Miranda, Marcello (2024) Novel perspectives for Horndeski gravity: from effective fluids to exact solutions. [Tesi di dottorato]

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Abstract

This thesis delves into the study of scalar-tensor gravitational theories that extend General Relativity. Such alternative formulations arise primarily due to the shortcomings of the standard cosmological model. By introducing an additional scalar field, these theories seek to deepen our understanding of gravity and resolve both theoretical and observational challenges. The focus is mainly on the viable (or reduced) subclass of Horndeski gravity, which represents the most general non-degenerate scalar-tensor theory, characterized by manifestly second-order field equations and luminal propagation of tensor modes. Despite this observational constraint, viable models of Horndeski gravity remain quite general due to the presence of unknown functions within the theory. To gain insights and criteria for selecting the functional form of the theory, we explore novel perspectives. Framing the discussion within the effective fluid approach, we interpret the scalar-tensor contributions to the field equations as the effective stress-energy tensor of a dissipative fluid, leading to a classification of Horndeski gravity in terms of “Newtonian” and “non-Newtonian” fluids. We discuss the formal analogy with first-order thermodynamics of imperfect fluids, examining cosmological applications and possible alternative formulations. Another approach involves studying covariant effective formulations of a non-singular bounce, replacing the Big Bang initial singularity. In this framework, the selected models correspond to scalar-tensor theories without additional propagating degrees of freedom, such as cuscuton and extended cuscuton. Next, the case of Horndeski gravity as a source for non-rotating black holes embedded in a dynamic universe is explored. This again selects a non-dynamic scalar field, which is stealth at small scales near the central object but, at large scales, influences the evolution of the universe and its matter content. Finally, the last criterion analyzed is the requirement for the theory to possess a Noether symmetry. Based on this, a general classification of Horndeski gravity is provided.

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