$$f(\mathcal {G})$$ Noether cosmology

Abstract

We develop the n-dimensional cosmology for $$f(\mathcal {G})$$f(G) gravity, where $$\mathcal {G}$$G is the Gauss–Bonnet topological invariant. Specifically, by the so-called Noether Symmetry Approach, we select $$f(\mathcal {G})\simeq \mathcal {G}^k$$f(G)≃Gk power-law models where k is a real number. In particular, the case $$k = 1/2$$k=1/2 for $$n=4$$n=4 results equivalent to General Relativity showing that we do not need to impose the action $$R+f(\mathcal {G})$$R+f(G) to reproduce the Einstein theory. As a further result, de Sitter solutions are recovered in the case where $$f(\mathcal {G})$$f(G) is non-minimally coupled to a scalar field. This means that issues like inflation and dark energy can be addressed in this framework. Finally, we develop the Hamiltonian formalism for the related minisuperspace and discuss the quantum cosmology for this model.

Non-local curvature and Gauss–Bonnet cosmologies by Noether symmetries

“…Sec. IV deals with the application of the method to models containing only non-local terms of the topological invariant G. We show that GR is recovered in the special case f (G) ∼ √ G (see also [28]). Furthermore, it is shown that considering a Einstein-Hilbert action corrected with non-local terms of G is just a subcase of the more general theory f (G, −1 G).…”

“…A similar procedure can be applied to models containing only the GB invariant. As discussed in [28], a theory containing only combinations of G can reduce to GR, at least in a cosmological background.…”

Unification of a bounce with a viable dark energy era in Gauss-Bonnet gravity

“…One promising sector of modified gravity theories is Gauss-Bonnet gravity [44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59], in which the Gauss-Bonnet invariant appears in the Lagrangian in a nonlinear way. Also, extensions of general relativity that contain higher orders of the Riemann and Ricci tensors can be found in Refs.…”

Constraining theories of gravity by GINGER experiment

“…Essentially, these effective actions can be distinguished in two main categories: Extended Theories of Gravity [35][36][37][38][39][40][41][42] which improve the Hilbert-Einstein action involving higherorder curvature invariants or scalar fields, and Alternative Theories of Gravity, where some basic assumptions of GR are relaxed, as well as the torsionless connection, the metricity or the universal validity of the equivalence principle [43][44][45][46][47][48][49].…”