Equation of state for a van der Waals universe during Reissner-Nordström expansion

Abstract

In a previous work [E.M. Prodanov, R.I. Ivanov, and V.G. Gueorguiev, 2007], we proposed a classical model for the expansion of the Universe during the radiation-dominated epoch based on the gravitational repulsion of the Reissner-Nordström geometrynaked singularity description of particles that "grow" with the drop of the temperature. In this work we model the Universe during the Reissner-Nordström expansion as a van der Waals gas and determine the equation of state.

Daemon decay and inflation

“…However, the temperature of the outside fraction of the Unniverse continues to drop after the rapid accelerated expansion as a different expansion mechanism has naturally taken over. This is the recently proposed Reissner-Nordström expansion mechanism [5,6]: with constant charges of daemons, the Universe continues to cool: T t −1/2 , and expand: a t 1/2 . This is the start of the radiation dominated epoch.…”

“…Under minute density fluctuation in the volume density of one type of charges at some point, the domain of all other like charges within radius r − are trapped gravitationally into a cluster. We will call this domain a daemon (for dark electric matter objects, as introduced by [9], and in line with our previous work [5,6] on Reissner-Nordström expansion). There will be no charges of this type between r − and r + , while charges of this type on the outside of r + would be strongly repelled.…”

“…We will be interested in the case of a naked singularity only, namely: |Q| > M . The radial motion of an ultra-relativistic test particle of mass m and charge q in Reissner-Nordström geometry can be modeled by an effective one-dimensional motion of a particle in non-relativistic mechanics with the following equation of motion [5,6,7] (see also [8] for Schwarzschild geometry) :…”

“…Equation (2) determines the region (r − , r + ) within which classical motion is impossible. The turning radii are given by [5,6,7]:…”

“…There is no inner turning radius r − for particles of specific charge q/m such that sign(Q)q/m < 1. For particles such that sign(Q)q/m < −1, there is neither inner turning radius, nor outer turning radius [5,6,7]. Such particles will fly unopposed into the centre.…”