Constraints on primordial curvature power spectrum with pulsar timing arrays

Abstract

The stochastic signal detected by NANOGrav, PPTA, EPTA, and CPTA can be explained by the scalar-induced gravitational waves. In order to determine the scalar-induced gravitational waves model that best fits the stochastic signal, we employ both single- and double-peak parameterizations for the power spectrum of the primordial curvature perturbations, where the single-peak scenarios include the δ-function, box, lognormal, and broken power law model, and the double-peak scenario is described by the double lognormal form. Using Bayesian inference, we find that there is no significant evidence for or against the single-peak scenario over the double-peak model, with log (Bayes factors) among these models ln ℬ < 1. Therefore, we cannot distinguish the different shapes of the power spectrum of the primordial curvature perturbation with the current sensitivity of pulsar timing arrays.

Model-independent reconstruction of the primordial curvature power spectrum from PTA data

“…The red line and black dashed line represent the primordial curvature power spectrum using the lognormal form and the broken power-law form, respectively. These two parameterizations utilize the best-fitted values that account for the NANOGrav 15-year data set via SIGWs [18]. The model-independent reconstruction is consistent with the model-dependent results.…”

“…This is consistent with the previous results that the NANOGrav 15-year data set can not effectively differentiate between various parameterizations of the primordial curvature power spectrum, as discussed in refs. [8,18].…”

“…In exploring the possibility of SIGWs as an explanation for the PTA signal, the primordial curvature power spectrum is commonly characterized through special models, such as the δ-function, lognormal form, or broken power law parameterizations [8,18]. By employing these parameterizations and using the PTA data, one can derive constraints on the primordial curvature power spectrum at small scales.…”

The Pulsar Timing Array Signal from Infrared Regions of Scalar-Induced Gravitational Waves

“…7 −0.6 × 10 −15 at a reference frequency of 1 yr −1 [86]. While supermassive black hole binaries are considered as an explanation [93][94][95][96][97][98][99], alternative interpretations include cosmic inflation [94,95], first-order phase transitions [100][101][102][103][104][105][106][107], cosmic strings [108][109][110][111][112][113][114][115], domain walls [116][117][118], or scalar-induced gravitational waves [4,[119][120][121][122][123][124][125][126][127][128][129][130][131]. For more about the physical explanation of signals in the PTA band, please refer to the references [132][133][134]…”