Extended Cosmology in Palatini f(R)-theories

TL;DR

This paper explores cosmological models based on Palatini f(R) gravity with a specific function form, interpreting them through Weyl geometry, and examines their fit to supernova data while highlighting the impact of atomic clock modeling.

Contribution

It introduces a novel interpretation of Palatini f(R) models via Weyl geometry and discusses the influence of atomic clock models on cosmological predictions.

Findings

Extended definitions of cosmological distances in Weyl geometry.

Fitted model parameters to SNIa data.

Identified potential observable effects from atomic clock modeling.

Abstract

We consider the cosmological models based on Palatini f(R)-theory for the function f(R)=aR-2bR^2-3c/R, which, when only dust visible matter is considered, is called dune cosmology in view of the shape of the function f(R(a)) (being a the scale factor). We discuss about the meaning of solving the model, and interpret it according to Ehlers-Pirani-Schild framework as defining a Weyl geometry on spacetime. Accordingly, we extend the definitions of luminosity distance, proper distance, and redshift to Weyl geometries and fit the values of parameters to SNIa data. Since the theoretical prediction is model-dependent, we argue that the it is affected by an extra choice, namely a model for atomic clocks, which, in principle, produces observable effects. To the best of our knowledge, these effects have not being considered in the literature before.