Contact variational integrators

We present geometric numerical integrators for contact flows that stem from a discretization of Herglotz' variational principle. First we show that the resulting discrete map is a contact transformation and that any contact map can be derived from a variational principle. Then we discuss the backward error analysis of our variational integrators, including the construction of a modified Lagrangian. Throughout the paper we use the damped harmonic oscillator as a benchmark example to compare our integrators to their symplectic analogues

Updated constraints on f(R)f(\mathcal{R}) gravity from cosmography

We address the issue of constraining the class of $f(\mathcal{R})$ able to reproduce the observed cosmological acceleration, by using the so called cosmography of the universe. We consider a model independent procedure to build up a $f(z)$-series in terms of the measurable cosmographic coefficients; we therefore derive cosmological late time bounds on $f(z)$ and its derivatives up to the fourth order, by fitting the luminosity distance directly in terms of such coefficients. We perform a Monte Carlo analysis, by using three different statistical sets of cosmographic coefficients, in which the only assumptions are the validity of the cosmological principle and that the class of $f(\mathcal{R})$ reduces to $\Lambda$CDM when $z\ll1$. We use the updated union 2.1 for supernovae Ia, the constrain on the $H_0$ value imposed by the measurements of the Hubble space telescope and the Hubble dataset, with measures of $H$ at different $z$. We find a statistical good agreement of the $f(\mathcal{R})$ class under exam, with the cosmological data; we thus propose a candidate of $f(\mathcal{R})$, which is able to pass our cosmological test, reproducing the late time acceleration in agreement with observations.Comment: 10 pages, 9 figures, accepted for publication in Phys. Rev.

Cosmographic reconstruction of f(T)f(\mathcal{T}) cosmology

A cosmographic reconstruction of $f(\mathcal T)$ models is here revised in a model independent way by fixing observational bounds on the most relevant terms of the $f(\mathcal T)$ Taylor expansion. We relate the $f(\mathcal T)$ models and their derivatives to the cosmographic parameters and then adopt a Monte Carlo analysis. The experimental bounds are thus independent of the choice of a particular $f(\mathcal T)$ model. The advantage of such an analysis lies on constraining the dynamics of the universe by reconstructing the form of $f(\mathcal T)$, without any further assumptions apart from the validity of the cosmological principle and the analyticity of the $f(\mathcal T)$ function. The main result is to fix model independent cosmographic constraints on the functional form of $f(\mathcal T)$ which are compatible with the theoretical predictions. Furthermore, we infer a phenomenological expression for $f(\mathcal T)$, compatible with the current cosmographic bounds and show that small deviations are expected from a constant $f(\mathcal T)$ term, indicating that the equation of state of dark energy could slightly evolve from the one of the $\Lambda$CDM model.Comment: Accepted in Phys. Rev.