Gravitational lensing constraints on dark energy from modified Friedmann equations

The existence of a dark energy component has usually been invoked as the most plausible way to explain the recent observational results. However, it is also well known that effects arising from new physics (e.g., extra dimensions) can mimic the gravitational effects of a dark energy through a modification of the Friedmann equation. In this paper we investigate some observational consequences of a flat, matter dominated and accelerating/decelerating scenario in which this modification is given by $H^{2} = g(\rho_m, n, q)$ where $g(\rho_m, n, q)$ is a new function of the energy density $\rho_m$, the so-called generalized Cardassian models. We mainly focus our attention on the constraints from statistical properties of gravitationally lensed quasars on the parameters $n$ and $q$ that fully characterize the models. We show that these models are in agreement with the current gravitationally lensed quasar data for a large interval of the $q - n$ parametric space. The dependence of the acceleration redshift (the redshift at which the universe begins to accelerate) on these parameters is also briefly discussed.