Response approach to the squeezed-limit bispectrum: application to the correlation of quasar and Lyman-$\alpha$ forest power spectrum

摘要: The squeezed-limit bispectrum, which is generated by nonlinear gravitational evolution as well inflationary physics, measures the correlation of three wavenumbers, in configuration where one wavenumber much smaller than other two. Since bispectrum encodes impact a large-scale fluctuation on small-scale power spectrum, it can be understood how spectrum "responds" to fluctuation. Viewed this way, calculated using response approach even cases do not submit perturbative treatment. To illustrate point, we apply cross-correlation between quasar density field and Lyman-$\alpha$ forest flux spectrum. In particular, separate universe simulations implement changes density, velocity gradient, primordial amplitude, measure responds local, long-wavelength overdensity, equivalently their bispectrum. We perform Fisher forecast for ability future experiments constrain local non-Gaussianity quasars forest. Combining with spectra biases, find that DESI expected $1-\sigma$ constraint ${\rm err}[f_{\rm NL}]\sim60$. Ability $f_{\rm NL}$ through channel limited primarily aliasing instrumental noise combination provides novel technique explore constraints from different observables.