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

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 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 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.