Exploring inflation with cosmic microwave background and gravitational waves

The exploration of primordial Gravitational Waves (GWs) stands as a pivotal force in modern Cosmology, providing a unique window into the mechanisms at the birth of the Universe. Particularly, in the early moments of the cosmos, we hypothesize an extreme accelerated expansion, known as inflation. One of its main predictions is a primordial background of GWs, which have propagated almost undisturbed to our present time. Due to their nature, these GWs retain information about their production mechanism, enabling us to investigate inflation by observing them or their indirect imprints on various aspects of the Universe, as the Cosmic Microwave Background (CMB) polarization. In this Thesis, we leverage GWs and their relics to address two key questions: Does the standard cosmological model sufficiently explain our observations? What is known about these primordial GWs with current data? Before delving into these questions, Part I describes a Universe devoid of GWs, characterized by an inflationary period with only scalar perturbations. The hot Big-Bang model and its thermal history are explained through the concept of thermal decoupling (see Chap. 2). After addressing some inconsistencies in this model in Chap. 3, we turn our attention to the inflationary model in Chap. 4 as a solution to these issues. In this context, we explore two key components: the physics of scalar perturbations and the CMB, which serves as a cornerstone in contemporary Cosmology. This initial part lays the groundwork for highlighting the imprints of GWs in Part II, where tensor perturbations are introduced into the inflationary paradigm. In Chap. 5, we explore predictions for single-field slow-roll inflation and beyond. Additionally, we present a comprehensive computation of the Boltzmann equations for GWs, yielding key observable quantities related to the Cosmological Gravitational Wave Background (CGWB) (see Chap. 6). For example, the observation of CMB B-mode polarization offers invaluable information on inflation, as it is directly linked to the presence of primordial GWs. At this juncture of the manuscript, we possess a holistic view of the Universe with both scalar and tensor perturbations, enabling us to address the first question mentioned earlier. In Part III, we challenge aspects such as the cosmological principle, which advocates the homogeneity and isotropy of the Universe. The CMB reveals signatures of a departure from statistical isotropy, manifested in the form of the hemispherical power asymmetry (see Chap. 7). This feature suggests a preferred direction in the sky, prompting an investigation of the role of GWs in understanding its physical origin in Chap. 8 and Chap. 9. Another intriguing aspect of the CMB is the lack-of-correlation anomaly observed in its two-point angular correlation. It seems that this correlation is almost null on scales larger than 60 degree, in contrast to what we would expect from our current understanding. Chap. 10 discusses the possibility of detecting a similar characteristic in the CGWB. In Part IV, the focus shifts to data analysis in pursuit of answering the second question. Bayesian and frequentist statistics are introduced in Chap. 11 and Chap. 12, emphasizing two well-known techniques in Cosmology: Markov-Chain Monte-Carlo (MCMC) and Profile Likelihood (PL). Subsequently, Chap. 13 delves into the Bayesian perspective on the tensor sector of parameter space, considering different prior choices and assumptions. This analysis highlights the strengths and weaknesses of MCMC, prompting a frequentist test on the same datasets in Chap. 14 using the PL. By the end of these chapters, the current status of the search for primordial GWs from the perspectives of CMB and GW interferometers’ observations becomes clear. Although these chapters may not fully answer our driving questions due to their broad and ambitious nature, they underscore my contribution to the field. The original results obtained during this Philosophiae Doctor (PhD) degree include theoretical predictions for the CGWB, accounting for CMB anomalies, statistical tools for simulating and estimating the significance of the lack-of-correlation, novel forecasts on the CGWB, and a comprehensive and statistically sound analysis of CMB B-mode data using both Bayesian and frequentist tools, alongside direct GW observations. Not covered in this Thesis is the research within the Lite (Light) satellite for the studies of B-mode polarization and Inflation from cosmic background Radiation Detection (LiteBIRD) collaboration. LiteBIRD represents a significant future venture for exploring CMB B-mode polarization, providing a unique opportunity to inspect its largest scales, being a space-based mission. As an active member of different working groups, my contributions encompass forecasts on LiteBIRD’s capability to distinguish different inflationary models, forecasts on the science achievable through cross-correlating LiteBIRD with galaxy surveys, validation tests on simulations, likelihood analysis, and parameter estimation in various contexts.