The NANOGrav 15 yr Data Set: Running of the Spectral Index
Authors: Agazie Gabriella , Anumarlapudi Akash , Archibald Anne M. , Arzoumanian Zaven , Baier Jeremy G. , Baker Paul T. , Bécsy Bence , Blecha Laura , Brazier Adam , Brook Paul R. , Burke-Spolaor Sarah , Casey-Clyde J. Andrew , Charisi Maria , Chatterjee Shami , Cohen Tyler , Cordes James M. , Cornish Neil J. , Crawford Fronefield , Cromartie H. Thankful , Crowter Kathryn , DeCesar Megan E. , Demorest Paul B. , Deng Heling , Dey Lankeswar , Dolch Timothy , Esmyol David , Ferrara Elizabeth C. , Fiore William , Fonseca Emmanuel , Freedman Gabriel E. , Gardiner Emiko C. , Garver-Daniels Nate , Gentile Peter A. , Gersbach Kyle A. , Glaser Joseph , Good Deborah C. , Gültekin Kayhan , Hazboun Jeffrey S. , Jennings Ross J. , Johnson Aaron D. , Jones Megan L. , Kaplan David L. , Kelley Luke Zoltan , Kerr Matthew , Key Joey S. , Laal Nima , Lam Michael T. , Lamb William G. , Larsen Bjorn , Lazio T. Joseph W. , Lewandowska Natalia , Lino dos Santos Rafael R. , Liu Tingting , Lorimer Duncan R. , Luo Jing , Lynch Ryan S. , Ma Chung-Pei , Madison Dustin R. , McEwen Alexander , McKee James W. , McLaughlin Maura A. , McMann Natasha , Meyers Bradley W. , Meyers Patrick M. , Mingarelli Chiara M. F. , Mitridate Andrea , Ng Cherry , Nice David J. , Ocker Stella Koch , Olum Ken D. , Pennucci Timothy T. , Perera Benetge B. P. , Pol Nihan S. , Radovan Henri A. , Ransom Scott M. , Ray Paul S. , Romano Joseph D. , Runnoe Jessie C. , Saffer Alexander , Sardesai Shashwat C. , Schmiedekamp Ann , Schmiedekamp Carl , Schmitz Kai , Schröder Tobias , Shapiro-Albert Brent J. , Siemens Xavier , Simon Joseph , Siwek Magdalena S. , Sosa Fiscella Sophia V. , Stairs Ingrid H. , Stinebring Daniel R. , Stovall Kevin , Susobhanan Abhimanyu , Swiggum Joseph K. , Taylor Stephen R. , Turner Jacob E. , Unal Caner , Vallisneri Michele , van Haasteren Rutger , Vigeland Sarah J. , von Eckardstein Richard , Wahl Haley M. , Witt Caitlin A. , Wright David , Young Olivia 
Published: January 2025

Abstract
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,

γ

run

(
f
)
=
γ
+
β
ln

f
/

f

ref

. 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,

β
∈

−
0.80
,
2.96

, and an inconclusive Bayes factor,

B

RPL

versus

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 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.