Curvature dark energy reconstruction through different cosmographic distance definitions

Understand

In the context of $f(\mathcal{R})$ gravity, dark energy is a geometrical fluid with negative equation of state.

• Since the function $f(\mathcal{R})$ is not known \emph{a priori}, the need of a model independent reconstruction of its shape represents a relevant technique to determine which $f(\mathcal{R})$ model is really favored with respect to others.
• To this aim, we relate cosmography to a generic $f(\mathcal R)$ and its derivatives in order to provide a model independent investigation at redshift $z \sim 0$.
• Our analysis is based on the use of three different cosmological distance definitions, in order to alleviate the duality problem, i.e.