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

Abstract

A geometrical phase transition in the very early Universe, from de Sitter to Gödel and back to de Sitter (dGd) spacetimes, can explain the universal phenomenon of rotation of many large scale structures. This phase transition is shown to induce fluctuations on the matter and radiation fields with possibly observable traces. In this work we simulate the dGd-induced inhomogeneities and use their power spectrum, parametrized by the parameter pair (p 1 , p 2 ), as possible seeds of CMB anisotropies along with the standard inflationary perturbations. With the Planck 2018 observations, we find p 1 = 0.008 +0.003 −0.008 and p 2 = 0.002 +0.001 −0.002 consistent with pure inflationary power spectrum and no hint for the dGd transition. Future large scale surveys can further tighten the constraints and probe the physics of the early Universe.