The NANOGrav 15 yr Data Set: Running of the Spectral Index - Gabriella Agazie; Akash Anumarlapudi; Anne M. Archibald; Zaven Arzoumanian; Jeremy G. Baier; Paul T. Baker; Bence Bécsy; Laura Blecha; Adam Brazier; Paul R. Brook; Sarah Burke-Spolaor; J. Andrew Casey-Clyde; et al. (The Astrophysical Journal Letters)
The NANOGrav 15 yr data provide 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 of a simple power-law fit involving two parameters: an amplitude A and a spectral index γ . In this Letter, we consider the next logical step beyond this minimal spectral model, allowing for a running (i.e., logarithmic frequency dependence) of the spectral index, ${\gamma }_{{\rm{run}}}(f)=\gamma +\beta \mathrm{ln}\left(f/{f}_{{\rm{ref}}}\right)$ . We fit this running-power-law (RPL) model to the NANOGrav 15 yr 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 β consistent with no running, $\beta \in \left[-0.80,2.96\right]$ , and an inconclusive Bayes factor, ${ \mathcal B }\left({\rm{RPL}}\,{\rm{versus}}\,{\rm{CPL}}\right)=0.69\pm 0.01$ . 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 β . 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.