Limitations of cosmography in extended theories of gravity

TL;DR

Cosmography, while useful for testing cosmological models, faces significant limitations in accurately reconstructing theories involving higher-order derivatives in gravity or matter sectors, highlighting the need for alternative approaches.

Contribution

This paper critically examines the shortcomings of cosmography in extended gravity theories with higher derivatives, providing examples, explanations, and potential solutions.

Findings

Cosmography struggles with higher-order derivative theories.

Limitations affect the reconstruction of modified gravity models.

Potential cures for these limitations are discussed.

Abstract

The cosmographic approach, which only relies upon the homogeneity and isotropy of the Universe on large scales, has become an essential tool in dealing with an increasing number of theoretical possibilities for explaining the late-time acceleration of the Universe, ranging from Modified Gravity theories to Dark Energy alternatives passing from testing the cosmological concordance Lambda-CDM model. Despite its generality, we show that this method has a number of shortcomings when trying to adequately reconstruct theories with higher-order derivatives in either the gravitational or the matter sector. Herein some paradigmatic examples of such an inability, explanations of the limitations and prospective cures will be presented.