The study of cosmic phase transitions are of central interest in modern cosmology. In the standard model of cosmology the Universe begins in a very hot state, right after at the end of inflation via the process of reheating/preheating, and cools to its present temperature as the Universe expands. Both new and existing physics at any scale can be responsible for catalyzing either first, second or cross over phase transition, which could be either thermal or non-thermal with a potential observable imprints. Thus this field prompts a rich dialogue between gravity, particle physics and cosmology. It is all but certain that at least two cosmic phase transitions have occurred -the electroweak and the QCD phase transitions. The focus of this review will be primarily on phase transitions above such scales, We review different types of phase transitions that can appear in our cosmic history, and their applications and experimental signatures in particular in the context of exciting gravitational waves, which could be potentially be constrained by LIGO/VIRGO, Kagra, and eLISA.Let us briefly summarize the early Universe cosmology in chronological order. How the Universe began remains a profound question, for which we do not have direct experimental evidence yet. Nonetheless, we can speculate based on sound physical arguments and the observations confirmed by the detection of cosmic microwave background (CMB) radiation [46,47].
How did the Universe begin?Einstein's theory of gravity (GR) is extremely successful in the infrared (IR) matching of all possible observables [48], including the recent discovery of gravitational waves from mergers of two blackholes [49], and binary neutron star mergers [50]. However at short distances and small time scales, i.e. in the ultraviolet (UV), GR has pathologies, besides being a non-renormalizable theory, GR introduces cosmological and blackhole singularities, see [51], and in some cases naked singularities, see [52]. In GR, our Universe has a distinct starting point, a singular spacetime -as long as all the standard energy conditions are always satisfied, i.e. strong, weak, and null energy conditions, see [51]. It is possible to address the cosmological singularity problem without violating the matter energy conditions by weakening the gravitational interaction in the UV. This can happen in ghost free infinite derivative gravity inspired from string field theory [53,54]. There could be two consequences for such study; one could be a realization of a non-singular bounce [55,56], and the other scenario would be that Universe could be frozen in time in the UV, such that the Universe becomes conformal as t → 0 [57]. Bouncing cosmologies and cosmological density perturbations have been reviewed in this nice review [58,59]. There is a strong indication that this non-singular initial phase of the Universe has a key role to play towards understanding the subsequent phases of the Universe such as cosmic inflation, horizon, homogeneity and isotropy of the Universe , to create appropriate initial co...