Pulsar timing array constraints on the induced gravitational waves

Abstract

If the black holes detected by LIGO/VIRGO are primordial black holes (PBHs) sourcing from a large primordial curvature perturbation at small scales, the corresponding induced gravitational waves (GWs) would peak at nanohertz that is detectable by the current and future observations of pulsar timing array (PTA). In this paper we show that with the mass function estimated from the merger rate of LIGO O1 and O2 events, the induced GWs from such a curvature perturbation with a Gaussian narrow peak at some small scale would be in a seemingly mild tension with current constraints from PTA. However, if the curvature perturbation is of local-type non-Gaussianity with a non-linear parameter f NL O(10), the tension could be relieved. Nevertheless, such an induced GWs must be detectable by the Square Kilometer Array in a decade or less.

Scalar Induced Gravitational Waves Review

“…A study using current PTA and LIGO data on SGWBs can be found in Refs. [136][137][138][139] and an analysis of future GW prospects in Refs. [33,75,[140][141][142][143][144][145][146]; -SGWB anisotropies: In the far future we may not only observe the GW spectrum but also its anisotropies.…”

Gauge independence of induced gravitational waves

“…Such an enhancement of the curvature perturbations are often considered in the context of the primordial black hole (PBH) [23][24][25] (see also Refs. [7,[26][27][28][29][30][31]). PBHs have recently been studied by many authors mainly because they can be a dark matter (DM) candidate and may explain the binary black hole merger events observed by LIGO/Virgo [32].…”

From primordial black holes abundance to primordial curvature power spectrum (and back)

“…Several authors have proposed different ways to probe such scales, including CMB spectral distortions [98], analyses of Silk damping effects [99], exploiting WIMP properties [100,101] (in the last case assuming they are the main component of dark matter), reconstructing quasar light curves [102] or through the detection of gravitational waves generated by large scalar perturbations, see e.g., Refs. [103][104][105][106][107][108][109][110][111] and references therein for constraints coming from ongoing (PTA [112][113][114]) and future (SKA [115,116], LISA [115,117]) experiments.…”