Topology of large scale structure as test of modified gravity

TL;DR

This paper proposes using the topology measure called genus of iso-density contours to test modified gravity theories by observing their distinct scale-dependent growth of density fluctuations in large scale structure.

Contribution

It introduces the genus statistic as a novel observational tool to distinguish between general relativity and modified gravity models through their different growth patterns.

Findings

Genus remains nearly conserved in general relativity during structure growth.

Modified gravity models show a change in the genus-smoothing scale relation over time.

Forecasts indicate future surveys can constrain modified gravity parameters.

Abstract

The genus of the iso-density contours is a robust measure of the topology of large scale structure, and it is relatively insensitive to nonlinear gravitational evolution, galaxy bias and redshift-space distortion. We show that the growth of density fluctuations is scale-dependent even in the linear regime in some modified gravity theories, which opens a new possibility of testing the theories observationally. We propose to use the genus of the iso-density contours, an intrinsic measure of the topology of large scale structure, as a statistic to be used in such tests. In Einstein's general theory of relativity, density fluctuations are growing at the same rate on all scales in the linear regime, and the genus per comoving volume is almost conserved as structures are growing homologously, so we expect that the genus-smoothing scale relation is basically time-independent. However, in some modified gravity models where structures grow with different rates on different scales, the genus-smoothing scale relation should change over time. This can be used to test the gravity models with large scale structure observations. We studied the case of the f(R) theory, DGP braneworld theory as well as the parameterized post-Friedmann (PPF) models. We also forecast how the modified gravity models can be constrained with optical/IR or redshifted 21cm radio surveys in the near future.