using an approach distinct from previous literature. Comparisons with numerical solutions identify the scales and observational regimes where third-order corrections become relevant, including large-scale structure surveys, CMB spectral distortions, 21 cm experiments, and primordial black hole limits. Constraints on slow- roll parameters have been obtained, and forecasts for upcoming experiments such as LiteBIRD andtheSimonsObservatoryassessthepotentialobservationalimpactofhigher-ordercorrections. Physics beyond the Standard Model can violate parity symmetry, inducing a rotation of the CMB polarization plane by an angle β, an effect known as Cosmic Birefringence. Planck data indicate a 5σ detection of an EB signal, whose origin remains uncertain: it could arise from pseudoscalar particles (axions or axion-like particles, ALPs) coupled to the electromagnetic field via the Chern–Simons interaction, or result from systematic calibration uncertainties in the po- larimeters. A comprehensive analysis of Planck PR3 data has been performed, including pipeline validation and consistency checks across different component-separation methods (Commander, NILC, SEVEM, and SMICA), confirming the signal of β ≃0.30 ±0.05 degrees (68% CL), consistent with previous literature but excluding possible systematic errors. The key focus is the investi- gation of the scale dependence of β(ℓ) through harmonic-space estimators applied to different multipole subsets, independently of the signal’s physical origin. Two complementary methods—a parametric power-law fit and a non-parametric Bayesian reconstruction—have been used to test whether Planck data are consistent with scale independence. Such tests constrain the birefrin- gence spectrum and narrow the viable axion/ALP mass range to ultra-light regimes. Forecasts suggest that LiteBIRD, Simons Observatory, and CMB-S4 will significantly improve constraints on both the birefringence amplitude and its scale dependence. CMB photons passing through galactic halos can convert into axions via the Chern–Simons interaction, producing spectral distortions in the CMB. These distortions may be detectable by future CMB experiments such as the Simons Observatory when combined with galaxy surveys from the Vera Rubin Observatory Legacy Survey of Space and Time (LSST), Dark Energy Spec- troscopic Instrument (DESI), and Euclid. The photon–axion conversion probability, modeled by a two-level Schrödinger equation, is often estimated using the Landau–Zener approxima- tion, which assumes linear halo profiles. However, the validity of this approximation under realistic conditions—characterized by non-linear profiles, multiple resonances, and stochastic noise—remains uncertain. Here, the Schrödinger equation has been solved numerically using the Wentzel–Kramers–Brillouin (WKB) approximation, enabling a systematic exploration of the applicability of the Landau–Zener approximation and determining the scenarios where a full numerical approach is essential for accurate cosmological predictions.