Abstract
Observed accelerated behavior of the Hubble flow, usually related to the existence of a mysterious unknown fluid dubbed dark energy, can be framed in natural extensions of General Relativity that work at infrared scales. This approach gives rise to a geometric view of the phenomenon that does not require any new particle to be addressed. In this review paper, without claiming for completeness, we will give the main ingredients of such an approach considering models like f(R) gravity, with R the Ricci curvature scalar, and, in general, higher-order theories of gravity including other curvature invariants. In this context, we will review also Teleparallel Equivalent General Relativity and its extensions like f(T) gravity, where T is the torsion scalar. We will show that the curvature picture and the torsion picture can be related each other giving an equivalent paradigm where the observed cosmological acceleration can be addressed by extending the gravitational sector.
Highlights
Explaining the observed accelerated phase of the late Universe [1,2] is till an argument of debate
Many classes of models have been proposed to address the problem. They can be classified as follows: (i) models with cosmological constant Λ; (ii) dark energy related to some fundamental field; and (iii) possible modifications of gravity
F (R) remains a viable theory, but remarkably, F (R, G) can be retained because it is a singularity free theory where the Gauss–Bonnet contribution enhances the reliable behavior of curvature quintessence [87] and inflation [74]. In this short review paper, without claiming for completeness, we restrict ourselves to curvature based theories of gravity in their various formulations, and we focus the possibility that they can address the accelerated behavior of the present observed Universe
Summary
Explaining the observed accelerated phase of the late Universe [1,2] is till an argument of debate. F (R) remains a viable theory, but remarkably, F (R, G) can be retained because it is a singularity free theory where the Gauss–Bonnet contribution enhances the reliable behavior of curvature quintessence [87] and inflation [74] In this short review paper, without claiming for completeness, we restrict ourselves to curvature based theories of gravity in their various formulations, and we focus the possibility that they can address the accelerated behavior of the present observed Universe. We will sketch them and their relations with dark energy
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