Search for nontensorial gravitational-wave backgrounds in the NANOGrav 15-year dataset

The recent detection of a stochastic signal in the NANOGrav 15-year dataset 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 paper, we search for an isotropic nontensorial GWB, allowed by general metric theories of gravity, in the NANOGrav 15-year dataset. 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 Aₒₓ=7. 8-₃. ₅^+5. 110^-15 at the frequency of 1/year. Furthermore, we find that the vector longitudinal (VL) and scalar longitudinal (SL) correlations are weakly and strongly disfavored by data, respectively, yielding upper limits on the amplitudes: Aₕ₋^95%1. 710^-15 and Aₒ₋^95%7. 410^-17. Lastly, we fit the NANOGrav data with the general transverse (GT) correlations parametrized by a free parameter. Our analysis yields =1. 74-₁. ₄₁^+1. 18, thus excluding both the TT (=3) and ST (=0) models at the 90% confidence level.