Exact Solutions and Scalar Fields in Gravity - Instituto Avanzado de ...

CONFORMAL SYMMETRY AND
DEFLATIONARY GAS UNIVERSE
Winfried Zimdahl
Universität Konstanz, PF M678 D-78457 Konstanz, Germany
Alexander B. Balakin
Kazan State University, 420008 Kazan, Russia
Abstract
Keywords:
We describe the “deflationary” evolution from an initial de Sitter phase
to a subsequent Friedmann–Lemaître–Robertson–Walker (FLRW) period
as a specific non–equilibrium configuration of a self-interacting gas.
The transition dynamics corresponds to a conformal, timelike symmetry
of an “optical” metric, characterized by a refraction index of the cosmic
medium which continuously decreases from a very large initial value to
unity in the FLRW phase.
Conformal symmetry, inflation, cosmology.
1. INTRODUCTION
It is well known that a thermodynamic equilibrium in the expanding
universe is only possible under special circumstances. For a simple gas
model of the cosmic medium e.g., the relevant equilibrium condition can
be satisfied only for massless particles, corresponding to an equation of
state where P is the pressure and is the energy density
[1, 2]. This equilibrium condition is equivalent to a symmetry requirement
for the cosmological dynamics: The quantity where is
the four velocity of the medium and T is its temperature, has to be a
conformal Killing vector (CKV) [3, 4]. For deviations from
the conformal symmetry is violated and no equilibrium is possible for
the gaseous fluid. If we give up the diluted gas approximation on which
this model is based and take into account additional interactions inside
the many–particle system, the situation changes. Suitable interaction
terms give rise to a generalization of the equilibrium conditions of the
gas (“generalized equilibrium”) [5, 6, 7, 8, 9]. Among these generalized
Exact Solutions and Scalar Fields in Gravity: Recent Developments
Edited by Macias et al., Kluwer Academic/Plenum Publishers, New York, 2001 247