If one modifies GR for the cosmic acceleration at the background level, additional degrees of freedom (dof) usually appear to mediate the so-called the 5th force, which changes the structure formation on various scales. Given that GR is found to be working well in our solar system, these new dof’s must be shielded, or screened by some mechanisms, such as the chameleon and Vainshtein mechanisms, to evade the stringent solar system constraint for modified gravity (MG).

N-body simulations are needed to investigate the nonlinear dynamics in both GR and MG, but MG simulations are much more difficult to do than the GR ones because of the screening mechanisms, which are highly nonlinear processes. My collaborators and I have spent quite a while to develop numeric codes (MGMLAPM, ECOSMOG) for these simulations and have simulated several MG models including f(R), dilaton, symmetron, general chameleon, DGP and Galileon. Gallery and movies for the f(R) simulation are here.

We have made applications of these expensive simulations including,

[1] I developed an accurate fitting formula for the nonlinear matter power

spectrum of f(R) gravity called MGHalofit [Zhao, ApJS, 2014].

Fitting formulae for more MG models are being developed;

[2] The matter power spectrum, mass function, halo profile of f(R) gravity

(Hu-Sawicki) model have been measured at the highest resolution so

far [Zhao et al, PRD 2011];

[3] The environment-dependent screening for f(R) gravity was discovered

and quantified [Zhao et al, PRL 2011];

[4] Galactic halos spin faster in f(R) gravity [Lee et al, ApJ 2013];

[5] The RSD measurement in f(R) gravity [Jennings et al, MNRAS 2012];

[6] A 3D screening map of the nearby Universe [Cabre et al, JCAP 2012];

[7] Halos and voids in f(R) gravity [Li et al, MNRAS 2012];

[8] Cluster profile in f(R) gravity [Lombriser et al, PRD 2012].

We are performing larger N-body and hydrodynamical simulations for a wider class of MG models. This will allow us to investigate interesting MG effects on galactic scales, for example, the segregation of different components of galaxies, different internal dynamics of different tracers, the alteration of stellar evolution and so on. All this interesting phenomenology are being tested and quantified using high-resolution hydrodynamical MG simulations.

On linear scales, the effect of modified gravity on observables, including CMB, weak lensing, galaxy counts, etc, can be calculated using linear perturbation theory. I have written a numeric code called MGCAMB [Zhao et al, PRD 08] (To compute power spectrum for Hu-Sawicki model using MGCAMB, see this instruction), which is based on CAMB, to do such calculations. This bridges the gap between MG theory and observation, making observational tests of MG theories possible.

There are various way to parametrise the MG effect. One of those is to use functions m and g defined as follows,

In GR, these two functions become a constant of 1, so any significant deviation of these functions at any k and z from 1 would be a smoking gun for MG. In order to perform observational tests, these two functions can be further parametrised and observations are used to constrain the corresponding parameters. For example, see my work [Zhao et al, PRD 10]. More generally, one can pixilise these functions in the {k,z} plane and try to constrain the pixels observationally. However, this is practically impossible even for future observations. A solution would be to investigate the best constrained linear combinations of these pixels, called modes, using a principal component analysis. For attempts in this direction, see [Zhao et al, PRL 09, Hojjati et al, PRD 12, Asaba et al, JCAP, 13]