The NANOGrav 15 yr Data Set: Running of the Spectral Index
Creators: name: Agazie, Gabriella
name: Anumarlapudi, Akash
name: Archibald, Anne M.
name: Arzoumanian, Zaven
name: Baier, Jeremy George
name: Baker, Paul T.
name: Bécsy, Bence
name: Blecha, Laura
name: Brazier, Adam
name: Brook, Paul R.
name: Burke-Spolaor, Sarah
name: Casey-Clyde, J. Andrew
name: Charisi, Maria
name: Chatterjee, Shami
name: Cohen, Tyler
name: Cordes, James M.
name: Cornish, Neil J.
name: Crawford, Fronefield
name: Cromartie, H. Thankful
name: Crowter, Kathryn
name: DeCesar, Megan E.
name: Demorest, Paul B.
name: Deng, Heling
name: Dey, Lankeswar
name: Dolch, Timothy
name: Esmyol, David
name: Ferrara, Elizabeth C.
name: Fiore, William
name: Fonseca, Emmanuel
name: Freedman, Gabriel E.
name: Gardiner, Emiko C.
name: Garver-Daniels, Nate
name: Gentile, Peter A.
name: Gersbach, Kyle A.
name: Glaser, Joseph
name: Good, Deborah C.
name: Gültekin, Kayhan
name: Hazboun, Jeffrey S.
name: Jennings, Ross J.
name: Johnson, Aaron D.
name: Jones, Megan L.
name: Kaplan, David L.
name: Kelley, Luke Zoltan
name: Kerr, Matthew
name: Key, Joey S.
name: Laal, Nima
name: Lam, Michael T.
name: Lamb, William G.
name: Larsen, Bjorn
name: Lazio, T. Joseph W.
name: Lewandowska, Natalia
name: Santos, Rafael R. Lino dos
name: Liu, Tingting
name: Lorimer, Duncan R.
name: Luo, Jing
name: Lynch, Ryan S.
name: Ma, Chung-Pei
name: Madison, Dustin R.
name: McEwen, Alexander
name: McKee, James W.
name: McLaughlin, Maura A.
name: McMann, Natasha
name: Meyers, Bradley W.
name: Meyers, Patrick M.
name: Mingarelli, Chiara M. F.
name: Mitridate, Andrea
name: Ng, Cherry
name: Nice, David J.
name: Ocker, Stella Koch
name: Olum, Ken D.
name: Pennucci, Timothy T.
name: Perera, Benetge B. P.
name: Pol, Nihan S.
name: Radovan, Henri A.
name: Ransom, Scott M.
name: Ray, Paul S.
name: Romano, Joseph D.
name: Runnoe, Jessie C.
name: Saffer, Alexander
name: Sardesai, Shashwat C.
name: Schmiedekamp, Ann
name: Schmiedekamp, Carl
name: Schmitz, Kai
name: Schröder, Tobias
name: Shapiro-Albert, Brent J.
name: Siemens, Xavier
name: Simon, Joseph
name: Siwek, Magdalena S.
name: Fiscella, Sophia V. Sosa
name: Stairs, Ingrid H.
name: Stinebring, Daniel R.
name: Stovall, Kevin
name: Susobhanan, Abhimanyu
name: Swiggum, Joseph K.
name: Taylor, Stephen R.
name: Turner, Jacob E.
name: Unal, Caner
name: Vallisneri, Michele
name: van Haasteren, Rutger
name: Vigeland, Sarah J.
name: von Eckardstein, Richard
name: Wahl, Haley M.
name: Witt, Caitlin A.
name: Wright, David
name: Young, Olivia
Publisher: name: arXiv
Year: 2024
Subjects: subject: High Energy Astrophysical Phenomena (astro-ph.HE)
subject: Cosmology and Nongalactic Astrophysics (astro-ph.CO)
subject: General Relativity and Quantum Cosmology (gr-qc)
subject: High Energy Physics - Phenomenology (hep-ph)
subject: FOS: Physical sciences
subject: FOS: Physical sciences

description: 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 γ. 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, γ_run(f) = γ+ β\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 βconsistent with no running, β\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 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.
description: 18 pages, 4 figures, 2 tables. v2: matches version published in ApJ Letters