SHORT ABSTRACT:
We will go through a novel parameterisation of modified gravity which
allows us, after specifying only two free functions, to model almost all
known modified gravity models including scalar fields in one framework.
The exception being models with non-linear kinetic terms like the
Galileons. The parametrisation, which is found through a reversed
engineering procedure from the mass and coupling functions, has the
strength that it allows us not only to cover not only background
cosmology and linear growth of perturbations, but also to do local
constraints and go deep into the non-linear regime of structure
formation via N-body simulations.
LONG ABSTRACT:
The discovery of the accelerated expansion of the Universe has led to a
reappraisal of some of the tenants of modern cosmology. In particular,
the possibility of modifying the laws of gravity on short or large
scales is taken more and more seriously. In particular, the possibility
of modifying the laws of gravity on large scales.
Today there is a plethora of dark energy models in the literature and
the majority of models involve scalar fields like f(R), chameleon,
galileons, symmetrons, dilatons, etc. Some models are essentially
spin-offs of the previous one like the f(R) theories which are only
valid when they behave like chameleon theories with a thin shell
mechanism in dense environments. In all these examples, the large scale
properties on cosmological distances are intimately linked to the small
scale physics as probed solar systems or laboratory tests of gravity.
Most of these models, when agreeing with local gravity experiments,
reduce to LCDM at the background level which is a major drawback.
Fortunately, this is not the case for the perturbations. It turns out
that the perturbation equation at the linear level depend on the time
evolution of the scalar field mass and the coupling constant to matter.
With these two functions, all the time and space properties of the
linear perturbations can be calculated. In fact, these two time
dependent functions capture a lot more about the modified gravity models
with screening properties: they allow one to reconstruct fully and
uniquely the whole non-linear dynamics of the models. Hence given these
two functions, not only one can compute linear perturbations but one can
study the gravitational properties of the models in the solar system and
laboratory experiments.
One can also analyse the cosmological behaviour of the models with
N-body simulations. This way of defining the models, a reversed
engineering procedure from the mass and coupling functions to the
non-linear dynamics, is a lot more versatile than the usual direct route
where a model is defined by its Lagrangian comprising the kinetic terms
and an interacting potential. Indeed, all the usual mod- els such as
chameleons, f(R), dilaton and symmetrons can be explicitly rediscovered
by specifying the particular ways the mass and coupling functions behave
in time. Moreover, one can design new families of models. This approach
is equivalent to a space and time dependent parameterisation in terms of
the two Newtonian potentials obtained in the Jordan frame: the modified
Poisson equation and the constitutive relation linking the two Newtonian
potentials are directly and uniquely determined by the mass and coupling
functions in the Einstein frame.