Gravitational waves from stochastic relativistic sources: primordial turbulence and magnetic fields

Details Gravitational waves from stochastic relativistic sources: primordial turbulence and magnetic fields Gravitational waves from stochastic relativistic sources: primordial turbulence and magnetic fields

2006-03-17

arxiv.org/abs/astro-ph/0603476v3

Phys.Rev.D74:063521,2006

Astronomy and Astrophysics

Astrophysics

Replaced with revised version accepted for publication in Phys Rev D

Scientific paper

10.1103/PhysRevD.74.063521

The power spectrum of a homogeneous and isotropic stochastic variable, characterized by a finite correlation length, does in general not vanish on scales larger than the correlation scale. If the variable is a divergence free vector field, we demonstrate that its power spectrum is blue on large scales. Accounting for this fact, we compute the gravitational waves induced by an incompressible turbulent fluid and by a causal magnetic field present in the early universe. The gravitational wave power spectra show common features: they are both blue on large scales, and peak at the correlation scale. However, the magnetic field can be treated as a coherent source and it is active for a long time. This results in a very effective conversion of magnetic energy in gravitational wave energy at horizon crossing. Turbulence instead acts as a source for gravitational waves over a time interval much shorter than a Hubble time, and the conversion into gravitational wave energy is much less effective. We also derive a strong constraint on the amplitude of a primordial magnetic field when the correlation length is much smaller than the horizon.

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