Cosmography of f(R) gravity

Understand

It is nowadays accepted that the universe is undergoing a phase of accelerated expansion as tested by the Hubble diagram of Type Ia Supernovae (SNeIa) and several LSS observations.

• Future SNeIa surveys and other probes will make it possible to better characterize the dynamical state of the universe renewing the interest in cosmography which allows a model independent analysis of the distance - redshift relation.
• On the other hand, fourth order theories of gravity, also referred to as $f(R)$ gravity, have attracted a lot of interest since they could be able to explain the accelerated expansion without any dark energy.
• We show here how it is possible to relate the cosmographic parameters (namely the deceleration $q_0$, the jerk $j_0$, the snap $s_0$ and the lerk $l_0$ parameters) to the present day values of $f(R)$ and its derivatives $f^{(n)}(R) = d^nf/dR^n$ (with $n = 1, 2, 3$) thus offering a new tool to constrain such higher order models.