Nonlocal Gravity Research Articles

Apparent dark matter as a non-local manifestation of emergent gravity

We disclose a close correspondence between Verlinde’s Emergent Gravity (VEG) theory and the non-local gravity theories. Such non-local effects can play crucial role at small distances as well as in large scale structures. In particular, we argue that the emergent gravity effectively is a manifestation of the entanglement entropy and can modify Newton’s law of gravity as well as address the flat rotation curves of spiral galaxies. In the cosmological setup, we have considered three different models for the apparent dark matter density. In the first model, we have found that Friedmann equations get modified due to the presence of the apparent dark matter (DM) in such a way that Newton’s constant of gravity shifts as G→G1+ζ, where ζ is a dimensionless small parameter. Using the flat rotating curves we estimate ζ∼10−7. For such a model, we find out that by rescaling the radial coordinate, r, the curvature space constant, k, and the scale factor of the universe, a, the effect of apparent DM can change the geometry of the universe and can shift the curvature space constant as k⋆=k(1−ζ). To this end, we study a more realistic model with evolving densities where we obtain the ΛCDM model in Verlinde’s gravity and comment on the Hubble tension problem with evolving densities.

Quantum avoidance of Gödel’s closed timelike curves

In a large class of nonlocal as well as local higher derivative theories minimally coupled to the matter sector, we investigate the exactness of two different classes of homogeneous Gödel-type solutions, which may or may not allow closed time-like curves (CTC). Our analysis is limited to spacetimes solving the Einstein’s EoM, thus we can not exclude the presence of other Gödel-type solutions solving the EoM of local and nonlocal higher derivative theories but not the Einstein’s EoM. It turns out that the homogeneous Gödel spacetimes without CTC are basically exact solutions for all theories, while the metrics with CTC are not exact solutions of (super-)renormalizable local or nonlocal gravitational theories. Hence, the quantum renormalizability property excludes theories suffering of the Gödel’s causality violation. We also comment about nonlocal gravity non-minimally coupled to matter. In this class of theories, all the Gödel’s spacetimes, with or without CTC, are exact solutions at classical level. However, the quantum corrections, although perturbative, very likely spoil the exactness of such solutions. Therefore, we can state that the Gödel’s Universes with CTC and the super-renormalizability are mutually exclusive.

Asymptotically nonlocal gravity

Asymptotically nonlocal field theories interpolate between Lee-Wick theories with multiple propagator poles, and ghost-free nonlocal theories. Previous work on asymp- totically nonlocal scalar, Abelian, and non-Abelian gauge theories has demonstrated the existence of an emergent regulator scale that is hierarchically smaller than the lightest Lee-Wick partner, in a limit where the Lee-Wick spectrum becomes dense and decoupled. We generalize this construction to linearized gravity, and demonstrate the emergent regula- tor scale in three examples: by studying the resolution of the singularity (i) at the origin in the classical solution for the metric of a point particle, and (ii) in the nonrelativistic gravitational potential computed via a one-graviton exchange amplitude; (iii) we also show how this derived scale regulates the one-loop graviton contribution to the self energy of a real scalar field. We comment briefly on the generalization of our approach to the full, nonlinear theory of gravity.

The energy–momentum complex in non-local gravity

In General Relativity, the issue of defining the gravitational energy contained in a given spatial region is still unresolved, except for particular cases of localized objects where the asymptotic flatness holds for a given spacetime. In principle, a theory of gravity is not self-consistent, if the whole energy content is not uniquely defined in a specific volume. Here, we generalize the Einstein gravitational energy–momentum pseudotensor to non-local theories of gravity where analytic functions of the non-local integral operator [Formula: see text] are taken into account. We apply the Noether theorem to a gravitational Lagrangian, supposed invariant under the one-parameter group of diffeomorphisms, that is, the infinitesimal rigid translations. The invariance of non-local gravitational action under global translations leads to a locally conserved Noether current, and thus, to the definition of a gravitational energy–momentum pseudotensor, which is an affine object transforming like a tensor under affine transformations. Furthermore, the energy–momentum complex remains locally conserved, thanks to the non-local contracted Bianchi identities. The continuity equations for the gravitational pseudotensor and the energy–momentum complex, taking into account both gravitational and matter components, can be derived. Finally, the weak field limit of pseudotensor is performed to lowest order in metric perturbation in view of astrophysical applications.

Explicit holography for vector models at finite N, volume and temperature

In previous work we constructed an explicit mapping between large N vector models (free or critical) in d dimensions and a non-local high-spin gravity theory on AdSd+1, such that the gravitational theory reproduces the field theory correlation functions order by order in 1/N. In this paper we discuss three aspects of this mapping. First, our original mapping was not valid non-perturbatively in 1/N, since it did not include non- local correlations between the gravity fields which appear at finite N. We show that by using a bi-local G − Σ type formalism similar to the one used in the SYK model, we can construct an exact mapping to the bulk that is valid also at finite N. The theory in the bulk contains additional auxiliary fields which implement the finite N constraints. Second, we discuss the generalization of our mapping to the field theory on Sd, and in particular how the sphere free energy matches exactly between the two sides, and how the mapping can be consistently regularized. Finally, we discuss the field theory at finite temperature, and show that the low-temperature phase of the vector models can be mapped to a high-spin gravity theory on thermal AdS space.

On the Schwarzschild-de Sitter metric of nonlocal de sitter gravity

Earlier constructed a simple nonlocal de Sitter gravity model has a cosmological solution in a very good agreement with astronomical observations. In this paper, we continue the investigation of the nonlocal de Sitter model of gravity, focusing on finding an appropriate solution for the Schwarzschild-de Sitter metric. We succeeded to solve the equations of motion in a certain approximation. The obtained approximate solution is of particular interest for examining the possible role of non-local de Sitter gravity in describing the effects in galactic dynamics that are usually attributed to dark matter.

Addressing Cosmological Tensions by Non-Local Gravity

Alternative cosmological models have been under deep scrutiny in recent years, aiming to address the main shortcomings of the ΛCDM model. Moreover, as the accuracy of cosmological surveys improved, new tensions have risen between the model-dependent analysis of the Cosmic Microwave Background and lower redshift probes. Within this framework, we review two quantum-inspired non-locally extended theories of gravity, whose main cosmological feature is a geometrically driven accelerated expansion. The models are especially investigated in light of the Hubble and growth tension, and promising features emerge for the Deser–Woodard one. On the one hand, the cosmological analysis of the phenomenological formulation of the model shows a lowered growth of structures but an equivalent background with respect to ΛCDM. On the other hand, the study of the lensing features at the galaxy cluster scale of a new formulation of non-local cosmology, based on Noether symmetries, makes room for the possibility of alleviating both the H0 and σ8 tension. However, the urgent need for a screening mechanism arises for this non-local theory of gravity.

Testing time-delayed cosmology

Inspired by nonlocal gravity theories, time-delayed cosmology proposes a delayed Friedmann equation that generically predicts an inflationary period with a natural end. The key parameter of this proposal is a time delay that is presumed to be very small in order for the model to evade potential astrophysical constraints. This work subjects this small-delay assumption to a test. We address the question of just how large a time delay can be accommodated within our current cosmological data. In order to do so, we do not restrict the model to the inflationary era and consider its possible operation in the late Universe as well, with an eye for any smoking-gun features that may indicate the presence of a time delay. We study the background evolution predicted by the delayed Friedmann equation and determine the growth of Newtonian perturbations in this delayed background. We show that a surprisingly large late-time cosmic delay is statistically consistent with Hubble expansion rate and growth data. Based on these observables, we also find that the standard varLambda CDM model has no advantage over time-delayed cosmology in terms of the Bayes factor.

Nonlocal de Sitter gravity and its exact cosmological solutions

This paper is devoted to a simple nonlocal de Sitter gravity model and its exact vacuum cosmological solutions. In the Einstein-Hilbert action with Λ term, we introduce nonlocality by the following way: R-2Lambda =sqrt{R-2Lambda}kern1em sqrt{R-2Lambda}to sqrt{R-2Lambda}kern1em Fleft(square right)kern1em sqrt{R-2Lambda} , where Fleft(square right)=1+{sum}_{n=1}^{+infty}left({f}_n{square}^n+{f}_{-n}{square}^{-n}right) is an analytic function of the d’Alembert-Beltrami operator □ and its inverse □−1. By this way, R and Λ enter with the same form into nonlocal version as they are in the local one, and nonlocal operator F(□) is dimensionless. The corresponding equations of motion for gravitational field gμν are presented. The first step in finding some exact cosmological solutions is solving the equation square sqrt{R-2Lambda}=qsqrt{R-2Lambda} , where q = ζΛ (ζ ∈ R) is an eigenvalue and sqrt{R-2Lambda} is an eigenfunction of the operator □. We presented and discussed several exact cosmological solutions for homogeneous and isotropic universe. One of these solutions mimics effects that are usually assigned to dark matter and dark energy. Some other solutions are examples of the nonsingular bounce ones in flat, closed and open universe. There are also singular and cyclic solutions. All these cosmological solutions are a result of nonlocality and do not exist in the local de Sitter case.

On the impact of nonlocal gravity on compact stars

We study the impact of nonlocal modifications of General Relativity on stellar structure. In particular, assuming an analytic distortion function and specific equations of state, we made use of remnant stars to put qualitative constraints on a parameter not directly restricted by solar system tests. Using current data sets available for white dwarfs and strange quark stars candidates, we find that the most stringent bounds come from the objects displaying the highest core densities, namely strange quark stars. Specifically, the constraints obtained from this class of stars are three to four orders of magnitude tighter than those obtained using white dwarfs.

Non-local gravity wormholes

We consider Non-local Gravity in view to obtain stable and traversable wormhole solutions. In particular, the class of Non-local Integral Kernel Theories of Gravity, with the inverse d'Alembert operator in the gravitational action, is taken into account. We obtain constraints for the null energy condition and derive the field equations. Two special cases for the related Klein-Gordan equation are assumed: one where the function in the gravitational action has a linear form and another one with exponential form. In each case, we take into account two forms for scalar fields and derive the shape functions. Asymptotic flatness and flaring-out conditions are checked. Energy conditions and dynamics of the solutions are examined at the throat. The main result is that non-local gravity contributions allow stability and traversability of the wormhole without considering any exotic matter.

Ultracompact object within a nonlocal Tolman VII model

Tolman VII (TVII) is an analytical model for the nonrotating perfect fluid sphere with a simple quadratic density profile where its value is zero at the surface and a finite critical density value at the center. Therefore, compared to another analytical model like the constant density star, TVII is more realistic. Except for the dominant energy condition (DEC), which is violated in the region near the star's center, the TVII satisfies all energy conditions. However, the causal condition is also violated for $\mathcal{C}>0.26$, and the maximum compactness of the TVII is restricted, i.e., ${\mathcal{C}}_{\mathrm{max}}\ensuremath{\approx}0.38$. Here, we investigate the impacts of nonlocal gravity on the properties of the star of TVII within the range of the compactness of an ultracompact star ($0.33\ensuremath{\le}\mathcal{C}\ensuremath{\le}0.44$). This nonlocal gravity version of TVII (NGTVII) is parametrized by the nonlocal parameters ($\stackrel{\texttildelow{}}{\ensuremath{\beta}}$) and the compactness ($\mathcal{C}$). We have found that NGTVII can reach ${\mathcal{C}}_{\mathrm{max}}=0.43$ with ${\stackrel{\texttildelow{}}{\ensuremath{\beta}}}_{\mathrm{max}}=3$ which is significantly more compact than TVII. The nonlocal density and pressure profile differs from the TVII, depending on the stars' compactness and nonlocal parameter. We have also found that for the relatively small value of $\stackrel{\texttildelow{}}{\ensuremath{\beta}}$ and the compactness, i.e., $\mathcal{C}\ensuremath{\lesssim}0.31$, the causality condition and the DEC are not violated. We have also found that the NGTVII's effective potential in the interior can be larger and deeper than that of the TVII model, indicating the deceleration of the echo time. Moreover, using the effective potential of NGTVII, the quasinormal mode and gravitational echo are calculated using Bohr-Sommerfeld fitting and solving the time-dependent Reggae-Wheeler equation. We can infer that the NGVTII with the maximum compactness and nonlocal parameter values enables the existence of the ultracompact star with more trapped modes.

Nonlocal Gravity: Fundamental Tetrads and Constitutive Relations

Nonlocal gravity (NLG) is a classical nonlocal generalization of Einstein’s theory of gravitation based on a certain analogy with the nonlocal electrodynamics of media. The history dependence enters NLG through a constitutive relation involving a causal kernel that should ultimately be determined via observational data. The purpose of this paper is to reformulate nonlocal gravity such that the nonlocal aspect of the constitutive relation directly connects measurable quantities as in the nonlocal electrodynamics of media. The resulting constitutive relation turns out to coincide with the recent suggestion of Puetzfeld, Obukhov, and Hehl. With the new constitutive relation of NLG, it is possible to show that de Sitter spacetime is not a solution of NLG.

The phase-space view of non-local gravity cosmology

We consider non-local Integral Kernel Theories of Gravity in a homogeneous and isotropic universe background as a possible scenario to drive the cosmic history. In particular, we investigate the cosmological properties of a gravitational action containing the inverse d'Alembert operator of the Ricci scalar proposed to improve Einstein's gravity at both high and low-energy regimes. In particular, the dynamics of a physically motivated non-local exponential coupling is analyzed in detail by recasting the cosmological equations as an autonomous system of first-order differential equations with dimensionless variables. Consequently, we study the phase-space domain and its critical points, investigating their stability and main properties. In particular, saddle points and late-time cosmological attractors are discussed in terms of the free parameters of the model. Finally, we discuss the main physical consequences of our approach in view of dark energy behavior and the ΛCDM model.

Nonlocal Gravity: Modification of Newtonian Gravitational Force in the Solar System

Nonlocal gravity (NLG) is a classical nonlocal generalization of Einstein’s theory of gravitation developed in close analogy with the nonlocal electrodynamics of media. It appears that the nonlocal aspect of the universal gravitational interaction could simulate dark matter. Within the Newtonian regime of NLG, we investigate the deviation of the gravitational force from the Newtonian inverse square law as a consequence of the existence of the effective dark matter. In particular, we work out the magnitude of this deviation in the solar system out to 100 astronomical units. Moreover, we give an improved lower limit for the short-range parameter of the reciprocal kernel of NLG.

Velocity distribution of elliptical galaxies in the framework of Non-local Gravity model

We investigate the velocity distribution of elliptical galaxies in the framework of Non-local Gravity. According to this approach, it is possible to recover the fundamental plane of elliptical galaxies without the dark matter hypothesis. Specifically, we compare theoretical predictions for circular velocity in Non-local Gravity context with the corresponding values coming from a large sample of observed elliptical galaxies. We adopt the surface brightness, effective radius and velocity dispersion as structural parameters for the fundamental plane. As final result, it is possible to show that non-local gravity effects can reproduce the stellar dynamics in elliptical galaxies and fit consistently observational data.

Testing non-local gravity by clusters of galaxies

Extended theories of gravity have been extensively investigated during the last thirty years, aiming at fixing infrared and ultraviolet shortcomings of General Relativity and of the associated varLambda CDM cosmological model. Recently, non-local theories of gravity have drawn increasing attention due to their potential to ameliorate both the ultraviolet and infrared behavior of gravitational interaction. In particular, Integral Kernel theories of Gravity provide a viable mechanism to explain the late time cosmic acceleration so as to avoid the introduction of any form of unknown dark energy. On the other hand, these models represent a natural link towards quantum gravity. Here, we study a scalar-tensor equivalent model of General Relativity corrected with non-local terms, where corrections are selected by the existence of Noether symmetries. After performing the weak field limit and generalizing the results to extended mass distributions, we analyse the non-local model at galaxy cluster scales, by comparing the theoretical predictions with gravitational lensing observations from the CLASH program. We obtain agreement with data at the same level of statistical significance as General Relativity. We also provide constraints for the Navarro–Frenk–White parameters and lower bounds for the non-local length scales. The results are finally compared with those from the literature.

Characteristics of Effective Dark Matter in Nonlocal Gravity

Nonlocal gravity (NLG) is a classical nonlocal generalization of Einstein’s theory of gravitation that has been constructed in close analogy with the nonlocal electrodynamics of media. According to NLG, what appears as dark matter in astrophysics and cosmology is in reality the nonlocal aspect of the universal gravitational interaction. We focus here on two main features of the effective dark matter in NLG, namely, (a) the density of effective dark matter in NLG is always finite and therefore cusp-free, and (b) there is less effective dark matter in dwarf galaxies than is generally assumed in the standard particle dark matter paradigm. The corresponding astrophysical implications of NLG in connection with three ultra-diffuse galaxies AGC 114905, 242019, and 219533 are discussed.

A Linear Theory of Wind Farm Efficiency and Interaction

Abstract We investigate the role of gravity waves (GW), farm shape, and wind direction on the efficiency and interaction of wind farms using a two-layer linearized dynamical model with Rayleigh friction. Five integrated diagnostic quantities are used: total wind deficit, the first moment of vorticity, turbine work, disturbance kinetic energy, and vertical energy flux. The work done on the atmosphere by turbine drag is balanced by dissipation of disturbance kinetic energy. A new definition of wind farm efficiency is proposed based on “turbine work.” While GWs do not change the total wind deficit or the vorticity pattern, they alter the spatial pattern of wind deficit and typically make a wind farm less efficient. GWs slow the winds upwind and reduce the wake influence on nearby downstream wind farms. GWs also propagate part of the disturbance energy upward into the upper atmosphere. We applied these ideas to the proposed 45 km × 15 km wind energy areas off the coast of New England. The proximity of these farms allows GWs to play a significant role in farm interaction, especially in winter with northwesterly winds. The governing equations are solved directly and by using fast Fourier transforms (FFT). The computational speed of the linear FFT model suggests its future use in optimizing the design and day-by-day operation of these and other wind farms. Significance Statement When a wind farm is generating electricity, the drag of the wind turbines slows the regional winds. As wind farms grow larger and more closely spaced, this wind reduction will limit the efficiency of wind farms and their economic return. In this paper we analyze an idealized mathematical model of the atmospheric response to wind farm drag including nonlocal gravity wave effects. We propose a new definition of farm efficiency based on the atmospheric disturbance that a farm creates. We also propose a fast Fourier transform (FFT) method for carrying out these estimates.

Gravitational radiation in higher order non-local gravity

In this paper, we examine gravitational radiation in higher order non-local gravity described by the non-local gravitational Lagrangian density [Formula: see text]. This non-local theory of gravitation always exhibits the tensor transverse gravitational radiation for [Formula: see text], corresponding to the angular frequency [Formula: see text], composed of two standard [Formula: see text] and [Formula: see text] polarization modes, massless and of helicity 2. Furthermore, it shows, under suitable constraint and [Formula: see text], an additional massive transverse scalar gravitational radiation with helicity 0. It is composed of [Formula: see text] modes associated to [Formula: see text] angular frequencies [Formula: see text], each of which is of breathing polarization [Formula: see text] to lowest order in [Formula: see text], a parameter that takes into account the difference in speed between the slightly massive wave and the massless one. Thanks to NP formalism, we find that the [Formula: see text] class of non-local gravitational waves is [Formula: see text], according to Petrov classification, where the presence or absence of all modes are observer independent. Also, the scalar radiation is forbidden for [Formula: see text] and [Formula: see text] cases, when some conditions are satisfied. Finally, in [Formula: see text] gravity where [Formula: see text], a possible degenerate case with a continuous infinity of transverse massive scalar breathing modes appears under a particular constraint, which reproduces in two-dimensional spacetime the Polyakov–effective action.