Constraints on Single-Field Inflation from the BOSS Galaxy Survey

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, <math display="inline"><mrow><msubsup><mrow><mi>f</mi></mrow><mrow><mi>NL</mi></mrow><mrow><mtext>equil</mtext></mrow></msubsup><mo>=</mo><mn>940</mn><mo>±</mo><mn>600</mn></mrow></math> and <math display="inline"><mrow><msubsup><mrow><mi>f</mi></mrow><mrow><mi>NL</mi></mrow><mrow><mtext>ortho</mtext></mrow></msubsup><mo>=</mo><mo>-</mo><mn>170</mn><mo>±</mo><mn>170</mn></mrow></math> (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 <math display="inline"><mrow><msub><mrow><mi>c</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>≥</mo><mn>0.013</mn></mrow></math> at 95% CL. Fixing the quadratic galaxy bias and cosmological parameters, the constraints can be tightened to <math display="inline"><mrow><msubsup><mrow><mi>f</mi></mrow><mrow><mi>NL</mi></mrow><mrow><mtext>equil</mtext></mrow></msubsup><mo>=</mo><mn>260</mn><mo>±</mo><mn>300</mn></mrow></math> and <math display="inline"><mrow><msubsup><mrow><mi>f</mi></mrow><mrow><mi>NL</mi></mrow><mrow><mtext>ortho</mtext></mrow></msubsup><mo>=</mo><mo>-</mo><mn>23</mn><mo>±</mo><mn>120</mn></mrow></math> (68% CL).