On the theory and applications of modern cosmography

TL;DR

This review explores the principles, applications, limitations, and recent advancements of cosmography as a model-independent approach to understanding the universe's expansion without assuming specific cosmological models.

Contribution

It provides a comprehensive overview of cosmography, including its methodology, relation to dark energy models, limitations, and recent improvements like rational approximations with Padé polynomials.

Findings

Cosmography can directly match cosmological data without assuming a specific model.

Limitations exist in standard cosmographic approaches affecting model reconstructions.

Recent developments include the use of rational approximations to improve accuracy.

Abstract

Cosmography represents an important branch of cosmology which aims to describe the universe without the need of postulating \emph{a priori} any particular cosmological model. All quantities of interest are expanded as a Taylor series around here and now, providing in principle, a way of directly matching with cosmological data. In this way, cosmography can be regarded a model-independent technique, able to fix cosmic bounds, although several issues limit its use in various model reconstructions. The main purpose of this review is to focus on the key features of cosmography, emphasising both the strategy for obtaining the observable cosmographic series and pointing out any drawbacks which might plague the standard cosmographic treatment. In doing so, we relate cosmography to the most relevant cosmological quantities and to several dark energy models. We also investigate whether cosmography is able to provide information about the form of the cosmological expansion history, discussing how to reproduce the dark fluid from the cosmographic sound speed. Following this, we discuss limits on cosmographic priors and focus on how to experimentally treat cosmographic expansions. Finally, we present some of the latest developments of the cosmographic method, reviewing the use of rational approximations, based on cosmographic Pad\'e polynomials. Future prospects leading to more accurate cosmographic results, able to better reproduce the expansion history of the universe are also discussed in detail.