From quantum fluctuations to galaxy power spectrum multipoles

Abstract

These notes trace large-scale structure from primordial curvature perturbations generated by inflationary quantum fluctuations to galaxy power-spectrum multipoles. Three core lectures develop the linear matter power spectrum, spherical and anisotropic collapse, galaxy bias, redshift-space distortions, the Kaiser model, and multipole estimators with Gaussian covariance. The extension develops nonlinear bias and the one-loop effective field theory model used in full-shape analyses. Derivations are explicit; appendices collect longer calculations and solutions. The core lectures assume undergraduate-level cosmology; the extension assumes familiarity with perturbation theory.

arXiv comment51 pages (39 pages plus appendices and references); 14 figures, 1 table, a few exercises. Extended version of the lectures delivered at the "10th Vietnam School of Astrophysics" (VSOA10), July 27 - Aug 1 2026; v1: prepared for submission to SciPost Physics Lecture Notes; v2: Submission to SciPost