Extension Of General Relativity Research Articles

Non-Local Cosmology: From Theory to Observations

We examine the key aspects of gravitational theories that incorporate non-local terms, particularly in the context of cosmology and spherical symmetry. We thus explore various extensions of General Relativity, including non-local effects in the action through the function F(R,□−1R), where R denotes the Ricci curvature scalar and the operator □−1 introduces non-locality. By selecting the functional forms using Noether Symmetries, we identify exact solutions within a cosmological framework. We can thus reduce the dynamics of these chosen models and obtain analytical solutions for the equations of motion. Therefore, we study the capability of the selected models in matching cosmological observations by evaluating the phase space and the fixed points; this allows one to further constrain the non-local model selected by symmetry considerations. Furthermore, we also investigate gravitational non-local effects on astrophysical scales. In this context, we seek symmetries within the framework of f(R,□−1R) gravity and place constraints on the free parameters. Specifically, we analyze the impact of non-locality on the orbits of the S2 star orbiting SgrA*.

Effective cuscuton theory

Cuscuton field theory is an extension of general relativity that does not introduce additional propagating degrees of freedom, or violate relativistic causality. We construct a general geometric description of the cuscuton field theory by introducing curvature corrections to both the volume (potential) and the surface (kinetic) terms in the original cuscuton action. Our assumptions involve a stack of spacelike branes, separated by 4-dimensional bulks. We conjecture that the cuscuton, initially a discrete field, becomes continuous in the limit, there are many such transitions. From this we derive an effective action for the cuscuton theory and show that at the quadratic level our theory propagates only the two tensorial degrees of freedom.

Towards galaxy cluster models in Aether-Scalar-Tensor theory: isothermal spheres and curiosities

The Aether-Scalar-Tensor (AeST) theory is an extension of General Relativity (GR) which can support Modified Newtonian Dynamics (MOND) behaviour in its staticweak-field limit, and cosmological evolution resembling ΛCDM.We consider static spherically symmetric weak-field solutions in this theory and show that the resulting equations can be reduced to a single equation for the gravitational potential.The reduced equation has apparent isolated singularities at the zeros of the derivative of the potential and we show how these are removedby evolving, instead, the canonical momentum of the corresponding Hamiltonian system that we find. We construct solutions in three cases: (i) in vacuum outside a bounded spherical object, (ii) within an extended prescribed source, and (iii) for an isothermal gas in hydrostatic equilibrium, serving as a simplified model for galaxy clusters.We show that the oscillatory regime that follows the Newtonian and MOND regimes, obtained in previous works in the vacuum case, also persists for isothermal spheres, and we show that the gas density profiles in AeST can become more compressed than their Newtonian or MOND counterparts.We construct the Radial Acceleration Relation (RAR) in AeST for isothermal spheres and find that it can display a peak, an enhancement with respect to the MOND RAR, at an acceleration range determined by the value of the AeST weak-field mass parameter, the mass of the system and the boundary value of the gravitational potential. For lower accelerations, the AeST RAR drops below the MOND expectation,as if there is a negative mass density. Similar observational features of the galaxy cluster RAR have been reported. This illustrates the potential of AeST to address the shortcomings of MOND in galaxy clusters, but a full quantitative comparison with observations will require going beyond the isothermal case.

The κ-Model under the Test of the SPARC Database

Our main goal here is to conduct a comparative analysis between the well-known MOND theory and a more recent model called the κ-model. An additional connection, between the κ-model and two other novel MOND-type theories, Newtonian Fractional-Dimension Gravity (NFDG) and Refracted Gravity (RG), is likewise presented. All these models are built to overtake the DM paradigm, or at least to strongly reduce the dark matter content. Whereas they rely on different formalisms, however, all four seem to suggest that the universal parameter, a0, appearing in MOND theory could intrinsically be correlated to either the sole baryonic mean mass density (RG and κ-model) and/or to the dimension of the object under consideration (NFDG and κ-model). We then confer to parameter a0 a more flexible status of multiscale parameter, as required to explain the dynamics together in galaxies and in galaxy clusters. Eventually, the conformal gravity theory (CFT) also seems to have some remote link with the κ-model, even though the first one is an extension of general relativity, and the second one is Newtonian in essence. The κ-model has been tested on a small sample of spiral galaxies and in galaxy clusters. Now, we test this model on a large sample of galaxies issued from the SPARC database.

Constraining extended cosmologies with GW×LSS cross-correlations

The rapid development of gravitational wave astronomy provides the unique opportunity of exploring the dynamics of the Universe using clustering properties of coalescing binary black hole mergers. Gravitational wave data, along with information coming from future galaxy surveys, have the potential of shedding light about many open questions in Cosmology, including those regarding the nature of dark matter and dark energy. In this work we explore which combination of gravitational wave and galaxy survey datasets are able to provide the best constraints both on modified gravity theories and on the nature of the very same binary black hole events. In particular, by using the public Boltzmann code Multi_CLASS, we compare cosmological constraints on popular ΛCDM extensions coming from gravitational waves alone and in conjunction with either deep and localized or wide and shallow galaxy surveys. We show that constraints on extensions of General Relativity will be at the same level of existing limits from gravitational waves alone or one order of magnitude better when galaxy surveys are included. Furthermore, cross-correlating both kind of galaxy survey with gravitational waves datasets will allow to confidently rule in or out primordial black holes as dark matter candidate in the majority of the allowed parameter space.

Confront f(R,T)={mathcal {R}}+beta T modified gravity with the massive pulsar {textit{PSR J0740+6620}}

Many physically inspired general relativity (GR) modifications predict significant deviations in the properties of spacetime surrounding massive neutron stars. Among these modifications is f({mathcal {R}}, {mathbb {T}}), where {mathcal {R}} is the Ricci scalar, {mathbb {T}} is the trace of the energy–momentum tensor, the gravitational theory that is thought to be a neutral extension of GR. Neutron stars with masses above 1.8 M_{odot } expressed as radio pulsars are precious tests of fundamental physics in extreme conditions unique in the observable universe and unavailable to terrestrial experiments. We obtained an exact analytical solution for anisotropic perfect-fluid spheres in hydrostatic equilibrium using the frame of the linear form of f({mathcal {R}},{mathbb {T}})={mathcal {R}}+beta {mathbb {T}} where beta is a dimensional parameter. We show that the dimensional parameter beta and the compactness, C=frac{2GM}{Rc^2} can be used to express all physical quantities within the star. We fix the dimensional parameter beta to be at most beta _1=frac{beta }{kappa ^2}= 0.1 in positive values through the use of observational data from NICER and X-ray Multi-Mirror telescopes on the pulsar {textit{PSR J0740+6620}}, which provide information on its mass and radius. The mass and radius of the pulsar {textit{PSR J0740+6620}} were determined by analyzing data obtained from NICER and X-ray Multi-Mirror telescopes. It is important to mention that no assumptions about equations of state were made in this research. Nevertheless, the model demonstrates a good fit with linear patterns involving bag constants. Generally, when the dimensional parameter beta is positive, the theory predicts that a star of the same mass will have a slightly larger size than what is predicted by GR. It has been explained that the hydrodynamic equilibrium equation includes an additional force resulting from the coupling between matter and geometry. This force partially reduces the effect of gravitational force. As a result, we compute the maximum compactness allowed by the strong energy condition for f({mathcal {R}}, {mathbb {T}})={mathcal {R}}+beta {mathbb {T}} and for GR, which are C = 0.757 and 0.725, respectively. These values are approximately 3% higher than the prediction made by GR.. Furthermore, we estimate the maximum mass Mapprox 4.26 M_{odot } at a radius of Rapprox 15.9 km for the surface density at saturation nuclear density rho _{text {nuc}} = 2.7times 10^{14} g/cm^3.

Generalized non-local R2-like inflation

The R2 inflation which is an extension of general relativity (GR) by quadratic scalar curvature introduces a quasi-de Sitter expansion of the early Universe governed by Ricci scalar being an eigenmode of d’Alembertian operator. In this paper, we derive a most general theory of gravity admitting R2 inflationary solution which turned out to be higher curvature non-local extension of GR. We study in detail inflationary perturbations in this theory and analyse the structure of form-factors that leads to a massive scalar (scalaron) and massless tensor degrees of freedom. We argue that the theory contains only finite number of free parameters which can be fixed by cosmological observations. We derive predictions of our generalized non-local R2-like inflation and obtain the scalar spectral index ns ≈ 1 − frac{2}{N} and any value of the tensor-to-scalar ratio r < 0.036. In this theory, tensor spectral index can be either positive or negative nt ≶ 0 and the well-known consistency relation r = –8nt is violated in a non-trivial way. We also compute running of the tensor spectral index and discuss observational implications to distinguish this model from several classes of scalar field models of inflation. These predictions allow us to probe the nature of quantum gravity in the scope of future CMB and gravitational wave observations. Finally we comment on how the features of generalized non-local R2-like inflation cannot be captured by established notions of the so-called effective field theory of single field inflation and how we must redefine the way we pursue inflationary cosmology.

Paths to gravitation via the gauging of parametrized field theories

In special-relativistic physics, spacetime is imbued with a fixed, non-dynamical metric tensor. A path to gravitational theory is to promote this tensor to a genuine dynamical field. An alternative description of special-relativistic physics involves no fixed geometry but instead the inclusion of scalar fields $X^{I}(x^{\mu})$ which dynamically may take the form of inertial coordinates in spacetime. This suggests an alternative approach to gravity where the invariance of actions under global Poincar\'{e} transformations of $X^{I}$ is promoted to either a local Poincar\'{e} or local Lorentz symmetry via the introduction of gauge fields. Points of commonality and departure of the resulting gravitational theories as compared to General Relativity are discussed. It is shown that the model based on local Lorentz symmetry is an extension of General Relativity that can introduce a standard of time into the dynamics of the gravitational field and allows for spacetimes described by a Minkowski metric or flat Euclidean signature metric despite the gravitational gauge field possessing non-zero curvature.

Third post-Newtonian effective-one-body Hamiltonian in scalar-tensor and Einstein-scalar-Gauss-Bonnet gravity

We build an effective-one-body (EOB) Hamiltonian at third post-Newtonian (3PN) order in scalar-tensor (ST) and Einstein-scalar-Gauss-Bonnet (ESGB) theories of gravity. The latter is an extension of general relativity that predicts scalar hair for black holes. We start from the known two-body Lagrangian at 3PN order, and use order-reduction methods to construct its ordinary Hamiltonian counterpart. We then reduce the conservative two-body dynamics to the (nongeodesic) motion of a test particle in an effective metric by means of canonical transformations. The resulting EOB Hamiltonian is a modification of the general relativistic Hamiltonian, and already at 3PN order, it must account for nonlocal-in-time tail contributions. We include the latter beyond circular orbits and up to sixth order in the binary's orbital eccentricity. We finally calculate the orbital frequency at the innermost stable circular orbit (ISCO) of binary black holes in the shift-symmetric ESGB model. Our work extends F.L. Juli\'e and N. Deruelle [Phys. Rev. D 95, 124054 (2017)], and it is an essential step toward the accurate modeling of gravitational waveforms beyond general relativity.

Gravidynamics, spinodynamics and electrodynamics within the framework of gravitational quantum field theory

By noticing the fact that the charged leptons and quarks in the standard model are chirality-based Dirac spinors since their weak interaction violates maximally parity symmetry though they behave as Dirac fermions in electromagnetic interaction, we show that such a chirality-based Dirac spinor possesses not only electric charge gauge symmetry U(1) but also inhomogeneous spin gauge symmetry WS(1,3) = SP(1,3)$\rtimes$W$^{1,3}$, which reveals the nature of gravity and spacetime. The gravitational force and spin gauge force are governed by the gauge symmetries $W^{1,3}$ and SP(1,3), respectively, and a biframe spacetime with globally flat Minkowski spacetime as base spacetime and locally flat gravigauge spacetime as a fiber is described by the gravigauge field through emergent non-commutative geometry. The gauge-geometry duality and renormalizability in gravitational quantum field theory (GQFT) are carefully discussed. A detailed analysis and systematic investigation on gravidynamics and spinodynamics as well as electrodynamics are carried out within the framework of GQFT. A full discussion on the generalized Dirac equation and Maxwell equation as well as Einstein equation and spin gauge equation is made in biframe spacetime. New effects of gravidynamics as extension of general relativity are particularly analyzed. All dynamic equations of basic fields are demonstrated to preserve the spin gauge covariance and general coordinate covariance due to the spin gauge symmetry and emergent general linear group symmetry GL(1,3,R), so they hold naturally in any spinning reference frame and motional reference frame.

Spontaneous nonlinear scalarization of Kerr black holes

As it became well known in the past years, Einstein-scalar-Gauss-Bonnet (EsGB) theories evade no-hair theorems and allow for scalarized compact objects including black holes (BH). The coupling function that defines the theory is the main character in the process and nature of scalarization. With the right choice, the theory becomes an extension of general relativity (GR) in the sense any solution to the GR field equations remains a solution in the EsGB theory, but it can destabilize if a certain threshold value of the spacetime curvature is exceeded. Thus BHs can spontaneously scalarized. The most studied driving mechanism to this phenomenon is a tachyonic instability due to an effective negative squared mass for the scalar field. However, even when the coupling is chosen such that this mass is zero, higher order terms with respect to the scalar field can lead to what is coined nonlinear scalarization. In this paper we investigate how Kerr BHs spontaneously scalarize by evolving the scalar field on a fixed background via solving the nonlinear Klein-Gordon equation. We consider two different coupling functions with higher order terms, one that yields a non-zero effective mass and another that does not. We sweep through the Kerr parameter space in its mass and spin and obtain the scalar charge by the end of the evolution when the field settles in an equilibrium stationary state. When there is no tachyonic instability present, there is no probe limit in which the BH scalarizes with zero charge, i.e. there is a gap between bald and hairy BHs and they only connect when the mass goes to zero together with the charge.

Searching for dark energy with the Sun

General extensions of general relativity (GR) based on bona fide degrees of freedom predict a fifth force which operates within massive objects, opening up an exciting opportunity to perform precision tests of gravity at stellar scales. Here, focussing on general scalar-tensor theories for dark energy, we utilise the Sun as our laboratory and search for imprints of the fifth-force effect on the solar equilibrium structure. With analytic results and numerical simulations, we explain how the different solar regions offer powerful ways to test gravity. Accounting for the delicate interplay between the fifth force and solar microphysics such as opacity, diffusion, equation of state, and metallicity, we demonstrate that the fifth force still leaves a sharp signature on the solar sound speed, in a region where simple estimates of input physics uncertainties become negligible. For general scalar-field extensions of GR, known as (U-)DHOST, based solely on the observational helioseismic errors, our analysis at the equilibrium level allows us to place an approximate constraint on the fifth-force coupling strength of −10−3 ≲ 𝒴 ≲ 5 × 10−4 at 2σ. This result improves previous stellar constraints by ∼3 orders of magnitude, and should be confirmed and improved by future helioseismic inversions in modified gravity, combined with an elaborate accounting of theoretical uncertainties. Our analysis can be applied to a wide set of theories beyond GR, and also paves the way for helioseismic analyses in this context. In this regard, we discuss how the solar radiative and convective zone can be employed as promising laboratories to test generic theories of gravity.

Event horizon of a charged black hole binary merger

We analyze the formation and evolution of the event horizon of a black hole binary merger when the black holes are charged. We find that the presence of charge influences the properties of the merger and can be useful for investigating the validity of various theories of modified gravity and several proposals for dark matter candidates. It can moreover give insights into various aspects of astrophysical phenomena involving black holes, such as degeneracies in the gravitational wave parameter determination. We perform our analysis both analytically and numerically, in $D=4$ dimensions, in the extreme mass ratio (EMR) limit and compare the results. The development of analytical results in the EMR limit is of uttermost importance in view of the upcoming observations of the LISA interferometer. We then use our analysis to describe how the horizon evolves in time during the merger and to investigate the growth in the area of the event horizon and the duration of the merger. We moreover provide a numerical solution valid in arbitrary dimensions $D\ensuremath{\ge}4$ which could be of interest in the context of the $\mathrm{AdS}/\mathrm{CFT}$ correspondence or for examining possible extensions of general relativity.

Spatiotemporal jumps as particular solutions in geodesic trajectories with the Gödel metric on an extended manifold

Using the Gödel metric, we obtain some relevant solutions compatible with spatiotemporal jumps for the geodesic equations, by using an extension of General Relativity with nonzero boundary terms, which are described on an extended manifold generated by the connections delta Gamma ^{mu }_{alpha beta } = b,U^{mu },g_{alpha beta }. These terms are given by a flow of velocities with components U^{nu }: 3,b^2,nabla _{nu }U^{nu }=g^{alpha beta }, delta R_{alpha beta } = lambda left[ sleft( x^{alpha }right) right] ,g^{alpha beta }, delta g_{alpha beta } in the varied Einstein–Hilbert action. The solutions are valid for an arbitrary equation of state with ordinary matter: Omega =P/(c^2,rho ) = frac{left( frac{omega }{c}right) ^2-lambda (s)}{left( frac{omega }{c}right) ^{2}+lambda (s)}.

Junction conditions of Palatini f(R,T) gravity

We work out the junction conditions for the Palatini $f(\mathcal{R},T)$ extension of General Relativity, where $f$ is an arbitrary function of the curvature scalar $\mathcal{R}$ of an independent connection, and of the trace $T$ of the stress-energy tensor of the matter fields. We find such conditions on the allowed discontinuities of several geometrical and matter quantities, some of which depart from their metric counterparts, and in turn extend their Palatini $f(\mathcal{R})$ versions via some new $T$-dependent terms. Moreover, we also identify some "exceptional cases" of $f(\mathcal{R},T)$ Lagrangians such that some of these conditions can be discarded, thus allowing for further discontinuities in $\mathcal{R}$ and $T$ and, in contrast with other theories of gravity, they are shown to not give rise to extra components in the matter sector e.g. momentum fluxes and double gravitational layers. We discuss how these junction conditions, together with the non-conservation of the stress-energy tensor ascribed to these theories, may induce non-trivial changes in the shape of specific applications such as traversable thin-shell wormholes.

Scalar–tensor gravity from thermodynamic and fluid-gravity perspective

Out of several possible extensions of general relativity, the scalar-tensor theory is the most popular for several reasons. Since the quantum description of gravity is yet to be formulated properly, the understanding of a gravitational theory remains incomplete until the study of thermodynamic and fluid-gravity aspects, which provides an alternative viewpoint to understand the gravitational theory. In this review, we study these features (thermodynamics and the fluid gravity analogy) in a rigorous and yet in a concise manner for the scalar-tensor gravity, which has been revealed in our recent works. In addition, the issue of conformally connected frames (\textit{i.e.} whether the two frames, which are conformally related are physically equivalent) has been explored in an explicit manner at the action level as well as from the viewpoint of thermodynamics and fluid-gravity correspondence.

Gravitational ringing of rotating black holes in higher-derivative gravity

We study gravitational perturbations of slowly rotating black holes in a general effective-field-theory extension of general relativity that includes up to eight-derivative terms. We show that two Schr\"odinger-like equations with spin-dependent effective potentials govern the odd- and even-parity master variables. These equations are coupled for parity-violating corrections, and this coupling affects the quasinormal modes even at linear order in the higher-derivative corrections, due to their isospectrality in general relativity. We provide results for the shifts in the fundamental quasinormal mode frequencies at linear order in the spin, which we expect to be valuable for high-precision phenomenology through future gravitational wave observations.

Post-Newtonian gravitational and scalar waves in scalar-Gauss–Bonnet gravity

Gravitational waves emitted by black hole binary inspiral and mergers enable unprecedented strong-field tests of gravity, requiring accurate theoretical modeling of the expected signals in extensions of general relativity. In this paper we model the gravitational wave emission of inspiralling binaries in scalar Gauss–Bonnet gravity theories. Going beyond the weak-coupling approximation, we derive the gravitational waveform to relative first post-Newtonian order beyond the quadrupole approximation and calculate new contributions from nonlinear curvature terms. We also compute the scalar waveform to relative 0.5PN order beyond the leading −0.5PN order terms. We quantify the effect of these terms and provide ready-to-implement gravitational wave and scalar waveforms as well as the Fourier domain phase for quasi-circular binaries. We also perform a parameter space study, which indicates that the values of black hole scalar charges play a crucial role in the detectability of deviation from general relativity. We also compare the scalar waveforms to numerical relativity simulations to assess the impact of the relativistic corrections to the scalar radiation. Our results provide important foundations for future precision tests of gravity.

Star Mass Inertia Dictates the Speed of Light

This paper indicated that Newton’s law of gravitation is a statistical relation of two adjacent objects with a distance and Einstein’s general relativity shows the internal connection of material distribution through space-time warping in our universe so general relativity is referred as a gravity theory. Here the paper gives an extension of general relativity in the sense of the metric theory of gravity which is consistent with Einstein’s equivalence principle and generates a weak field approximation which extends Newtonian dynamics. Thus, the extended theory of gravity can infer that the light has a speed limit of photon escaping the mass inertia of a star.

Widened R&amp;lt;sup&amp;gt;&amp;lt;i&amp;gt;n&amp;lt;/i&amp;gt;&amp;lt;/sup&amp;gt; General Relativity

An extension of General Relativity is presented based on a scalar Lagrangian density which is a general function of all the independent invariant scalars that one is able to build by the powers of the Ricci tensor. It is shown how the new terms arising in the generalized Einstein filed equations may be interpreted as dark matter and dark energy contributions. Metricity condition fulfilled by a new tensor different than the usual metric tensor is also obtained. Moreover, it is shown that Schwarzschild-De Sitter, Robertson-Walker-De Sitter and Kerr-De Sitter metrics are exact solutions to the new field equations. Remarkably, the form of the equation of the geodesic trajectories of particle motions across space-time remains the same as in Einstein General Relativity unless the cosmological constant Lambda is no longer a constant becoming a function of the space-time co-ordinates.