Nonlocal primordial non-Gaussianity (NLPNG) is a smoking gun of interactions in single-field inflationary models and can be written as a combination of the equilateral and orthogonal templates. We present the first constraints on these from the redshift-space galaxy power spectra and bispectra of the BOSS data. These are the first such measurements independent of the cosmic microwave background fluctuations. We perform a consistent analysis that includes all necessary nonlinear corrections generated by NLPNG and vary all relevant cosmological and nuisance parameters in a global fit to the data. Our conservative analysis yields joint limits on the amplitudes of the equilateral and orthogonal shapes, $f_{\mathrm{NL}}^{\text{equil}}=940\pm 600$ and $f_{\mathrm{NL}}^{\text{ortho}}=-170\pm 170$ (both at 68% CL). These can be used to derive constraints on coefficients of the effective single-field inflationary Lagrangian; in particular, we find that the sound speed of inflaton fluctuations has the bound $c_s\ge 0.013$ at 95% CL. Fixing the quadratic galaxy bias and cosmological parameters, the constraints can be tightened to $f_{\mathrm{NL}}^{\text{equil}}=260\pm 300$ and $f_{\mathrm{NL}}^{\text{ortho}}=-23\pm 120$ (68% CL).

• Received 27 January 2022
• Revised 7 April 2022
• Accepted 15 June 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.021301

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society