Higher-Order dark matter: from non-relativistic Proca stars to cosmological spinor production

Abstract

This thesis explores the possibilities of forming compact dark matter objects as solutions to the Einstein-Klein-Gordon and Einstein-Proca field equations, as well as accounting for the mechanism of dark matter production through gravitational particle production. According to quantum mechanics, particles are subdivided into two groups: those with integer spin (bosons) and those with half-integer spin (fermions). The former are capable of forming particle condensates in the ground state, while the latter, limited by FermiDirac statistics, are forced to successively occupy higher energy levels. Here we will focus on describing the equilibrium configurations of compact objects of self-gravitating and self-interacting particles with spin s = 0 and s = 1, which share similar characteristics to their counterparts, the compact objects composed of fermions. On the other hand, one of the most notable results of the semiclassical treatment of quantum fields on curved spaces predicts the gravitational production of particles due to gravitational effects, in abundances that could account for the dark matter bounds imposed by current observations [4, 5]. Here we will focus on describing this phenomenon for quantum fields with spin s = 0 and spin s = ½ at different orders of approximation. In both objectives, we describe dark matter as a field that interacts only gravitationally with the rest of the matter. Both objectives aim to address particular issues (one intends to solve astrophysical and cosmological problems, while the other intends to explain the mechanism of production of these particles); however, they equally intend to account for the gravitational presence of dark matter in the observable universe. In both cases, we will explore different regimes of approximations for the bosonic or fermionic dark matter field according to each chapter.