Using pulsar timing arrays and the quantum normalization condition to constrain relic gravitational waves

Nov 27, 2013
17 pages
Published in:
  • Class.Quant.Grav. 31 (2014) 035001
  • Published: Dec 23, 2013
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Abstract: (IOP)
In the non-standard model of relic gravitational waves (RGWs) generated in the early universe, the theoretical spectrum is mainly described by an amplitude r and a spectral index β, the latter usually being determined by the slope of the inflaton potential. Pulsar timing arrays (PTAs) data have imposed constraints on the amplitude of strain spectrum for a power-law form as a phenomenological model. Applying these constraints to a generic, theoretical spectrum with r and β as independent parameters, we convert the PTAs constraint into an upper bound on the index β, which turns out to be less stringent than those upper bounds from the Big Bang nucleosynthesis, cosmic microwave background and LIGO/VIRGO, respectively. Moreover, it is found that PTAs constrain the non-standard RGWs more stringently than the standard RGWs. If the condition of the quantum normalization is imposed upon a theoretical spectrum of RGWs, r and β become related. With this condition, a minimum requirement of the horizon size during inflation is greater than the Planck length that results in an upper bound on β, which is comparable in magnitude to that by PTAs. When both PTAs and the quantum normalization are applied to a theoretical spectrum of RGWs, constraints can be obtained for other cosmic processes of the early universe, such as the reheating, a process less understood observationally so far. The resulting constraint is consistent with the slow-roll, massive scalar inflation model. The future square kilometer array will be able to constrain RGWs further and might even detect RGWs, rendering an important probe to the very early universe.
Note:
  • Accepted for publication in Class. Quant. Grav
  • inflation: model
  • horizon: size
  • pulsar
  • cosmic background radiation
  • gravitational radiation: power spectrum
  • reheating
  • scale: Planck
  • VIRGO
  • LIGO
  • inflaton: potential