Scalar stars and effective field theory

The axion is one of the favored candidates to form the cold dark matter in the universe. This pseudo-scalar field may form compact objects called axion stars, whose physics is well captured by means of non-relativistic effective field theory coupled to Newtonian gravity. The interplay between gradient energy, self-interactions and gravity gives rise to both dilute and dense axion stars. While the existence of the dilute axion stars is well established, the situation is more complicated in the case of the so-called dense axion stars, an extra physically stable solution of the system of differential equations describing the dynamics of the axion field in the regime where self-interactions play an important role. The existence of the dense axion stars has not been settled in the literature. In this thesis, we discuss first the appropriate non-relativistic formalism for the study of these clumps by means of the various non-relativistic reductions found in the literature. We analyze the stability, for different sizes and number of particles, of these objects considering quartic self-interaction potentials. This allows us to corroborate the results for these cases already presented by other authors. We also go beyond the simplest case, by analyzing more complicated potentials describing with higher precision the axion self-interactions. By employing the correct non-relativistic axion effective field theory we show that the dense branch is an artefact of the non-relativistic reduction procedure.