Modified Gravity
Programs for testing gravity using astrophysical objects are in their infancy. Their promise is virtually unlimited sample size, but this is offset by the shear complexity of physical processes at play. For a start, the fact that such objects typically involve mild to strongly nonlinear gravitational collapse (albeit in the weak field regime) is a severe hindrance: although a range of sophisticated semianalytic and numerical methods have been developed to explore this regime, their precision and control of systematic uncertainties is not comparable with achievements on large (linear) or small scales. Furthermore, nongravitational physics can play a significant role in the formation and resulting morphology of astrophysical structures. The interaction of gas, plasma and radiation leads to a slew of baryonic effects capable of either suppressing or enhancing the gravitational collapse that one would expect from Nbody dynamics alone. If one adds to this the effect of feedback from energetic astrophysical phenomena such as supernovae or active galactic nuclei, it becomes very difficult to extract purely gravitational information from observations of collapsed objects.
In this review we will lay the groundwork for a thorough exploration of the weak field, nonlinear regime with an eye to exploiting the current and next generation of observations. We begin by setting the scene for how gravitational theories beyond GR might behave, covering large scales (including accelerated expansion) but focusing primarily on nonlinear dynamics. Gravitational screening looms large, and we take particular care in fleshing out the main concepts involved in this phenomenon. Our goal is for this review to be of use to theorists and observers in equal measure, and hence we describe the techniques (both analytic and numerical) for exploring this regime as well as the pertinent observational strategies and prospects for future measurements. With these in hand we describe a range of astrophysical tests of gravity, many of which target fifth forces.
Review Outline

The Novel Probes Project

Introduction

Modified gravity after GW170817

Screening mechanisms

Principles of screening

Thinshell screening

Chameleon screening

Symmetron screening


Kinetic screening

Vainshtein screening

Vainshtein breaking: beyond Horndeski and DHOST

Kmouflage


Observational signatures

Equivalence principle violations

Searching for screening



Surveys

Types of survey and available datasets

Planned surveys


Nonlinear structure formation: (semi)analytic approaches

Nonlinear structure in GR vs. modified gravity

(Semi)Analytic approaches in GR

(Semi)Analytic approaches in modified gravity


Baryonic effects and small scale structure

Novel estimators for the nonlinear regime


Cosmological simulations

The algorithm: relaxations with multigrid acceleration

The validity of the quasistatic approximation

Approximate speedup methods


Cosmological tests

Parametrized vs. modelbymodel approaches

Main cosmological datasets and observational signatures


Astrophysical tests

Galaxy velocities and redshift space distortions
 Cluster and halo tests
 Cluster abundance, profiles and gas fractions
 Lensing vs dynamical mass estimators
 The splashback feature in dark matter halos

Voids in galaxy surveys

Observational screening maps

Tests of thinshell screening

Stellar evolution

Distance indicators

Dynamical and structural galaxy properties


Tests of Vainshtein screening

Vainshtein screening on small scales

Strong equivalence principle violations: offset supermassive black holes


Vainshtein breaking

Existence of stars

Tests with dwarf stars



Future directions

Current status of modified gravity theories

Future directions for theory

Future directions for observations

Outlook
