Classical properties of non-local, ghost- and singularity-free gravity

Abstract

In this paper we will show all the linearized curvature tensors in the infinite derivative ghost and singularity free theory of gravity in the static limit. We have found that in the region of non-locality, in the ultraviolet regime (at short distance from the source), the Ricci tensor and the Ricci scalar are not vanishing, meaning that we do not have a vacuum solution anymore due to the smearing of the source induced by the presence of non-local gravitational interactions. It also follows that, unlike in Einstein's gravity, the Riemann tensor is not traceless and it does not coincide with the Weyl tensor. Secondly, these curvatures are regularized at short distances such that they are singularityfree, in particular the same happens for the Kretschmann invariant. Unlike the others, the Weyl tensor vanishes at short distances, implying that the spacetime metric becomes conformally flat in the region of non-locality, in the ultraviolet. As a consequence, the non-local region can be approximated by a conformally flat manifold with non-negative constant curvatures. We briefly discuss the solution in the non-linear regime, and argue that 1/r metric potential cannot be the solution where non-locality is important in the ultraviolet regime.

Cosmological solutions of a nonlocal square root gravity

“…One of actual approaches to modification of GR in domain of cosmology is nonlocal modified gravity, see e.g. [7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22].…”

Generalized ghost-free propagators in nonlocal field theories

“…(74) can be solved analytically only for n = 0, which gives Φ (0) (r) = − Gm r Erf( r 2 ), while for any other theory with n ≥ 1 we have to do it numerically. The case n = 0 has been already intensively studied in the literature [18,26,81,82], while the theory with n = 1 has been investigated only recently in Ref. [63].…”

“…[20] for a more general treatment including some non-maximally symmetric spacetime. It was also noticed that the presence of nonlocality can regularize infinities and many efforts have been made towards the resolution of black hole [17,18,[21][22][23][24][25][26][27][28][29][30][31][32][33] and cosmological [16,[34][35][36][37] singularities. At the quantum level, the high energy behavior of loop integrals has been investigated in [38][39][40][41] and properties of causality and unitarity in [42,43] and [44][45][46][47], respectively.…”

Nonlocal gravity with worldline inversion symmetry

“…In Fig.1 we plot the gravitational potential (4.5) along with Newton's potential (which is singular) and with the potential corresponding to the choice (2.2) of proper-time function, which gives Φ (t+1/M 2 ) (r) = −GmErf(rM/2)/r [12,14,21]. Note that both nonlocal potentials are strictly monotonic and are regularised at the origin with the only difference being that, in the case of worldline inversion symmetry, the spacetime metric describes a less compact gravitational system, namely Φ(0) < Φ (t+1/M 2 ) (0).…”

“…[12][13][14][15] which demonstrated the possibility of constructing a quadratic curvature theory of gravity that is classically stable and unitary at the quantum level. It has also been noted that nonlocality can regularise infinities, and many efforts have been made to resolve black hole [13,14,[16][17][18][19][20][21][22][23][24][25][26][27]52] and cosmological [12,[28][29][30] singularities. Furthermore, renormalisability [31][32][33], causality [34,35], unitarity [36][37][38][39][40], scattering amplitudes [41][42][43], spontaneous breaking of symmetry [44,45] and counting of initial conditions [46,47] have also been discussed and analysed.…”