Nonlocal gravity cosmology: An overview

Abstract

We discuss some main aspects of theories of gravity containing nonlocal terms in view of cosmological applications. In particular, we consider various extensions of general relativity based on geometrical invariants as [Formula: see text], [Formula: see text] and [Formula: see text] gravity where [Formula: see text] is the Ricci curvature scalar, [Formula: see text] is the Gauss–Bonnet topological invariant, [Formula: see text] the torsion scalar and the operator [Formula: see text] gives rise to nonlocality. After selecting their functional form by using Noether symmetries, we find out exact solutions in a cosmological background. It is possible to reduce the dynamics of selected models and to find analytic solutions for the equations of motion. As a general feature of the approach, it is possible to address the accelerated expansion of the Hubble flow at various epochs, in particular the dark energy issues, by taking into account nonlocality corrections to the gravitational Lagrangian. On the other hand, it is possible to search for gravitational nonlocal effects also at astrophysical scales. In this perspective, we search for symmetries of [Formula: see text] gravity also in a spherically symmetric background and constrain the free parameters, Specifically, by taking into account the S2 star orbiting around the Galactic Center SgrA[Formula: see text], it is possible to study how nonlocality affects stellar orbits around such a massive self-gravitating object.

Non-local Lagrangian fields: Noether's theorem and Hamiltonian formalism

“…For the particular way in which we have defined equation (8) as an extension of (6), the constraints (16) are stable under spacetime translations, and therefore the generators X a are tangent to the submanifold D ⊂ K . Indeed, including (16) and (10), we have that…”

“…So far, this Hamiltonian system in the extended phase space Γ has little to do with the Lagrangian system (16) or the generator of time evolution X 4 in the space D . However, they can be connected by the injection map…”

“…These non-local models of gravity are called Infinite Derivative Theories of Gravity (IDGs), and their results are quite promising; for instance, they can show the regularisation of the gravitational potential 1/r of pointlike sources at the linearised level [8], as well as other sorts of sources [9][10][11][12][13][14][15]. Likewise, other non-local gravity models are also being used to explain the cosmic expansion of the Universe [16]. It was shown that the 1/ operator applied on the R-curvature scalar results in an accelerated expansion of the Universe without relying on a contribution from dark energy [17].…”

Linearized Field Equations and Extra Force in $f(R,{\bf T}^{(n)})$ Extended Gravity

“…Several attempts have been pursued in this direction (e.g. non-local theories [14][15][16], String Theory [17], Loop Quantum Gravity [18,19], etc. ), but all of them lack at least one necessary condition among full renormalizability, unitarity and physical predictability.…”

Minisuperspace Quantum Cosmology in Metric and Affine Theories of Gravity

“…However, in the high-energy regime, GR exhibits several other shortcomings. For this reason, many alternative models have been proposed over the years, such as Kaluza-Klein Theory [12][13][14][15][16], String Theory [17][18][19][20][21], Non-Local Gravity [22][23][24][25][26], Loop Quantum Gravity [27][28][29][30][31], etc.…”