Constraining the graviton mass with the NANOGrav 15 year data set
Yu-Mei Wu, Zu-Cheng Chen, Yan-Chen Bi, Qing‐Guo Huang
Abstract
Abstract The recently detected stochastic signal by several pulsar timing array collaborations, offers an opportunity to scrutinize the fundamental properties of gravity, including the potential mass of the graviton. In this study, we analyze the North American Nanohertz Observatory for Gravitational Waves 15 year data set to search for a stochastic gravitational wave background with modified Hellings–Downs correlations predicted by massive gravity. While the Bayesian analysis comparing the massive gravity to massless gravity within the effective searchable mass range of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>m</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">g</mml:mi> </mml:mrow> </mml:msub> <mml:mo>∈</mml:mo> <mml:mo stretchy="false">[</mml:mo> <mml:mn>3</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>25</mml:mn> </mml:mrow> </mml:msup> <mml:mo>,</mml:mo> <mml:mn>8</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>24</mml:mn> </mml:mrow> </mml:msup> <mml:mo stretchy="false">]</mml:mo> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">e</mml:mi> <mml:mi mathvariant="normal">V</mml:mi> <mml:mi mathvariant="normal">c</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:math> does not yield an explicit upper bound as all the Bayes factors are smaller than 3, the combined consideration of the minimum frequency inherent in a massive gravity and the observed spectrum leads to an upper limit of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>m</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">g</mml:mi> </mml:mrow> </mml:msub> <mml:mo><</mml:mo> <mml:mn>8.2</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>24</mml:mn> </mml:mrow> </mml:msup> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">e</mml:mi> <mml:mi mathvariant="normal">V</mml:mi> <mml:mi mathvariant="normal">c</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:math> .