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

Abstract

The recently released data by pulsar timing array (PTA) collaborations have amassed substantial evidence corroborating the existence of a stochastic signal consistent with a gravitational-wave background at frequencies around the nanohertz regime. We investigate the situation in which the PTA signal originates from scalar-induced gravitational waves (SIGWs), which serves as a valuable tool to probe the equation of state parameterwduring the Universe's early stages. The joint consideration of the PTA data from the NANOGrav 15-year data set, PPTA DR3, and EPTA DR2 yields thatw = 0.60+0.32-0.39(median + 90% credible interval), indicating a period of condensate domination at the production of SIGWs is allowed by the data. Moreover, the data also supports radiation domination (w = 1/3) within the 90% credible interval. We also impose an upper bound on the reheating temperature thatTrh ≲ 0.2 GeV and the constraint onwreveals valuable information on the inflationary potential and the dynamics at the end of inflation.

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

“…Even though the NANOGrav data has relatively large errors, the best frequency bins lie in the low frequency band, that is f ∼ 10 −9 -10 −8 Hz, and data seem to follow a blue tilted power-law, which is better fitted by the low frequency tail of SIGWs [22][23][24][25][26][27][28][29][30][31][32][33][34][35]. As argued in refs.…”

“…In the NANOGrav analysis [22], and many subsequent papers [23][24][25][26][27][28][29][30][31][32][33][34][35], it is assumed that SIGWs are generated by large primordial adiabatic fluctuations when the universe is dominated by an adiabatic perfect fluid of relativistic particles (see e.g. refs.…”

Constraints on primordial curvature power spectrum with pulsar timing arrays

“…When considering the PBHs generated accompanied by SIGWs, there may be a challenge of potentially producing an excessive number of PBHs. One potential solution to address this concern is to take into account non-Gaussianities [10,11]. This is a critical matter in the context of SIGWs attempting to explain the NANOGrav 15-year data set, and we leave it to future research.…”

Constraints on the primordial curvature power spectrum by pulsar timing array data: a polynomial parameterization approach

“…We formed the log-likelihood function by evaluating the energy density of SIGWs at the 14 specific frequency intervals. Afterward, we computed the sum of the logarithms of probability density functions obtained from 14 independent kernel density estimates [36,40,43,44,161,162]. Consequently, we can represent the likelihood function as…”