Extended Gravity Cosmography (1904.01427v1)

Abstract: Cosmography can be considered as a sort of a model-independent approach to tackle the dark energy/modified gravity problem. In this review, the success and the shortcomings of the $\Lambda$CDM model, based on General Relativity and standard model of particles, are discussed in view of the most recent observational constraints. The motivations for considering extensions and modifications of General Relativity are taken into account, with particular attention to $f(R)$ and $f(T)$ theories of gravity where dynamics is represented by curvature or torsion field respectively. The features of $f(R)$ models are explored in metric and Palatini formalisms. We discuss the connection between $f(R)$ gravity and scalar-tensor theories highlighting the role of conformal transformations in the Einstein and Jordan frames. Cosmological dynamics of $f(R)$ models is investigated through the corresponding viability criteria. Afterwards, the equivalent formulation of General Relativity (Teleparallel Equivalent General Relativity) in terms of torsion and its extension to $f(T)$ gravity is considered. Finally, the cosmographic method is adopted to break the degeneracy among dark energy models. A novel approach, built upon rational Pad\'e and Chebyshev polynomials, is proposed to overcome limits of standard cosmography based on Taylor expansion. The approach provides accurate model-independent approximations of the Hubble flow. Numerical analyses, based on Monte Carlo Markov Chain integration of cosmic data, are presented to bound coefficients of the cosmographic series. These techniques are thus applied to reconstruct $f(R)$ and $f(T)$ functions and to frame the late-time expansion history of the universe with no \emph{a priori} assumptions on its equation of state. A comparison between the $\Lambda$CDM cosmological model with $f(R)$ and $f(T)$ models is reported.

• The paper provides a comprehensive review of f(R) and f(T) theories, highlighting their potential to overcome ΛCDM limitations.
• It introduces a cosmographic method with rational approximations like Padé and Chebyshev polynomials to address high-redshift convergence issues.
• The authors reconstruct f(R) and f(T) actions without initial assumptions, suggesting unified pathways for early inflation and late-time cosmic acceleration.

Extended Gravity Cosmography

The paper by Capozziello, D'Agostino, and Luongo explores the investigation of extended theories of gravity within the cosmographic framework, emphasizing model-independent approaches for addressing the dark energy problem. The principal aim is to explore the limitations of the standard $\Lambda$CDM model—built on General Relativity (GR) and the standard model of particle physics—in light of contemporary cosmological observations and to consider extensions of GR, particularly $f(R)$ and $f(T)$ theories, which introduce curvature or torsion fields, respectively, to the dynamical equations.

Main Findings and Methodology

1. Extended Theories Review: The authors provide a comprehensive review of the motivations for considering extended theories of gravity, particularly in relation to the shortcomings of the $\Lambda$CDM model. They discuss $f(R)$ gravity models in both metric and Palatini formalisms and explore their connections to scalar-tensor theories, emphasizing the role of conformal transformations in the Einstein and Jordan frames.
2. Teleparallel Equivalent General Relativity and $f(T)$ Gravity: The exploration extends to the theoretical formulation and implications of Teleparallel Equivalent General Relativity (TEGR), a paradigm where torsion rather than curvature provides the underpinning geometry. This equivalence provides a basis for developing $f(T)$ gravity, which offers an alternative method for extending GR.
3. Cosmography as a Model-Independent Tool: A significant contribution of the paper is advocating for a cosmographic approach to break the degeneracy among various dark energy models with emphasis on rational approximations (Padé and Chebyshev polynomials) to tackle the convergence issues at high redshift. This approach extends beyond standard Taylor expansions, providing a more reliable framework for model-independent cosmic diagnostics, which the authors numerically validate against observational datasets using techniques like Monte Carlo Markov Chain integration.
4. Reconstruction of $f(R)$ and $f(T)$ Actions: The authors apply the cosmographic method to derive $f(R)$ and $f(T)$ functions without prior assumptions, fundamentally aiming to reveal the underlying gravitational dynamics behind the observed acceleration of the universe. This reconstruction shows potential deviations from the $\Lambda$CDM model and outlines the viability criteria for the cosmological relevance of these alternative theories.

Implications and Speculative Possibilities

The paper's insights emphasize the ongoing quest for a more comprehensive understanding of the universe via extended theories of gravity, which might reconcile the need for dark energy. Practically, these models suggest routes to unify inflationary dynamics with late-time acceleration in cosmology. The implications for observational cosmology are profound, suggesting that future high-precision observations across various cosmic epochs could discriminate between these models and standard cosmology more effectively.

Conclusion

Capozziello, D'Agostino, and Luongo's work underscores the necessity of broadening our theoretical lens beyond GR, particularly given the theoretical and observational challenges posited by dark energy. By leveraging model-independent techniques like cosmography, the paper sets a methodological standard for testing alternative models, balancing theoretical innovation with empirical scrutiny. As such, this work is of particular significance to researchers seeking to extend the boundaries of cosmological models beyond the $\Lambda$CDM paradigm, reflecting both qualitative shifts in theoretical physics and quantitative advancements in observational cosmology.