Gravitational Wave Spectrum Induced by Primordial Scalar Perturbations

By D. Baumann, K. Ichiki, Paul J. Steinhardt, Keitaro Takahashi. 2007

605 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Oceanography

View Paper: https://www.semanticscholar.org/paper/97595a7469b98572852c99328c3a2812ac76a96f

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In Astronomy and Astrophysics

1. D. Baumann
2. C. Byrnes
3. L. Senatore
4. M. Zaldarriaga
5. K. Kohri
6. Marco Peloso
7. Misao Sasaki
8. Shi Pi

In Oceanography

1. C. Byrnes
2. L. Senatore
3. D. Baumann
4. Misao Sasaki
5. Guillem Domènech
6. M. Zaldarriaga
7. Shi Pi
8. K. Kohri

Citations in the corpus

• Gravitational waves induced by scalar perturbations during a gradual transition from an early matter era to the radiation era (2019, methodology): “In addition, there can also be cosmological origins such as vacuum quantum fluctuations during inflation, cosmic strings and scalar perturbations at the second order [2–6] (see also Ref.”
• Oscillations in the stochastic gravitational wave background from sharp features and particle production during inflation (2020, background): “These scalar-induced GWs will contain information about the scalar fluctuations and in particular the scalar power spectrum Pζ , as the energy density power spectrum of scalarinduced GWs is related to the scalar power spectrum as ΩGW ∼ ∫∫ P2 ζ [4, 5], see also [6, 7] for related earlier work.”
• New physics from the polarized light of the cosmic microwave background (2022, background): “There is a guaranteed lower bound for the amplitude of a stochastic background of GW sourced by the second-order scalar mode in the early Universe 205,206 .”
• Observable Spectra of Induced Gravitational Waves from Inflation (2012, methodology): “[25, 26]) and in this paper, the spectrum of induced gravitational waves is not as simple, and hence are distinguishable from each other.”
• Primordial black holes and second order gravitational waves from ultra-slow-roll inflation (2017, methodology): “14) by using the Green function method, we get the current relative energy density of gravitational waves [41]”
• Cosmological non-linearities as an effective fluid (2010, background): “In that case the biggest contribution is expected from modes with k ∼ keq [13].”
• Primordial black holes and gravitational waves from parametric amplification of curvature perturbations (2019, methodology): “After reentering the horizon in the radiation-dominated epoch, scalar perturbations will inevitably lead to GWs at second order since they are coupled at nonlinear order [23, 24].”
• Solar-mass primordial black holes explain NANOGrav hint of gravitational waves (2020, background): “This is due to the scalar-tensor mode couplings appearing at the second-order of the cosmological perturbation theory [11–16].”
• Induced gravitational waves as a probe of thermal history of the universe (2020, background): “In this respect, an interesting candidate is the so-called induced GWs generated from primordial density fluctuations [64, 65], which is an essential counterpart to the PBH scenario [4, 96] and a probe of the primordial spectrum on scales smaller than those probed by the CMB [73, 95, 97].”
• Non-Gaussianity and the induced gravitational wave background (2021, background): “28) reproduces the standard result [32, 33, 53].”
• Semianalytic calculation of gravitational wave spectrum nonlinearly induced from primordial curvature perturbations (2018, background): “[26, 27], and the analytic formula for I(v, u, x) was obtained there.”
• Challenges and opportunities of gravitational-wave searches at MHz to GHz frequencies (2020, background): “In particular, density perturbations can produce ‘induced’ (or ‘secondary’) GWs through a ζ + ζ → h process [89–91] (see also [92–94]).”