Etherington duality breaking: gravitational lensing in non-metric spacetimes versus intrinsic alignments

TL;DR

This paper investigates how violations of the Etherington distance duality in non-metric spacetimes, such as area-metric theories, could cause observable surface brightness fluctuations, comparing these effects to intrinsic galaxy alignments.

Contribution

It quantifies the potential observability of surface brightness fluctuations caused by non-metric gravity effects versus intrinsic alignments in upcoming surveys.

Findings

Intrinsic brightness fluctuations could be detectable with high confidence in Euclid-like surveys.

Surface brightness fluctuations from area-metric spacetimes depend on specific model parameters.

Natural parameter values for Etherington-breaking do not produce detectable signals in lensing surveys.

Abstract

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