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The fundamental plane (FP) is a widely used tool to investigate theproperties of early-type galaxies, and the tight relation between itsparameters has spawned several cosmological applications, including its use asa distance indicator for peculiar velocity surveys and as a means to suppressintrinsic noise in cosmic size magnification measurements. Systematic trendswith the large-scale structure across the FP could cause serious biases forthese cosmological probes, but may also yield new insights into the early-typepopulation. Here we report the first detection of spatial correlations amongoffsets in galaxy size from an FP that explicitly accounts for redshift trends,using a sample of about $95,000$ elliptical galaxies from the Sloan Digital SkySurvey. We show that these offsets correlate with the density field out to atleast $10h^{-1}$Mpc at $4\sigma$ significance in a way that cannot be explainedby systematic errors in galaxy size estimates. We propose a physicalexplanation for the correlations by dividing the sample into central,satellite, and field galaxies, identifying trends for each galaxy typeseparately. Central (satellite) galaxies lie on average above (below) the FP,which we argue could be due to a higher (lower) than average mass-to-lightratio. We fit a simple model to the correlations of FP residuals and use it topredict the impact on peculiar velocity power spectra, finding a contaminationlarger than $10\,\%$ for $k>0.04\,h/$Mpc. Moreover, cosmic magnificationmeasurements based on an FP could be severely contaminated over a wide range ofscales by the intrinsic FP correlations.

Detection of spatial correlations of fundamental plane residuals, and cosmological implications