We investigate whether there are any cosmological evidences for a scalar field with a mass and coupling to matter which change accordingly to the properties of the astrophysical system it lives in, without directly focusing on the underlying mechanis
m that drives the scalar field scale-dependent properties. We assume a Yukawa type of coupling between the field and matter and also that the scalar field mass grows with density, in order to overcome all gravity constraints within the solar system. We analyse three different gravitational systems assumed as cosmological indicators: supernovae type Ia, low surface brightness spiral galaxies and clusters of galaxies. Results show that: a) a quite good fit to the rotation curves of low surface brightness galaxies only using visible stellar and gas mass components is obtained; b) a scalar field can fairly well reproduce the matter profile in clusters of galaxies, estimated by X-ray observations and without the need of any additional dark matter; c) there is an intrinsic difficulty in extracting information about the possibility of a scale-dependent massive scalar field (or more generally about a varying gravitational constant) from supernovae type Ia.
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. Our analysis thus offers the possibility to relate the model independent results coming from cosmography to the theoretically motivated assumptions of $f(R)$ cosmology.
