Quantum gravity inspired nonlocal gravity model

We examine the origin of two opposite results for the growth of perturbations in the Deser-Woodard (DW) nonlocal gravity model. One group previously analyzed the model in its original nonlocal form and showed that the growth of structure in the DW model is enhanced compared to general relativity (GR) and thus concluded that the model was ruled out. Recently, however, another group has reanalyzed it by localizing the model and found that the growth in their localized version is suppressed even compared to the one in GR. The question was whether the discrepancy originates from an intrinsic difference between the nonlocal and localized formulations or is due to their different implementations of the sub-horizon limit. We show that the nonlocal and local formulations give the same solutions for the linear perturbations as long as the initial conditions are set the same. The different implementations of the sub-horizon limit lead to different transient behaviors of some perturbation variables; however, they do not affect the growth of matter perturbations at the subhorizon scale much. In the meantime, we also report an error in the numerical calculation code of the former group and verify that after fixing the error the nonlocal version also gives the suppressed growth. Finally, we discuss two alternative definitions of the effective gravitational constant taken by the two groups and some open problems.

Section: Discussionmentioning

confidence: 99%

Revival of the Deser-Woodard nonlocal gravity model: Comparison of the original nonlocal form and a localized formulation

Park

2018

“…Recent studies [1, [63][64][65] have pointed out that a new class of parametrizations describing spatially oscillating new forces on sub-mm scales is well motivated theoretically and viable experimentally. Such oscillating parametrizations may describe deviations of the gravitational force from a Newtonian force in a wide range of modified gravity theories[1], in theories involving small scale granularity of dark energy [66,67] and most importantly in non-local (infinite derivative) gravity theories [1,12,[63][64][65][68][69][70][71][72][73]. These theories can be free from singularities [70,71,74,75] (such as black holes) and instabilities [72,73,76], they can emerge from quantum effects [69] (such as light particle loops) and they do not need the existence of the cosmological constant Λ to in-terpret the cosmological observations [77].…”

Section: Introductionmentioning

confidence: 99%

Constraints on spatially oscillating sub-mm forces from the Stanford Optically Levitated Microsphere Experiment data

Antoniou

Perivolaropoulos

2017

A recent analysis by one of the authors[1] has indicated the presence of a 2σ signal of spatially oscillating new force residuals in the torsion balance data of the Washington experiment. We extend that study and analyse the data of the Stanford Optically Levitated Microsphere Experiment (SOLME) [2] (kindly provided by the authors of [2]) searching for sub-mm spatially oscillating new force signals. We find a statistically significant oscillating signal for a force residual of the form F (z) = α cos( 2π λ z + c) where z is the distance between the macroscopic interacting masses (levitated microsphere and cantilever). The best fit parameter values are α = (1.1 ± 0.4) × 10 −17 N , λ = (35.2 ± 0.6)µm. Monte Carlo simulation of the SOLME data under the assumption of zero force residuals has indicated that the statistical significance of this signal is at about 2σ level. The improvement of the χ 2 fit compared to the null hypothesis (zero residual force) corresponds to ∆χ 2 = 13.1. Private communication with the authors of Ref.[2] has indicated that this previously unnoticed signal is indeed in the data but is most probably induced by a systematic effect caused by diffraction of non-Gaussian tails of the laser beam. Thus the amplitude of this detected signal can only be useful as an upper bound to the amplitude of new spatially oscillating forces on sub-mm scales. In the context of gravitational origin of the signal emerging from a fundamental modification of the Newtonian potential of the form V ef f (r) = −G M r (1 + αO cos( 2π λ r + θ)) ≡ VN (r) + Vosc(r), we evaluate the source integral of the oscillating macroscopically induced force. If the origin of the SOLME oscillating signal is systematic, the parameter αO is bounded as αO < 10 7 for λ 35µm. Thus, the SOLME data can not provide useful constraints on the modified gravity parameter αO. However, the constraints on the general phenomenological parameter α (α < 0.3 × 10 −17 N at 2σ) can be useful in constraining other fifth force models related to dark energy (chameleon oscillating potentials etc).

“…It has been suggested that a nonlocal quantum effective action might derive from fundamental theory through the gravitational vacuum polarization of infrared gravitons vastly produced during primordial inflation [24,25]. However, since no such derivation is currently available, one may take a phenomenological approach, that is to guess what form of nonlocal actions would do the job of generating an accelerated expansion without dark energy [26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Does nonlocal gravity yield divergent gravitational energy-momentum fluxes?

Chu

Park

2019

Energy-momentum conservation requires the associated gravitational fluxes on an asymptotically flat spacetime to scale as 1/r 2 , as r → ∞, where r is the distance between the observer and the source of the gravitational waves. We expand the equations-of-motion for the Deser-Woodard nonlocal gravity model up to quadratic order in metric perturbations, to compute its gravitational energy-momentum flux due to an isolated system. The contributions from the nonlocal sector contains 1/r terms proportional to the acceleration of the Newtonian energy of the system, indicating such nonlocal gravity models may not yield well-defined energy fluxes at infinity. In the case of the Deser-Woodard model, this divergent flux can be avoided by requiring the first and second derivatives of the nonlocal distortion function f [X] at X = 0 to be zero, i.e., f ′ [0] = 0 = f ′′ [0]. It would be interesting to investigate whether other classes of nonlocal models not involving such an arbitrary function can avoid divergent fluxes.