[Paper Review] The recent gravitational wave observation by pulsar timing arrays and primordial black holes: the importance of non-gaussianities

Gabriele Franciolini, Antonio J. Iovino+2 more|PubMed|Jun 29, 2023

Cosmology and Gravitation TheoriesPhysics and Astronomy243 references12 citations

TL;DR

The paper analyzes if the NANOGrav/PTA GW signal can arise from scalar-induced GWs tied to primordial perturbations and PBHs, focusing on non-Gaussianities and their impact on PBH overproduction.

ABSTRACT

We study whether the signal seen by pulsar timing arrays (PTAs) may originate from gravitational waves (GWs) induced by large primordial perturbations. Such perturbations may be accompanied by a sizable primordial black hole (PBH) abundance. We improve existing analyses and show that PBH overproduction disfavors Gaussian scenarios for scalar-induced GWs at 2σ and single-field inflationary scenarios, accounting for non-Gaussianity, at 3σ as the explanation of the most constraining NANOGrav 15-year data. This tension can be relaxed in models where non-Gaussianities suppress the PBH abundance. On the flip side, the PTA data does not constrain the abundance of PBHs.

Motivation & Objective

• Assess whether large curvature perturbations can generate the PTA SGWB and accompany PBH production.
• Quantify how non-Gaussianities affect PBH overproduction and the viability of inflationary scenarios.
• Determine if PBH abundance constraints conflict with fitting the NANOGrav15 data.

Proposed method

• Model scalar-induced GW spectra with broken power-law and log-normal peaks around k_*; relate to curvature power spectrum P_{0}_{} (Eq. 1-2).
• Compute present-day SIGW h^2 Omega_GW from the transfer function and curvature spectrum (Eq. 3-7).
• Perform a log-likelihood analysis against NANOGrav15 and EPTA data using 14 and 9 frequency bins respectively.
• Incorporate non-Gaussianity through nonlinear relations between curvature and density perturbations and specific F() mappings for quasi-inflection-point and curvaton models (Eq. 9-13).
• Compute PBH abundance using threshold statistics on the compaction function with NG corrections (Eq. 14-18).
• Explore how NGs (including f_NL and model-specific NGs) affect PBH formation and SIGW amplitude.

Figure 1: Posterior for the parameters of a BPL model ( 1 ) for SIGWs, assuming no other source of GWs is present in both EPTA and NANOGrav15 data. The shaded regions in the off-diagonal panels show 2-D posteriors at the $1\sigma$ , $2\sigma$ , and $3\sigma$ confidence levels and the dashed lines in

Experimental results

Research questions

• RQ1 Can SIGWs produced by enhanced small-scale curvature perturbations account for the PTA GW signal without overproducing PBHs?
• RQ2 How do primordial non-Gaussianities modify PBH abundance and the allowed parameter space for inflationary scenarios generating large curvature peaks?
• RQ3 Do PBH abundance constraints independently limit or exclude the SIGW explanations of NANOGrav15?
• RQ4 Under what NG conditions can the PTA tension be alleviated while remaining consistent with PBH and CMB constraints?

Key findings

• Gaussian curvature perturbations or positive NGs tend to overproduce PBHs, creating tension with NANOGrav15 data at up to 3 sigma.
• Models with large negative f_NL or curvaton scenarios with high r_dec can suppress PBH abundance and relieve the tension.
• Best-fit PTA region corresponds to peak scales k_* > 10^7 Mpc^-1, implying sub-solar PBH masses; QCD effects have negligible impact on PBH abundance in this region.
• NGs can significantly alter PBH production non-perturbatively, affecting the allowed amplitude A and peak location to fit PTA data.
• PTA data itself does not constrain the overall PBH abundance, though PBH overproduction constraints disfavour certain inflationary peak scenarios.

Figure 2: Same as Fig. 1 , but for the LN model ( 2 ).