Observational assessment of the viability of de Sitter-Gödel-de Sitter phase transition

Abstract

de Sitter--Gödel--de Sitter phase transition(dGd) is a possible geometrical phase transition in the very early universe. It induces fluctuations with possibly observable traces on matter and radiation fields. Here we present a simulation based on dGd to investigate possible perturbations which could be along with the standard inflationary fluctuations in the cosmic microwave background (CMB) and distribution of the large-scale structure. The power spectrum of perturbations is characterized by a parameter pair, labeled here as ($p_1,p_2$). With {\it Planck} observations we find $p_1=0.008_{-0.008}^{+0.003}$ and $p_2=0.002_{-0.002}^{+0.001}$ consistent with pure inflationary power spectrum and no hint for the dGd transition. Also, it is estimated future large-scale surveys such as Euclid and SKA can further tighten the constraints up to an order of magnitude and probe the physics of the early universe with much higher precision.