Etherington duality breaking: gravitational lensing in non-metric space–times versus intrinsic alignments

ABSTRACT The Etherington distance duality relation is well-established for metric theories of gravity, and confirms the between luminosity angular diameter through conservation surface brightness. A violation due to lensing in a non-metric space–time would lead fluctuations brightness galaxies. Likewise, can arise classical astrophysics as consequence intrinsic tidal interaction galaxies with their environment. Therefore, we study these two cases detail: First, size resulting changes brightness, secondly, an area-metric example space–time, where itself acquires modifications. aim this work quantify whether fluctuation effect gravity be resolvable compared similar caused by alignment. We thus compare auto- cross-correlations spectra show that potentially measured cumulative signal-to-noise ratio Σ(ℓ) ≥ 3 Euclid-like survey. measurement space–times, however, depends on specific parameter choices, which also determine shape amplitude spectra. While surveys do have sensitivity lensing-induced does not seem possible natural values Etherington-breaking parameters.