Narrow Results

A modified form of nonlocally corrected theory of gravity is investigated in the context of cosmology and the Newtonian limit. This form of nonlocal correction to classic Einstein–Hilbert action can be locally represented by a triple-scalar–tensor theory in which one of the scalar degrees of freedom is phantom-like and the other two are quintessence-like. We show that there exists a stable de Sitter solution for the cosmological dynamics if a suitable form of potential function V(ϕ) (or equivalently, f(R)) is selected. However, no matter what a potential function is selected, there is always an early time repeller solution corresponding to a radiation dominated universe. Besides, the equations for linear scalar perturbations are presented and it is shown that the form of potential function V(ϕ) is stringently constrained by the solar system test, although the post-Newtonian parameter γ is not directly affected by this function.

A theoretical study of testing nonlocal gravity in its Newtonian regime with gravity gradient measurements in space is given. For certain solutions of the modification to Newton’s law in nonlocal gravity, a null test and a lower bound on related parameters may be given with future high precision multi-axis gravity gradiometers along elliptic orbits.

In this paper, we propose a nonlocal extension of the mimetic dark matter model based on the FALVA implementation of fractional calculus. Our primary objective to explore how certain properties of dark matter can be modeled within the FALVA framework rather than formulate a phenomenological model. We begin by constructing the action functional of the cosmological extension of the mimetic dark model and deriving the nonlinear equations of motion in the general case. Next, we focus on a fractional-power homogeneous mimetic dark field with an exponential expansion factor. We derive the equation of motion for the lapse field and obtain its general solution. Analytical solutions are then obtained for small time intervals and arbitrary values of the fractionality parameter. These solutions enable us to establish the physical line element of spacetime, incorporating the mimetic dark matter field. From this line element, we derive the Ricci tensor, Ricci scalar, and geodesic equations.

We study the cosmological evolution of some nonlocal gravity models, when the initial conditions are set during a phase of primordial inflation. We examine in particular three models, the so-called RT, RR and ${\mathrm{\Delta }}_4$ models, previously introduced by our group. We find that, during inflation, the RT model has a viable background evolution, but at the level of cosmological perturbations develops instabilities that make it nonviable. In contrast, the RR and ${\mathrm{\Delta }}_4$ models have a viable evolution even when their initial conditions are set during a phase of primordial inflation.

We investigate the cosmological dynamics of nonlocally corrected gravity involving a function of the inverse d’Alembertian acting on the Gauss-Bonnet term. Casting the dynamical equations in local form, we derive the reconstruction procedure. We find conditions on the model parameters that are sufficient for the existence of de Sitter solutions and obtain these solutions explicitly.

I analyze the possibility of reproducing MONDian dark matter effects by using a nonlocal model of gravity. The model was used before in order to recreate screening effects for the cosmological constant (Λ) value. Although the model in the weak-field approximation (in static coordinates) can reproduce the field equations in agreement with the AQUAL Lagrangian, the solutions are scale dependent and cannot reproduce the same dynamics in agreement with MOND.

We developed the nonlocal model recently published by Maggiore and Mancarella by introducing a new function $f$. This modification allows us to obtain a new analytical solution in the hyperbolic tangent form for the nonlocal distortion function. This model gives rise to an expansion history behaving exactly as $\mathrm{\Lambda }$CDM (Lambda Cold Dark Matter) with the same matter content, but without any need to neither cosmological constant nor dark energy. However, background evolution in our model and $\mathrm{\Lambda }$CDM are the same, but the results may be distinguishable in structure formation investigations or in light of new observations that probably contain additional information more than the background evolution.

Cosmic strings, as remnants of the symmetry breaking phase in the Early universe, may be susceptible to nonlocal physics. Here, we show that the presence of a Poincaré-invariant nonlocality—parametrized by a factor $exp(-\square {\ell }^2)$—regularizes the gravitational field and thereby changes the properties of spacetime: it is now simply connected and the angle deficit around the cosmic string becomes a function of the radial distance. Similar changes occur for the nonlocal gravitomagnetic field of a rotating cosmic string, and we translate these mathematical facts into the language of nonlocal gravitoelectromagnetism and thereby provide a physical interpretation. We hope that these insights might provide a helpful perspective in the search for traces of nonlocal physics in our universe.

The existence of a fundamental scale is expected to be a key feature of quantum gravity. Many approaches take this property as a starting assumption. Here, instead, we take a less conventional viewpoint based on a critical inspection of both fundamental principles and kinematic laws. We point out that rigorous arguments suggest a more urgent need to revise known theories to incorporate a fundamental acceleration scale already in flat space. The reciprocity principle can naturally do so. In addition to noticing links with string theory, we argue that the reciprocity principle implies an infinite-derivative generalization of the Einstein–Hilbert action that makes the gravitational interaction fundamentally nonlocal, thus providing a guiding principle that could lead us towards the formulation of a consistent theory of quantum gravity.

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 $f(R,{\square }^{-1}R)$, $f({𝒢},{\square }^{-1}{𝒢})$ and $f(T,{\square }^{-1}T)$ gravity where $R$ is the Ricci curvature scalar, ${𝒢}$ is the Gauss–Bonnet topological invariant, $T$ the torsion scalar and the operator ${\square }^{-1}$ 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 $f(R,{\square }^{-1}R)$ 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${}^{\ast }$, it is possible to study how nonlocality affects stellar orbits around such a massive self-gravitating object.

The field equations of the recent nonlocal generalization of Einstein’s theory of gravitation are presented in a form that is reminiscent of general relativity. The implications of the nonlocal field equations are studied in the case of conformally flat spacetimes. Even in this simple case, the field equations are intractable. Therefore, to gain insight into the nature of these equations, we investigate the structure of nonlocal gravity (NLG) in 2D spacetimes. While any smooth 2D spacetime is conformally flat and satisfies Einstein’s field equations, only a subset containing either a Killing vector or a homothetic Killing vector can satisfy the field equations of NLG.

We derive the dynamical equations for a non-local gravity model in the Palatini formalism and we discuss some of the properties of this model. We have show that, in some specific case, the vacuum solutions of general relativity are also vacuum solutions of the non-local model, so we conclude that, at least in this case, the singularities of Einstein’s gravity are not removed.

We consider the possibility to enlarge the class of symmetries realized in standard local field theories by introducing infinite order derivative operators in the actions, which become nonlocal. In particular, we focus on the Galilean shift symmetry and its generalization in nonlocal (infinite derivative) field theories. First, we construct a nonlocal Galilean model which may be UV finite, showing how the ultraviolet behavior of loop integrals can be ameliorated. We also discuss the pole structure of the propagator which has infinitely many complex conjugate poles, but satisfies tree level unitarity. Moreover, we will introduce the same kind of nonlocal operators in the context of linearized gravity. In such a scenario, the graviton propagator turns out to be ghost-free and the spacetime metric generated by a point-like source is non-singular.

Nonlocal gravity models are constructed to explain the current acceleration of the universe. These models are inspired by the infrared correction appearing in Einstein–Hilbert action. Here, we develop the Hamiltonian formalism of a nonlocal model by considering only terms to quadratic order in Riemann tensor, Ricci tensor and Ricci scalar. We show how to count degrees of freedom using Hamiltonian formalism including Ricci tensor and Ricci scalar terms. In this model, we have also worked out with a choice of a nonlocal action which has only two degrees of freedom equivalent to GR. Finally, we find the existence of additional constraints in Hamiltonian required to remove the ghosts in our full action. We also compare our results with that of obtained using Lagrangian formalism.

In this short paper we study how black hole singularities can be tackled in the context of nonlocal ghost-free gravity, in which the action is characterized by the presence of non-polynomial differential operators containing infinite order covariant derivatives. The ghost-freeness condition can be preserved by requiring that such nonlocal operators are made up of exponential of entire functions, thus avoiding the emergence of extra unhealthy poles in the graviton propagator. We will mainly focus on how infinite order derivatives can regularize the singularity at the origin by making explicit computations in the linear regime. In particular, we will show that this kind of non-polynomial operators can smear out point-like distribution and that the Schwarzschild metric can not be a solution of the field equations in the ghost-free infinite derivative gravity.

We study at classical level two ranges of weakly nonlocal gravitational theories that are super-renormalizable or finite at quantum level. We explicitly prove that for one out of the two classes of theories all Ricci-flat spacetimes are exact vacuum solutions of the classical equations of motion (EOM). For the second class of theories the EOM are exactly solved by all these FRW spacetimes, which are sourced by a traceless energy tensor. Therefore, the Big-Bang singularity persists when the nonlocal gravity is coupled to radiation. We here prove the above statements in three simple theorems.