MG15 - Talk detail

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Abstract

We propose a method to reconstruct the f(R) action both in the metric and in the Palatini formalism without postulating any specific functional form. To do that, we build model-independent approximations of the luminosity distance by means of rational polynomials, which are able to extend the convergence radius of the standard Taylor cosmographic series. We show that Pade' polynomials and ratios of Chebyshev polynomials can be used to accurately describe the late-time expansion history of the universe. We present the numerical procedure to obtain f(R) starting from the H(z) function obtained from the most recent bounds on the cosmographic parameters. Particularly, our strategy is to reconstruct f(z) functions first, assuming the Ricci scalar to be invertible with respect to the redshift z. Then, inverting the so-obtained f(z) functions, we easily obtain the corresponding f(R) terms. The treatment we follow naturally leads to evaluating curvature pressure, density and equation of state of the cosmic fluid at redshifts much higher than standard cosmographic approaches. Our results indicate small departures from LCDM and a time-evolving effective dark energy term.

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