The observed distribution of galaxies on the sky provides a plethora of cosmological information, both on the evolution of the Universe and on large-scale structure. To interpret these observations however, we need to relate the observed galaxy sky positions and redshifts to the underlying space-time and matter distribution, a relation which is nontrivial even on very large scales, because of general relativity: the Universe is not exactly homogeneous and isotropic, and this deviation from an exact FLRW space-time distorts its own image. Light from galaxies is distorted (lensed, redshifted) by the large-scale structure – by the very distribution that we seek to observe.
The papers Ginat et al. (2021) and Villey et al. (2025) seek to study these effects, with the help of the “cosmic ruler” formulation of large-scale structure observables.
The Mathematica files below are published together with Villey et al., and perform three non-trivial test on our results.
- Constant potential .
- Pure (second-order!) gradient mode .
- Separate Universe long mode (a curved FLRW background space-time, viewed as a perturbation to a flat one) .