Particle creation by the gravitational field, and the problem of the cosmological singularity

Details Particle creation by the gravitational field, and the problem of the cosmological singularity Particle creation by the gravitational field, and the problem of the cosmological singularity

Jun 1978

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978pazh....4..203m&link_type=abstract

(Pis'ma v Astronomicheskii Zhurnal, vol. 4, May 1978, p. 203-206.) Soviet Astronomy Letters, vol. 4, May-June 1978, p. 111-113.

Mathematics

1

Cosmology, Fermions, Gravitational Constant, Pair Production, Schwarzschild Metric, Singularity (Mathematics), Asymptotic Series, Bosons, Convergence, Flux Density, Relativistic Particles

Scientific paper

The effect of fermion pair production near the singularity in a homogeneous and isotropic Friedmann cosmology is investigated. The number density, energy density, and pressure of fermion pairs formed during the time interval from the singularity to an epoch corresponding to the reciprocal of particle mass are calculated. Divergences of a field-theoretic nature in the vacuum averages are eliminated by a renormalization of the gravitational constant equivalent to the regularization procedure of Zel'dovich et al. (1971) generalized to the fermion case. It is found that in the case of background matter with an ultrarelativistic equation of state, auxiliary divergences associated with the singularity in the metric arise, leading to production of fermions with infinite energy density and pressure, so that even in the isotropic case it is not possible to specify the fermion vacuum field at time t = 0. It is concluded that a universe filled with an ultrarelativistic gas cannot evolve directly from the epoch t = 0 according to a law following from Einstein's equations.

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