Universal infrared scaling of gravitational wave background spectra

By R. Cai, Shi Pi, Misao Sasaki. 2019

159 citations recorded by the source corpus.

We study the general infrared behavior of the power spectrum of a stochastic gravitational wave background produced by stress tensor in the form bilinear in certain dynamical degrees of freedom. We find $\Omega_{\text{GW}}\propto k^3$ for a very wide class of the sources which satisfy a set of reasonable conditions. Namely, the $k^3$ scaling is universally valid when the source term is bounded in both frequency and time, is effective in a radiation-dominated stage, and for $k$ smaller than all the physical scales associated with the source, like the peak frequency, peak width, and time duration, etc.. We also discuss possible violations of these conditions and their physical implications.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/93601fcec32a048058ccbdbd2a8269b1715f115b

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In Astronomy and Astrophysics

1. Shi Pi
2. Misao Sasaki
3. Guillem Domènech
4. K. Kohri
5. T. Terada
6. Marek Lewicki
7. John Ellis
8. V. Vaskonen

Citations in the corpus

• Gravitational waves induced by scalar perturbations with a lognormal peak (2020, background): “However, it was found that the infrared scaling of the GW spectrum depends sensitively on the width, which is f2 for a δ-function peak, while f3 for a finite width, and a transition from f3 to f2 was observed for a finite but small width [164, 165].”
• Gravitational wave constraints on the primordial black hole dominated early universe (2020, background): “Not only they are crucial PBH counterparts [35, 48–50] but constitute powerful probes of the primordial curvature power spectrum on small scales [51, 52] and the thermal history of the universe [37, 38, 53, 54].”
• Primordial black holes and gravitational waves from parametric amplification of curvature perturbations (2019, background): “ narrow peak of P Rin Fig.4results in a sharp peak of GW, while the wide plateau of P Rresults in a plateau in GW. In all those cases, GW has a power-law behavior in the infrared region, as stated in [36], while GW cuts o sharply in the ultraviolet region. From the location of the peak and the edges”
• Induced gravitational waves as a probe of thermal history of the universe (2020, background): “[99] argued that the infrared side of the GW spectrum has a universal slope given a certain w.”
• Solar-mass primordial black holes explain NANOGrav hint of gravitational waves (2020, background): “[99, 100] for the IR “cutoff” frequency), fs is the frequency at the source frame, z is the redshift, R is the comoving merger rate, and EGW is the energy of the GWs at the source frame.”
• Updated predictions for gravitational waves produced in a strongly supercooled phase transition (2020, background): “erent redshift factors [62]. Beyond the horizon size at the time of production, the spectrum from a short-lasting source, such as a phase transition, is /f3 in standard radiation-dominated expansion [111,112], but the behaviour changes to /f1 for scales re-entering the horizon during matter dominati”