Sizing the Universe with DESI Galaxy Sizes: Plain Fundamentals of Fundamental-Plane Lensing

Weak gravitational lensing provides a powerful way to map cosmic structure, but most current measurements rely on galaxy shape distortions from deep imaging surveys and are affected by systematics such as intrinsic alignments, photometric-redshift uncertainties and shape-measurement biases. Here we present a spectroscopic galaxy-galaxy lensing magnification measurement using Fundamental-Plane (FP) size residuals, δ r Δ 10R e, from 3.26 million DESI luminous red galaxy (LRG) sources behind DESI Bright Galaxy Survey lenses. The FP-like relation predicts the intrinsic sizes of LRGs from lensing-invariant quantities, including velocity dispersion σ 0 and surface brightness I e, with a scatter of about 0.06-0.07 dex. Lensing magnifies LRG sizes, giving the direct convergence response δ r(κ)=κ/ 10, but we show that the full lensing response is modified by magnification bias, because fitting R e with I e inevitably induces a magnitude dependence in δ r(m). After calibrating this response, we recover surface-density profiles with uncertainties comparable to those from individual Stage-III shear surveys using 5-20 million higher-redshift sources. The corresponding excess surface-density profiles agree with shear-based measurements. We further show that the estimator is robust to size-measurement uncertainties, with a convergence multiplicative bias only-0.2 times the size bias. FP lensing therefore provides a clean, spectroscopic and complementary probe of cosmic structure.