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Modified Gravity 

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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 non-linear gravitational collapse (albeit in the weak field regime) is a severe hindrance: although a range of sophisticated semi-analytic 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, non-gravitational 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 N-body 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.

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In this review we will lay the groundwork for a thorough exploration of the weak field, non-linear 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 non-linear 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.

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Link to review

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Review Outline

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  1. ​The Novel Probes Project

  2. Introduction  

  3. Modified gravity after GW170817

  4. Screening mechanisms  

    1. Principles of screening

    2. Thin-shell screening 

      1. Chameleon screening​

      2. Symmetron screening

    3. Kinetic screening 

      1. Vainshtein screening​

      2. Vainshtein breaking: beyond Horndeski and DHOST

      3. K-mouflage

    4. Observational signatures

      1. Equivalence principle violations​

      2. Searching for screening

  5. Surveys

    1. Types of survey and available datasets 

    2. Planned surveys

  6. Nonlinear structure formation: (semi-)analytic approaches

    1. Nonlinear structure in GR vs. modified gravity

      1. (Semi-)Analytic approaches in GR​

      2. (Semi-)Analytic approaches in modified gravity

    2. Baryonic effects and small scale structure

    3. Novel estimators for the nonlinear regime

  7. Cosmological simulations

    1. The algorithm: relaxations with multigrid acceleration

    2. The validity of the quasi-static approximation

    3. Approximate speed-up methods

  8. Cosmological tests

    1. Parametrized vs. model-by-model approaches

    2. Main cosmological datasets and observational signatures

  9. Astrophysical tests

    1. Galaxy velocities and redshift space distortions

    2. Cluster and halo tests
      1. Cluster abundance, profiles and gas fractions
      2. Lensing vs dynamical mass estimators
      3. ​The splashback feature in dark matter halos​

    3. Voids in galaxy surveys

    4. Observational screening maps

    5. Tests of thin-shell screening

      1. Stellar evolution​

      2. Distance indicators

      3. Dynamical and structural galaxy properties

    6. Tests of Vain​shtein screening

      1. Vainshtein screening on small scales​

      2. Strong equivalence principle violations: offset supermassive black holes

    7. Vainshtein breaking

      1. Existence of stars​

      2. Tests with dwarf stars​

  10. Future directions

    1. Current status of modified gravity theories

    2. Future directions for theory

    3. Future directions for observations

    4. Outlook

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