Gravitational waves from the early universe

Abstract

Even though different models could already be constrained using CMB data, these models remained unconstrained at higher frequency scales, and, therefore, the knowledge of new physics at these scales remained limited, relying on theoretical assumptions and extrapolations. Recently, however, we experienced the advent of gravitational-wave and multi-messenger astronomy, including the outstanding detections by the LIGO-Virgo collaboration and the searches for Hellings-Downs correlations in pulsar timing data. Over the next decades, ongoing and future collaborations will explore different frequency ranges of the gravitational wave spectrum, granting access to regimes inaccessible by the CMB and collider experiments. These include ground-based, space-borne, and pulsar timing array searches for gravitational waves. By comparing their data with model-dependent gravitational-wave predictions, we can unprecedentedly constrain or eliminate different models or even discover new physics. In these lecture notes, as an entrance door for graduate students, we focus on how we can search for a cosmological background of gravitational waves and how this can be used to probe cosmology and beyond-Standard-Model physics. For this purpose, we review the formalism of gravitational waves in General Relativity, introduce stochastic background gravitational waves, and derive the Hellings-Downs correlation for pulsar timing array searches. We comment on detection efforts and present some of the most important cosmological sources that could produce such a background. These lecture notes were inspired by the course "Gravitational Waves from the Early Universe" given at the 27th W.E. Heraeus "Saalburg" Summer School 2021 by Valerie Domcke.