Rotation of the cosmic objects is a universal phenomenon and it's origin is still an open question. Here a model for the origin of rotation is presented. After investigation of the phase transition of a scalar field in de-Sitter and Gödel backgrounds, the motion of a test particle during the phase transitions is studied. Then using computer simulation for a congruence of particles, we have shown that although the local induced rotation is non-zero, the global rotation is below the observational limit.

The Casimir force between two parallel plates in the Gödel universe is computed for a scalar field at finite temperature. It is observed that when the plates' separation is comparable with the scale given by the rotation of the space-time, the force becomes repulsive and then approaches zero. Since it has been shown previously that the universe may experience a Gödel phase for a small period of time, the induced inhomogeneities from the Casimir force are also studied.

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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.