Gravitational Wave Spectrum Induced by Primordial Scalar Perturbations

Abstract

We derive the complete spectrum of gravitational waves induced by primordial scalar perturbations ranging over all observable wavelengths. This scalar-induced contribution can be computed directly from the observed scalar perturbations and general relativity and is, in this sense, independent of the cosmological model for generating the perturbations. The spectrum is scale-invariant on small scales, but has an interesting scale-dependence on large and intermediate scales, where scalar-induced gravitational waves do not redshift and are hence enhanced relative to the background density of the Universe. This contribution to the tensor spectrum is significantly different in form from the direct model-dependent primordial tensor spectrum and, although small in magnitude, it dominates the primordial signal for some cosmological models. We confirm our analytical results by direct numerical integration of the equations of motion.

19 pages, 5 figures

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• Cosmological Constraints from the SDSS Luminous Red Galaxies
• The cosmological gravitational wave background from primordial density perturbations
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• Cosmic microwave background bispectrum on small angular scales
• Action approach to cosmological perturbations: the 2nd order metric in matter dominance
• The impact of cosmic neutrinos on the gravitational-wave background
• Vector modes generated by primordial density fluctuations
• Cosmic Shear from Scalar-Induced Gravitational Waves
• A Back-reaction Induced Lower Bound on the Tensor-to-Scalar Ratio
• Non-linear Preheating with Scalar Metric Perturbations
• Entropy growth in the early universe and confirmation of initial big bang conditions (Why the quark-gluon model is not the best analogy)