Extended Gravity Cosmography

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 Padé 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.

82 pages, 35 figures. Accepted for publication in IJMPD

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• Cosmography in $f(Q)$ gravity
• Non-Local Gravity Cosmology: an Overview
• Measurements of $H_0$ and reconstruction of the dark energy properties from a model-independent joint analysis
• Einstein, Planck and Vera Rubin: relevant encounters between the Cosmological and the Quantum Worlds
• Addressing the cosmological $H_0$ tension by the Heisenberg uncertainty
• Connecting early and late epochs by f(z)CDM cosmography
• Non-Local Gravity Wormholes
• Tracing dark energy history with gamma ray bursts
• High-redshift cosmography: Application and comparison with different methods
• Observational Constraints and Cosmological Implications of Scalar-Tensor $f(R,T)$ Gravity
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• Tensions with the flat $\mathbf{\Lambda }$CDM model from high-redshift cosmography
• Energy Conditions in Non-minimally Coupled $f(R,T)$ Gravity
• Estimating the Parameters of Extended Gravity Theories with the Schwarzschild Precession of S2 Star
• Cosmographic view on the $H_0$ and ${\sigma }_8$ tensions
• Tracing the cosmic history by Gauss-Bonnet gravity
• Questioning the $H_0$ tension via the look-back time
• Running vacuum versus Holographic dark energy: a cosmographic comparison
• The Raychaudhuri Equation in inhomogeneous FLRW space-time : A $f(R)$-gravity model
• The Heisenberg limit at cosmological scales
• Machine Learning and cosmographic reconstructions of quintessence and the Swampland conjectures
• A critical discussion on the $H_0$ tension
• Testing cosmic anisotropy with Pade approximation and Pantheon+ sample
• Searching for modified gravity in the astrophysical gravitational wave background: Application to ground-based interferometers
• Estimating the parameters of Hybrid Palatini gravity model with the Schwarzschild precession of S2, S38 and S55 stars: case of bulk mass distribution
• Teleparallel theory as a gauge theory of translations: comments and issues
• Exploring departures from Schwarzschild black hole in $f(R)$ gravity
• Joint Constraints on the Hubble Constant, Spatial Curvature, and Sound Horizon from the Late-time Universe with Cosmography
• Cosmological Tests of Gravity: A Future Perspective
• The Gauss-Bonnet topological scalar in the Geometric Trinity of Gravity
• Impact of curvature based geometric constraints on $F(R)$ theory
• Cosmic acceleration and ekpyrotic bounce with Chameleon field
• Velocity distribution of elliptical galaxies in the framework of Non-local Gravity model
• Does emergent scenario in Hořava-Lifshitz Gravity demand a ghost field?
• Pseudo generalized Ricci-recurrent spacetimes with certain applications to modified gravity
• Cosmography of the minimally extended Varying Speed of Light Model
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• Bayesian deep learning for dark energy
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• Intermediate redshift calibration of Gamma-ray Bursts and cosmic constraints in non-flat cosmology
• Constraints on Energy Conditions in $f(R,L_m)$ Gravity