Search for Non-Tensorial Gravitational-Wave Backgrounds in the NANOGrav 15-Year Data Set

The recent detection of a stochastic signal in the NANOGrav 15-year data set has aroused great interest in uncovering its origin. However, the evidence for the Hellings-Downs correlations, a key signature of the gravitational-wave background (GWB) predicted by general relativity, remains inconclusive. In this letter, we search for an isotropic non-tensorial GWB, allowed by general metric theories of gravity, in the NANOGrav 15-year data set. Our analysis reveals a Bayes factor of approximately 2.5, comparing the quadrupolar (tensor transverse, TT) correlations to the scalar transverse (ST) correlations, suggesting that the ST correlations provide a comparable explanation for the observed stochastic signal in the NANOGrav data. We obtain the median and the $90\%$ equal-tail amplitudes as $\mathcal{A}_\mathrm{ST} = 7.8^{+5.1}_{-3.5} \times 10^{-15}$ at the frequency of 1/year. Furthermore, we find that the vector longitudinal (VL) and scalar longitudinal (SL) correlations are weakly and strongly disfavoured by data, respectively, yielding upper limits on the amplitudes: $\mathcal{A}_\mathrm{VL}^{95\%} \lesssim 1.7 \times 10^{-15}$ and $\mathcal{A}_\mathrm{SL}^{95\%} \lesssim 7.4 \times 10^{-17}$. Lastly, we fit the NANOGrav data with the general transverse (GT) correlations parameterized by a free parameter $\alpha$. Our analysis yields $\alpha=1.74^{+1.18}_{-1.41}$, thus excluding both the TT ($\alpha=3$) and ST ($\alpha=0$) models at the $90\%$ confidence level.