Casimir force in the Gödel space-time and its possible induced cosmological inhomogeneity

Abstract

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.

Casimir force induced by electromagnetic wave polarization in Kerr, Gödel and Bianchi–I spacetimes

“…Results described in this work belong to a family of different behaviors of Casimir forces due to spacetime curvature. These have been studies in de Sitter [20], Schwarzschild [21][22][23], Gödel [54], wormhole [24] spacetimes, in cosmology [53,55,56], or in quantum cosmology [25], due to scalar [29,30,52] and vectorial fields [31], also showing that Casimir energy complies with the equivalence principle [26][27][28]. However, and differently, in this work we show that polarization of electromagnetic vacuum fluctuating fields interacting with curved spacetime (in a similar fashion to what occurs in the presence of materials) also modify the Casimir force.…”

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

“…Therefore the investigation of the local properties of dGd phase transition is worthwhile. These effects were recently studied through computing the Casimir force in Gödel spacetime [12]. The Casimir force is sensitive to the direction of the rotation of the Gödel space-time.…”

“…The Casimir force is sensitive to the direction of the rotation of the Gödel space-time. It was observed that for two parallel plates with a separation comparable to the rotation of Gödel spacetime (α), the Casimir force becomes repulsive and then approaches zero (see figure 4 of [12]).…”

“…In fact, after the dGd phase transition, the distance between local layers of matter would shrink in a direction perpendicular to the random Gödel rotation axis in an inhomogeneous way. The Casimir energy of a scalar field in the Gödel background and at finite temperature is given by [12] ĒCasimir d, β = Ē0 d + ∆F.T. d, β .…”

“…It was also shown that Casimir forces in the dGd transition would induce inhomogeneities in the matter and radiation fields, possibly observable in the Cosmic Microwave Background (CMB) radiation or large scale structure data [12]. The predictions of the dGd transition can therefore be directly tested against the existing data.…”