V. F. Cardone

CURVATURE QUINTESSENCE MATCHED WITH OBSERVATIONAL DATA

Quintessence issues can be achieved by taking into account higher order curvature invariants into the effective action of gravitational field. Such an approach is naturally related to fundamental theories of quantum gravity which predict higher order terms in loop expansion of quantum fields in curved space-times. In this framework, we obtain a class of cosmological solutions which are fitted against cosmological data. We reproduce encouraging results able to fit high redshift supernovae and WMAP observations. The age of the universe and other cosmological parameters are discussed in this context.

Low surface brightness galaxy rotation curves in the low energy limit of Rn gravity: no need for dark matter?

We investigate the possibility that the observed flatness of the rotation curves of spiral galaxies is not evidence for the existence of dark matter haloes, but rather a signal of the breakdown of General Relativity. To this aim, we consider power-law fourth-order theories of gravity obtained by replacing the scalar curvature R with f(R) =f 0 R n in the gravity Lagrangian. We show that, in the low energy limit, the gravitational potential generated by a point-like source may be written as Φ(r) ∝ r -1 [1 + (r/r c ) β ] with β a function of the slope n of the gravity Lagrangian and r c a scalelength depending on the gravitating system properties. In order to apply the model to realistic systems, we compute the modified potential and the rotation curve for spherically symmetric and for thin disc mass distributions. It turns out that the potential is still asymptotically decreasing, but the corrected rotation curve, although not flat, is higher than the Newtonian one, thus offering the possibility to fit rotation curves without dark matter. To test the viability of the model, we consider a sample of 15 low surface brightness galaxies with combined H [I and Ha measurements of the rotation curve extending in the putative dark matter dominated region. We find a very good agreement between the theoretical rotation curve and the data using only stellar disc and interstellar gas when the slope n of the gravity Lagrangian is set to the value n = 3.5 (giving β = 0.817) obtained by fitting the Type Ia supernova Hubble diagram with the assumed power-law f(R) model and no dark matter. The excellent agreement between theoretical and observed rotation curves and the values of the stellar mass-to-light ratios in agreement with the predictions of population synthesis models make us confident that R n gravity may represent a good candidate to solve both the dark energy problem on cosmological scales and the dark matter one on galactic scales with the same value of the slope n of the higher-order gravity Lagrangian.

Cosmography in f(T)-gravity

Being based on the only assumption that the universe is homogenous and isotropic on large scales, cosmography is an ideal tool to investigate the cosmic expansion history in a almost model-independent way. Fitting the data on the luminosity distance and Baryon Acoustic Oscillations allows to determine the confidence ranges for the cosmographic parameters hence giving some quantitative constraints that a whatever theory has to fulfill. As an application, we consider here the case of teleparallel gravity (TEGR) also referred to as f(T)-gravity. To this end, we first work out analytical expressions to express the present day values of f(T)-derivatives as a function of the cosmographic parameters which hold under quite general and physically motivated conditions. We then use the constraints coming from cosmography to find out the confidence ranges for f(T)-derivatives up to the fifth order and show how these can be used to check the viability of given TEGR models without the need to explicitly solve the second order dynamic equations.

Cosmography of f(R) gravity

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 large scale structure 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

An updated Gamma Ray Bursts Hubble diagram

f(R)

Constraining dark energy models using the lookback time to galaxy clusters and the age of the universe

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

Unified dark energy models: A Phenomenological approach

{q}_{0}

Accelerating f ( T ) gravity models constrained by recent cosmological data

, the jerk

Beyond the perfect fluid hypothesis for the dark energy equation of state

{j}_{0}

Gravitational lensing in fourth order gravity

, the snap