f(R) gravity on non-linear scales: The post-Friedmann expansion and the vector potential

Abstract

Many modified gravity theories are under consideration in cosmology as the source of the accelerated expansion of the universe and linear perturbation theory, valid on the largest scales, has been examined in many of these models. However, smaller non-linear scales offer a richer phenomenology with which to constrain modified gravity theories. Here, we consider the Hu-Sawicki form of $f(R)$ gravity and apply the post-Friedmann approach to derive the leading order equations for non-linear scales, i.e. the equations valid in the Newtonian-like regime. We reproduce the standard equations for the scalar field, gravitational slip and the modified Poisson equation in a coherent framework. In addition, we derive the equation for the leading order correction to the Newtonian regime, the vector potential. We measure this vector potential from $f(R)$ N-body simulations at redshift zero and one, for two values of the $f_{R_0}$ parameter. We find that the vector potential at redshift zero in $f(R)$ gravity can be close to 50\% larger than in GR on small scales for $|f_{R_0}|=1.289\times 10^{-5}$, although this is less for larger scales, earlier times and smaller values of the $f_{R_0}$ parameter. Similarly to in GR, the small amplitude of this vector potential suggests that the Newtonian approximation is highly accurate for $f(R)$ gravity, and also that the non-linear cosmological behaviour of $f(R)$ gravity can be completely described by just the scalar potentials and the $f(R)$ field.

Updated to match version published in JCAP

References in corpus (15)

• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• A Parameterized Post-Friedmann Framework for Modified Gravity
• Evading Equivalence Principle Violations, Cosmological and other Experimental Constraints in Scalar Field Theories with a Strong Coupling to Matter
• Searching for modified growth patterns with tomographic surveys
• N-body Simulations for f(R) Gravity using a Self-adaptive Particle-Mesh Code
• Non-linear evolution of f(R) cosmologies I: methodology
• How well is our universe described by an FLRW model?
• Theories of Dark Energy with Screening Mechanisms
• N-body methods for relativistic cosmology
• Testing the quasi-static approximation in $f(R)$ gravity simulations
• The missing link: a nonlinear post-Friedmann framework for small and large scales
• Vector modes generated by primordial density fluctuations
• The fully non-linear post-Friedmann frame-dragging vector potential: Magnitude and time evolution from N-body simulations
• On the Emergence of Accelerating Cosmic Expansion in f(R) Theories of Gravity
• A Relativistic view on large scale N-body simulations

Cited by in corpus (20)

• Finite-time Cosmological Singularities and the Possible Fate of the Universe
• A parametrisation of modified gravity on nonlinear cosmological scales
• GRAMSES: a new route to general relativistic $N$-body simulations in cosmology. Part I. Methodology and code description
• The fully non-linear post-Friedmann frame-dragging vector potential: Magnitude and time evolution from N-body simulations
• Cosmological gravity on all scales II: Model independent modified gravity $N$-body simulations
• $\text{Hi-COLA}$: Fast, approximate simulations of structure formation in Horndeski gravity
• Cosmological gravity on all scales: simple equations, required conditions, and a framework for modified gravity
• Lagrangian theory for cosmic structure formation with vorticity: Newtonian and post-Friedmann approximations
• $\text{fRevolution}$ $-$ Relativistic Cosmological Simulations in $f(R)$ Gravity I: Methodology
• Vector modes in $\Lambda$CDM: the gravitomagnetic potential in dark matter haloes from relativistic $N$-body simulations
• Looking for a twist: probing the cosmological gravitomagnetic effect via weak lensing-kSZ cross correlations
• fNL - gNL mixing in the matter density field at higher orders
• Scale-Dependent Gravitational Couplings in Parameterised Post-Newtonian Cosmology
• Full-sky weak lensing: a nonlinear post-Friedmann treatment
• Structure formation and quasi-spherical collapse from initial curvature perturbations with numerical relativity simulations
• EBWeyl: a Code to Invariantly Characterize Numerical Spacetimes
• Consistent cosmological structure formation on all scales in relativistic extensions of MOND
• Measuring the gravitomagnetic distortion from rotating halos I: methods
• Matter Creation Cosmologies and Accelerated Expansion
• The frame-dragging vector potential on galaxy scales from Dark-Matter-only Newtonian $N$-body simulations