Induced Gravitational Wave interpretation of PTA data: a complete study for general equation of state
arxiv(2024)
摘要
We thoroughly study the induced gravitational wave interpretation of the
possible gravitational wave background reported by PTA collaborations,
considering the unknown equation of state w of the early universe. We perform
a Bayesian analysis of the NANOGrav data using the publicly available
PTArcade code together with SIGWfast for the numerical
integration of the induced gravitational wave spectrum. We focus on two cases:
a monochromatic and a log-normal primordial spectrum of fluctuations. For the
log-normal spectrum, we show that, while the results are not very sensitive to
w when the GW peak is close to the PTA window, radiation domination is out of
the 2σ contours when only the infra-red power-law tail contributes. For
the monochromatic spectrum, the 2σ bounds yield 0.1≲
w≲0.9 so that radiation domination is close to the central value. We
also investigate the primordial black hole (PBH) counterpart using the peak
formalism. We show that, in general terms, a larger width and stiffer equation
of state alleviates the overproduction of PBHs. No PBH overproduction requires
w≳0.42 up to 2-σ level for the monochromatic spectrum.
Furthermore, including bounds from the cosmic microwave background, we find in
general that the mass range of the PBH counterpart is bounded by 10^-5
M_⊙≲ M_ PBH≲10^-1 M_⊙. Lastly, we find that the
PTA signal can explain the microlensing events reported by OGLE for
0.42≲ w≲ 0.50. Our work showcases a complete treatment of
induced gravitational waves and primordial black holes for general w for
future data analysis.
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