The NANOGrav 15 yr Data Set: Running of the Spectral Index

TL;DR

This paper analyzes the NANOGrav 15-year data for gravitational waves, extending the spectral model to include a running of the spectral index, and finds current data insufficient to confirm such running but leaves open future detection possibilities.

Contribution

It introduces and tests a running-power-law model for the gravitational wave spectrum, extending previous minimal models and performing Bayesian comparison with the constant spectral index model.

Findings

Bayesian analysis shows no significant evidence for spectral index running.

The credible interval for the running parameter includes zero, indicating no current detection.

Future data may reveal nonzero running of the spectral index.

Abstract

The NANOGrav 15-year data provides compelling evidence for a stochastic gravitational-wave (GW) background at nanohertz frequencies. The simplest model-independent approach to characterizing the frequency spectrum of this signal consists in a simple power-law fit involving two parameters: an amplitude A and a spectral index \gamma. In this paper, we consider the next logical step beyond this minimal spectral model, allowing for a running (i.e., logarithmic frequency dependence) of the spectral index, \gamma_run(f) = \gamma + \beta \ln(f/f_ref). We fit this running-power-law (RPL) model to the NANOGrav 15-year data and perform a Bayesian model comparison with the minimal constant-power-law (CPL) model, which results in a 95% credible interval for the parameter \beta consistent with no running, \beta \in [-0.80,2.96], and an inconclusive Bayes factor, B(RPL vs. CPL) = 0.69 +- 0.01. We thus conclude that, at present, the minimal CPL model still suffices to adequately describe the NANOGrav signal; however, future data sets may well lead to a measurement of nonzero \beta. Finally, we interpret the RPL model as a description of primordial GWs generated during cosmic inflation, which allows us to combine our results with upper limits from big-bang nucleosynthesis, the cosmic microwave background, and LIGO-Virgo-KAGRA.