Mathematics – Logic
Scientific paper
May 1992
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992phrvd..45.3394l&link_type=abstract
Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 45, Issue 10, 15 May 1992, pp.3394-3404
Mathematics
Logic
72
Particle-Theory And Field-Theory Models Of The Early Universe, Origin And Formation Of The Universe
Scientific paper
Cosmological consequences of the Peccei-Quinn field ψ=reiθ/ √2 are explored. It has a Mexican-hat potential W=1/4λ(r2-f2a)2. During inflation the potential may be modified so that fa has a different effective value fa1; it is assumed that r sits in the vacuum at r=fa1. After inflation the temperature is supposed to be less than fa so that r=fa, and the only degree of freedom is the axion field faθ. It has a Gaussian inhomogeneity coming from the vacuum fluctuation of θ during inflation. When the axion mass ma(T) becomes significant at T~1 GeV, θ has dispersion σθ~=(4/2π)(H1/fa1) and some mean θ¯ (in the observable Universe). The axion potential is U(θ)=(79 MeV)4(1-cosNθ), and the ensuing cosmology is determined by the three parameters fa/N, Nθ¯, and Nσθ. The entire domain of parameter space is considered, including the regime where the axion density perturbation is non-Gaussian and the regime where axionic domain walls are produced. Observational constraints on the parameters are established. At the end of the paper the additional assumption is made that during inflation the vacuum is at r=fa. Unless fa/N is near the Planck scale and axions make up only a small fraction of the dark matter, this leads to the bound V1/41<2×1015 GeV, where V1 is the energy density during inflation, at the epoch when the observable Universe leaves the horizon.
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