What celestial phenomena can illuminate our understanding of fundamental physics? This question serves as the guiding principle for this course. Beginning with a review of key principles in general relativity, we will delve into the foundations of the standard model of cosmology. Our aim is to comprehend the fundamental characteristics of the vast expanse of space-time: its geometry, energy distribution, and dynamic behavior.
To achieve this goal, we will explore cosmic symmetries and conservation laws, solve Einstein's field equations in the presence of various types of fluids, and analyze the relativistic kinematics of particles within a moving background. Once we establish the necessary formalism, we will embark on an exploration of the physics underlying different stages of cosmic evolution. Special emphasis will be placed on elucidating the primordial inflationary phase and the enigmatic dark energy phase. These phenomena will serve as intriguing avenues for investigating potential deviations from the predictions of general relativity, such as the existence of extra dimensions or additional scalar degrees of freedom besid the metric.
A significant portion of the course will be dedicated to relativistic perturbation theory, the gravitational framework that elucidates how galaxies and other large-scale structures of the universe emerged from minute quantum fluctuations in energy. We will examine theoretical predictions regarding the spatial distribution of matter and energy in the cosmos, contrasting them with available empirical evidence. On top of scalar perturbations we will also delve into tensor perturbations and discuss gravitational waves by presenting both the theoretical formalism and ongoing detection experiments.