Modification Of General Relativity Research Articles

New late-time constraints on [formula omitted] gravity

Modification of general relativity (GR) inspired by theories like f(R) gravity is among the most popular ones to explain the late-time acceleration of the Universe as an alternative to the ΛCDM model. In this work, we use the state-of-the-art BAO+BBN data and the most recent Type Ia supernovae (SNe Ia) sample namely PantheonPlus, including the Cepheid host distances and covariance from SH0ES samples, to robustly constrain the f(R) gravity framework via two of the most popular f(R) models in literature, namely, the Hu-Sawicki and Starobinsky models. Additionally, we consider how the time variation of the Newton’s gravitational constant affects the supernovae distance modulus relation. We find a minor evidence for f(R) gravity under the Hu-Sawicki dynamics from BAO+BBN and BAO+BBN+uncalibrated supernovae joint analysis, but the inclusion of Cepheid host distances, makes the model compatible with GR. Further, we notice tendency of this model to relax the H0 tension. In general, in all the analyses carried out in this study with the late time probes, we find both the f(R) models to be consistent with GR at 95% CL.

Cosmological Probes of Structure Growth and Tests of Gravity

The current standard cosmological model is constructed within the framework of general relativity with a cosmological constant Λ, which is often associated with dark energy, and phenomenologically explains the accelerated cosmic expansion. Understanding the nature of dark energy is one of the most appealing questions in achieving a self-consistent physical model at cosmological scales. Modification of general relativity could potentially provide a more natural and physical solution to the accelerated expansion. The growth of the cosmic structure is sensitive in constraining gravity models. In this paper, we aim to provide a concise introductory review of modified gravity models from an observational point of view. We will discuss various mainstream cosmological observables, and their potential advantages and limitations as probes of gravity models.

A derivation of the standard model particles from internal spacetime

‘Internal spacetime’ is a modification of general relativity that was recently introduced as an approximate spacetime geometric model of quantum nonlocality. In an internal spacetime, time is stationary along the worldlines of fundamental (dust) particles. Consequently, the dimensions of tangent spaces at different points of spacetime vary, and spin wavefunction collapse is modeled by the projection from one tangent space to another. In this paper, we develop spinors on an internal spacetime, and construct a new Dirac-like Lagrangian [Formula: see text] whose equations of motion describe their couplings and interactions. Furthermore, we show that hidden within [Formula: see text] is the entire standard model: [Formula: see text] contains precisely three generations of quarks and leptons, the electroweak gauge bosons, the Higgs boson, and one new massive spin-[Formula: see text] boson; gluons are considered in a companion paper. Specifically, we are able to derive the correct spin, electric charge, and color charge of each standard model particle, as well as predict the existence of a new boson.

Gödel-type universes in energy–momentum-squared gravity

In this paper, a modification of general relativity is considered. It consists of generalizing the Lagrangian of matter in a non-linear way, that is, replacing the curvature scalar R by a function f(R,T_{mu nu } T^{mu nu } ), where T_{mu nu } is the energy–momentum tensor. The main objective is to investigate the issue of causality in this gravitational model. To study the causality and/or its violation the Gödel-type solutions are used. For such development, different matter contents are chosen. A critical radius, beyond which causality is violated, is calculated. It is shown that both causal and non-causal solutions are allowed.

The Hamilton–Jacobi analysis for higher-order modified gravity

The Hamilton–Jacobi [HJ] study for the Chern–Simons [CS] modification of general relativity [GR] is performed. The complete structure of the constraints and the generalized brackets are reported, from these results the HJ fundamental differential is constructed and the symmetries of the theory are found. By using the constraints we remove an apparent Ostrogradsky’s instability and the new structure of the canonical Hamiltonian is reported. In addition, the counting of physical degrees of freedom is carried out and some remarks are discussed.

Constraining the evolution of Newton’s constant with slow inspirals observed from spaceborne gravitational-wave detectors

Spaceborne gravitational-wave (GW) detectors observing at milli-Hz and deci-Hz frequencies are expected to detect large numbers of quasi-monochromatic signals. The first and second time-derivative of the GW frequency ($\dot f_0$ and $\ddot f_0$) can be measured for the most favourable sources and used to look for negative post-Newtonian corrections, which can be induced by the source's environment or modifications of general relativity. We present an analytical, Fisher-matrix-based approach to estimate how precisely such corrections can be constrained. We use this method to estimate the bounds attainable on the time evolution of the gravitational constant $G(t)$ with different classes of quasi-monochromatic sources observable with LISA and DECIGO, two representative spaceborne detectors for milli-Hz and deci-Hz GW frequencies. We find that the most constraining source among a simulated population of LISA galactic binaries could yield $\dot G/G_0 \lesssim 10^{-6}\text{yr}^{-1}$, while the best currently known verification binary will reach $\dot G/G_0 \lesssim 10^{-4}\text{yr}^{-1}$. We also perform Monte-Carlo simulations using quasi-monochromatic waveforms to check the validity of our Fisher-matrix approach, as well as inspiralling waveforms to analyse binaries that do not satisfy the quasi-monochromatic assumption. We find that our analytical Fisher matrix produces good order-of-magnitude constraints even for sources well beyond its regime of validity. Monte-Carlo investigations also show that chirping stellar-mass compact binaries detected by DECIGO-like detectors at cosmological distances of tens of Mpc can yield constraints as tight as $\dot G/G_0 \lesssim 10^{-11}\text{yr}^{-1}$.

Spinning (A)dS black holes with slow-rotation approximation in dynamical Chern-Simons modified gravity

One of the most crucial areas of gravity research, after the direct observation of gravitational waves, is the possible modification of General Relativity at ultraviolet and infrared scales. In particular, the possibility of parity violation should be considered in strong field regime. The Chern-Simons gravity takes into account parity violation in strong gravity regime. For all conformally flat spacetimes and spacetimes with a maximally symmetric two-dimensional subspace, Chern-Simons gravity is identical to General Relativity. Specifically, the Anti-de Sitter (A)dS-Kerr/Kerr black hole is not a solution for Chern-Simons gravity. The slow-rotating BH and the quadratic order in spin solutions are some of the known solutions to quadratic order in spin and they are rotating solutions in the frame of dynamical Chern-Simons gravity. In the present study, for the (A)dS slow-rotating situation (correct to the first order in spin), we derive the linear perturbation equations controlling the metric and the dynamical Chern-Simons field equation corrected to the linear order in spin and to the second order in the Chern-Simons coupling parameter. We show that the black hole of the (A)dS-Kerr solution is stronger (i.e. more compact and energetic) than the Kerr black hole solution and the reason for this feature comes form contributions at Planck scales. Moreover, we calculate the thermodynamical quantities related to this black hole. Finally, we calculate the geodesic equation and derive the effective potential of the black hole.

Quasinormal modes of rotating black holes in Einstein-dilaton Gauss-Bonnet gravity: The second order in rotation

One of the most promising strategies to test gravity in the strong-field, large curvature regime is gravitational spectroscopy: the measurement of black hole quasi-normal modes from the ringdown signal emitted in the aftermath of a compact binary coalescence, searching for deviations from the predictions of general relativity. This strategy is only effective if we know how quasi-normal modes of black holes are affected by modifications of general relativity; and if we know this for rotating black holes, since binary coalescences typically lead to black holes with spins $J/M^2\sim 0.7$. In this article, we compute for the first time the gravitational quasi-normal modes of rotating black holes up to second order in the spin in a modified gravity theory. We consider Einstein-dilaton Gauss-Bonnet gravity, one of the simplest theories which modifies the large-curvature regime of gravity and which can be tested with black hole observations. To enhance the domain of validity of the spin expansion, we perform a Pad\'e resummation of the quasi-normal modes. We find that when the second order in spin is not included, the effect of gravity modifications may be seriously underestimated. A comparison with the general relativistic case suggests that this approach should be accurate up to spins $\sim 0.7$; therefore, our results can be used in the data analysis of ringdown signals.

Swampland criteria for f(R) gravity derived with a Gaussian process

A Gaussian Process (GP) is used to derive Swampland criteria for f(R) modifications of General Relativity (GR). The fact that observational data are directly taken into account allows obtaining clean upper and lower limits for the Swampland criteria, in an unbiased, natural way. They correspond to a dark-energy dominated Universe, having assumed the form of the f(R) gravity, only. To perform this study, 40-point H(z) data are used, consisting of 30-point samples deduced from the differential age method, and 10-point additional samples coming from the radial BAO method. The constraints obtained for each f(R) model parameter choice indicate whether it is possible to alleviate the H_{0} tension problem efficiently due to the used H_{0} values reported by the Planck and Hubble missions. The elaborated structure of the analysis forced to limit the number of specific models, but the methodology here discussed is applicable to study any form of f(R) gravity.

Measuring the propagation speed of gravitational waves with LISA

The propagation speed of gravitational waves, cT , has been tightly constrained by the binary neutron star merger GW170817 and its electromagnetic counterpart, under the assumption of a frequency-independent cT . Drawing upon arguments from Effective Field Theory and quantum gravity, we discuss the possibility that modifications of General Relativity allow for transient deviations of cT from the speed of light at frequencies well below the band of current ground-based detectors. We motivate two representative Ansätze for cT (f), and study their impact upon the gravitational waveforms of massive black hole binary mergers detectable by the LISA mission. We forecast the constraints on cT (f) obtainable from individual systems and a population of sources, from both inspiral and a full inspiral-merger-ringdown waveform. We show that LISA will enable us to place stringent independent bounds on departures from General Relativity in unexplored low-frequency regimes, even in the absence of an electromagnetic counterpart.

Full analytic expression of overlap reduction function for gravitational wave background with pulsar timing arrays

A pulsar timing array (PTA) is expected to detect a gravitational wave background (GWB) in the nanohertz band within the next decade. This provides an opportunity for one to test gravity theory and cosmology. A typical data analysis method to detect GWB is cross-correlation analysis. The overlap reduction function (ORF) plays an important role in the correlation data analysis of GWB. The present approach to dealing with the intricate integration in ORF is to use short-wave approximation to drop out the tricky terms. In this paper, we provide the full analytic expression of the ORF for PTA without any approximation for all possible polarizations allowed by modifications of general relativity. Compared with the numerical simulation and short-wave approximation, our results are more efficient and widely applicable. Especially for the scalar-longitudinal mode where the short-wave approximation is not available, our analytical expression is particularly significant.

A dynamical system representation of generalized Rastall gravity

In this work we study the phase-space analysis of generalized Rastall gravity (GRG) which has recently been introduced as a modification to the original version of Rastall gravity (RG). In GRG, the coupling parameter assumes a dynamical feature and may play the role of dark energy (DE) which is responsible for the present accelerating expansion of the Universe. Our investigation shows that such a modification of General Relativity (GR) admits a stable critical point corresponding to the late time accelerated expansion of the Universe. Assuming both dark matter (DM) and an ultra-relativistic perfect fluid (radiation) as the cosmic ingredients, we find that the underlying model presents a viable sequence of cosmic evolution, beginning from radiation dominated era passing then through DM domination and finally reaches the late time DE dominated era. Moreover, taking into account the contribution due to the spatial curvature within the total energy density leads to a growing mode for it in such a way that its present values are consistent with those reported in recent observations. We also present a numerical simulation of the model which particularizes our dynamical system representation. These studies demonstrate the ability of GRG to describe the present accelerated expansion of the Universe.

A geometric view on local Lorentz transformations in teleparallel gravity

Local Lorentz transformations play an important role in teleparallel gravity theories, in which a tetrad is conventionally employed as a fundamental field variable describing the gravitational field. It is commonly understood that modifications of general relativity in the teleparallel framework break a certain notion of local Lorentz invariance, which is present in the pure tetrad formulation of such theories, while another notion present in the covariant formulation is preserved. We illuminate these different notions from a geometric perspective, and distinguish them from what is commonly understood as breaking of local Lorentz invariance in the context of gravity phenomenology. Based on physical arguments, we present a geometric interpretation of the dynamical fields in teleparallel gravity, which unifies and refines the conventional approaches.

Two Approaches to Hamiltonian Bigravity

Bigravity is one of the most natural modifications of General Relativity (GR), as it is based on the equivalence principle. However, its canonical structure appears rather complicated because of the unusual form of the interaction between two metrics. As a consequence, there are different approaches that are difficult to compare in detail. This work is a first attempt to obtain a synthetic picture of the Hamiltonian formalism for bigravity. Here, we are trying to combine two rather different approaches to gain a binocular view of the theory. The first publications on the subject were based on metric formalism. It was proved that both massive gravity and bigravity with de Rham–Gabadadze–Tolley (dRGT) potential were free of Boulware–Deser (BD) ghosts. This proof was based on the transformation of variables involving a 3×3-matrix which could be treated as the root of a quadratic equation involving two spatial metrics and a new 3-vector introduced instead of the standard shift variable. Therefore, this matrix occurred as an implicit function of the abovementioned variables. After a substantial amount of time, it became possible to calculate the algebra of constraints in full using this method. However, in another approach also based on metric variables and implicit functions, similar calculations were completed earlier. It is not a new matrix, but the potential itself has been taken as an implicit function of two spatial metrics and four functions constructed of two pairs of lapses and shifts. Finally, a straightforward route to canonical bigravity is to apply tetrad (or vierbein) variables. The matrix square root involved in the dRGT potential can be explicitly extracted if tetrads fulfill the symmetry condition. A full treatment has been developed in first-order formalism by treating tetrads and connections as independent variables. In that case, the theory contains many more variables and constraints than in metric formalism. An essential simplification occurs in second-order vierbein formalism. The potential is given explicitly as a polynomial of bilinear combinations of the two tetrads. The 3×3-matrix introduced in the pioneer papers can be expressed explicitly through canonical coordinates, and the celebrated transformation of variables arises in the Dirac constraint analysis.

Geodesics of a Static Charged Black Hole Spacetime in f(R) Gravity

In recent years, the modification of general relativity (GR) through f(R) gravity is widely used to study gravity in a variety of scenarios. In this article, we study various physical properties of a black hole (BH) that emerged in the linear Maxwell f(R) gravity to constrain the values of different BH parameters, i.e., c and α. In particular, we study those values of the defining α and c for which the particles around the above-mentioned BH behave like other astrophysical BH in GR. The main motivation of the present research is to study the geodesics equations and discuss the possible orbits for c=0.5 in detail. Furthermore, the frequency shift of a photon emitted by a timelike particle orbiting around the BH is studied given different values of α and c. The stability of both timelike and null geodesics is discussed via Lyapunov’s exponent.

Image of the thin accretion disk around compact objects in the Einstein\u2013Gauss\u2013Bonnet gravity

We study the optical appearance of a thin accretion disk around compact objects within the Einstein–Gauss–Bonnet gravity. Considering static spherically symmetric black holes and naked singularities we search for characteristic signatures which can arise in the observable images due to the modification of general relativity. While the images of the Gauss–Bonnet black holes closely resemble the Schwarzschild black hole, naked singularities possess a distinctive feature. A series of bright rings are formed in the central part of the images with observable radiation 10^3 times larger than the rest of the flux making them observationally significant. We elucidate the physical mechanism, which causes the appearance of the central rings, showing that the image is determined by the light ring structure of the spacetime. In a certain region of the parametric space the Gauss–Bonnet naked singularities possess a stable and an unstable light ring. In addition the gravitational field becomes repulsive in a certain neighbourhood of the singularity. This combination of features leads to the formation of the central rings implying that the effect is not specific for the Einstein–Gauss–Bonnet gravity but would also appear for any other compact object with the same characteristics of the photon dynamics.

Analytic series expansion of the overlap reduction function for gravitational wave search with pulsar timing arrays

In our previous paper \cite{PTA1} we derived a generic expression for the pulse redshift the main observable for the Pulsar Timing Array (PTA) experiment for detection of gravitational waves for all possible polarizations induced by modifications of general relativity (GR). In this work we provide a generic expression of the overlap reduction function for PTA without using the short wavelength approximation for tensorial polarization. We are convinced, that the short wavelength approximation is not applicable to the overlap reduction function for PTA's, since the removal of the exponential terms in the integrand would lead to poles for $x, y$ and $l$ polarizations and discontinuities for $+$ and $\times$. In this work we provide a series expansion to calculate the integral exactly and investigate the behaviour of the series for short wavelength values via numerical evaluation of the analytical series. We find a disagreement for the limit of co-located pulsars with the Hellings \& Downs curve.

Probing fundamental physics with gravitational waves: The next generation

Gravitational wave observations of compact binary mergers are already providing stringent tests of general relativity and constraints on modified gravity. Ground-based interferometric detectors will soon reach design sensitivity and they will be followed by third-generation upgrades, possibly operating in conjunction with space-based detectors. How will these improvements affect our ability to investigate fundamental physics with gravitational waves? The answer depends on the timeline for the sensitivity upgrades of the instruments, but also on astrophysical compact binary population uncertainties, which determine the number and signal-to-noise ratio of the observed sources. We consider several scenarios for the proposed timeline of detector upgrades and various astrophysical population models. Using a stacked Fisher matrix analysis of binary black hole merger observations, we thoroughly investigate future theory-agnostic bounds on modifications of general relativity, as well as bounds on specific theories. For theory-agnostic bounds, we find that ground-based observations of stellar-mass black holes and LISA observations of massive black holes can each lead to improvements of 2-4 orders of magnitude with respect to present gravitational wave constraints, while multiband observations can yield improvements of 1-6 orders of magnitude. We also clarify how the relation between theory-agnostic and theory-specific bounds depends on the source properties.

МОДИФІКАЦІЇ СТАНДАРТНОЇ КОСМОЛОГІЧНОЇ МОДЕЛІ ТА "НОВА ФІЗИКА"

An overview of the problems associated with the possible going beyond the basic cosmological model is given. The focus is mainly on issues related to astronomical observations and the modifications of general relativity, which use a cosmological scalar field or nonlinear in curvature terms in gravitational Lagrangian. The main points are as follows: the problems of flatness and horison, discussion of the “Hubble Tension” and the simplest known models with one scalar field and the modified gravity. The general opinion is that that there is a number of ways to solve problems with the Hubble constant, but none of them explains all the completeness of the observational data. They are either phenomenological in nature or contain arbitrary functions that must be determined from experiment or from some fundamental principles. Therefore, it is natural to first turn to those models that either do not introduce “new entities”, or include a minimum number of new physical elements and a minimum number of additional parameters.

Wormhole solutions with scalar field and electric charge in modified gravity

In this paper, we have considered the modification of general relativity and presence of extra matter part for the exploration of traversable wormhole solutions. In particular, we have considered the background of f(R, T) gravity under the effect of scalar field and electric charge, which play the role of additional matter part. The energy conditions are detected in the presence of both scalar field and electric charge and the results are compared. Further, the existence of photon spheres, due to the strong gravitational lensing, is examined and the formation of relativistic images is studied.