Particle creation phenomenology, Dirac sea and the induced Weyl and Einstein-dilaton gravity

TL;DR

This paper develops a conformally invariant model for scalar particle creation in strong gravitational fields, linking Weyl tensor-based creation laws to induced gravity and exploring vacuum states including the Dirac sea.

Contribution

It introduces a novel conformally invariant framework connecting particle creation, Weyl and Einstein-dilaton gravity, and the Dirac sea within a self-consistent model.

Findings

Derived a conformally invariant particle creation model

Linked particle creation to Weyl tensor squared

Identified vacuum states including the Dirac sea

Abstract

We constructed the conformally invariant model for scalar particle creation induced by strong gravitational fields. Starting from the "usual" hydrodynamical description of the particle motion written in the Eulerian coordinates we substituted the particle number conservation law (which enters the formalism) by "the particle creation law", proportional to the square of the Weyl tensor (following the famous result by Ya.B.Zel`dovich and A. A.Starobinsky). Then, demanding the conformal invariance of the whole dynamical system, we have got both the (Weyl)-conformal gravity and the Einstein--Hilbert gravity action integral with dilaton field. Thus, we obtained something like the induced gravity suggested first by A. D.Sakharov. It is shown that the resulting system is self-consistent. We considered also the vacuum equations. It is shown that, beside the "empty vacuum", there may exist the "dynamical vacuum", which is nothing more but the Dirac sea.