Scalar-induced gravitational wave interpretation of PTA data: the role of scalar fluctuation propagation speed

Abstract

Pulsar timing arrays gathered evidence of the presence of a gravitational wave background around nHz frequencies. If the gravitational wave background was induced by large and Gaussian primordial fluctuations, they would then produce too many sub-solar mass primordial black holes. We show that if at the time of gravitational wave generation the universe was dominated by a canonical scalar field, with the same equation of state as standard radiation but a higher propagation speed of fluctuations, one can explain the gravitational wave background with a primordial black hole counterpart consistent with observations. Lastly, we discuss possible ways to test this model with future gravitational wave detectors.

Probing the equation of state of the early Universe with pulsar timing arrays

“…PBHs are formed through gravitational collapse when the density contrast δρ/ρ surpasses a threshold δ c in Hubble patches depending on the EoS parameter w at the moment of re-entry [87][88][89][144][145][146][147][148][149][150]. For the purpose of a cautious estimation, we adopt Carr's criterion in the uniform Hubble slice [145], which can be translated to the comoving slice as follows [112,139]…”

“…There is considerable room for new physics to manifest, allowing intriguing phenomena to emerge in the context of the SIGWs. Various aspects of the SIGWs provide avenues for potential new physics to be explored, such as investigating different equations of state for the Universe [132,133,136,137], exploring different propagation speeds of fluctuations [134,138,139], and investigating different initial conditions [140]. These fascinating scenarios can be tested and probed using the SIGWs as a powerful observational tool.…”

Spectrum of gravitational waves from long-lasting primordial sources

“…This corresponds to γ = 3.2 ± 0.6 in terms of the spectral index γ ≡ 5 − p commonly used by PTA collaborations.2 Namely, we do not discuss GWs produced by second order scalar fluctuations enhanced at the end of inflationary stage[15][16][17]. In that case one can obtain p ≈ 2, provided that the scalar power spectrum exhibits a strong peak-like feature[18][19][20][21][22][23][24][25].…”

Simultaneously probing the sound speed and equation of state of the early Universe with pulsar timing arrays

“…Consequently, SIGWs provide an invaluable opportunity to directly probe the expansion history of the primordial dark Universe. Multiple aspects of SIGWs offer avenues for exploring potential new physics, including the exploration of different equations of state for the Universe [50,173,174,[176][177][178], the investigation of different propagation speeds of fluctuations [88,175,179], and the examination of different initial conditions [180]. In particular, ref.…”

“…In particular, ref. [88] suggests that if the recent PTA signal is attributed to SIGWs, the Universe can be characterized as a perfect fluid with w = 1/3 and an arbitrary c s . Meanwhile, ref.…”