Fubini vacua as a classical de Sitter vacua

TL;DR

This paper explores the Fubini vacua as classical de Sitter vacua, revealing their entropy, radiation properties, and geometric structure, and connecting them to cosmological models and field theories.

Contribution

It demonstrates that Fubini vacua can be interpreted as classical de Sitter vacua with finite entropy, links them to Einstein and Yang-Mills theories, and describes their geometric and cosmological implications.

Findings

Fubini vacua have finite entropy similar to de Sitter space.

In Minkowski space, Fubini vacua resemble a radiation bath with Rayleigh-Jeans distribution.

The moduli space of Fubini vacua forms a (D+1)-dimensional AdS space.

Abstract

The Fubini's idea to introduce a fundamental scale of hadron phenomena by means of dilatation non-invariant vacuum state in the frame work of a scale invariant Lagrangian field theory is recalled. The Fubini vacua is invariant under the de Sitter subgroup of the full conformal group. We obtain a finite entropy for the quantum state corresponding to the classical Fubini vacua in Euclidean space-time resembeling the entropy of the de Sitter vacua. In Minkowski space-time it is shown that the Fubini vacua is mainly a bath of radiation with Rayleigh-Jeans distribution for the low energy radiation. In four dimensions, the critical scalar theory is shown to be equivalent to the Einstein field equation in the ansatz of conformally flat metrics and to the SU(2) Yang-Mills theory in the 't Hooft ansatz. In D-dimensions, the Hitchin formula for the information geometry metric of the moduli space of instantons is used to obtain the information geometry of the free-parameter space of the Fubini vacua which is shown to be a (D+1)-dimensional AdS space. Considering the Fubini vacua as a de Sitter vacua, the corresponding cosmological constant is shown to be given by the coupling constant of the critical scalar theory. In Minkowski spacetime it is shown that the Fubini vacua is equivalent to an open FRW universe.