Constraining Single-Field Inflation with MegaMapper

We forecast the constraints on single-field inflation from the bispectrum of future high-redshift surveys such as MegaMapper. Considering non-local primordial non-Gaussianity (NLPNG), we find that current methods will yield constraints of order <math altimg="si1.svg"><mi>σ</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">NL</mi></mrow><mrow><mi mathvariant="normal">eq</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>≈</mo><mn>23</mn></math>, <math altimg="si2.svg"><mi>σ</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">NL</mi></mrow><mrow><mi mathvariant="normal">orth</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>≈</mo><mn>12</mn></math> in a joint power-spectrum and bispectrum analysis, varying both nuisance parameters and cosmology, including a conservative range of scales. Fixing cosmological parameters and quadratic bias parameter relations, the limits tighten significantly to <math altimg="si3.svg"><mi>σ</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">NL</mi></mrow><mrow><mi mathvariant="normal">eq</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>≈</mo><mn>17</mn></math>, <math altimg="si4.svg"><mi>σ</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">NL</mi></mrow><mrow><mi mathvariant="normal">orth</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>≈</mo><mn>8</mn></math>. These compare favorably with the forecasted bounds from CMB-S4: <math altimg="si5.svg"><mi>σ</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">NL</mi></mrow><mrow><mi mathvariant="normal">eq</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>≈</mo><mn>21</mn></math>, <math altimg="si6.svg"><mi>σ</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">NL</mi></mrow><mrow><mi mathvariant="normal">orth</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>≈</mo><mn>9</mn></math>, with a combined constraint of <math altimg="si7.svg"><mi>σ</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">NL</mi></mrow><mrow><mi mathvariant="normal">eq</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>≈</mo><mn>14</mn></math>, <math altimg="si8.svg"><mi>σ</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">NL</mi></mrow><mrow><mi mathvariant="normal">orth</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>≈</mo><mn>7</mn></math>; this weakens only slightly if one instead combines with data from the Simons Observatory. We additionally perform a range of Fisher analyses for the error, forecasting the dependence on nuisance parameter marginalization, scale cuts, and survey strategy. Lack of knowledge of bias and counterterm parameters is found to significantly limit the information content; this could be ameliorated by tight simulation-based priors on the nuisance parameters. The error-bars decrease significantly as the number of observed galaxies and survey depth is increased: as expected, deep dense surveys are the most constraining, though it will be difficult to reach <math altimg="si9.svg"><mi>σ</mi><mo stretchy="false">(</mo><msub><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">NL</mi></mrow></msub><mo stretchy="false">)</mo><mo>≈</mo><mn>1</mn></math> with current methods. The NLPNG constraints will tighten further with improved theoretical models (incorporating higher-loop corrections and improved understanding of nuisance parameters), as well as the inclusion of additional higher-order statistics.