Based on Wheeler-DeWitt equation derived from general relativity, it had been found that only dark energy can lead to a normalizable cosmological wave function. It is shown in the present work that, for dRGT gravity, Eddington-inspired-Born-Infeld gravity and Ho$\check{\text{r}}$ava-Lifshitz gravity, the previous conclusion can also stand well in quantum cosmology induced from these modified gravities. This observation implies that there might be a universal relation between dark energy and normalizability of the cosmological wave function.
We investigate the hypothetical process of gravitational Cherenkov radiation, which may occur in modified gravity theories. We obtain a useful constraint on a modified dispersion relation for propagating modes of gravitational waves, which could be predicted as a consequence of violation of the Lorentz invariance in modified theories of gravity. The constraint from gravitational Cherenkov radiation and that from direct measurements of the gravitational waves emitted by a compact binary system are complementary to each other.
We present an investigation of nonlinear interactions between Gravitational Radiation and modified Alfvén modes in astrophysical dusty plasmas. Assuming that stationary charged dust grains form neutralizing background in an electron-ion-dust plasma, we obtain the three wave coupling coefficients, and calculate the growth rates for parametrically coupled gravitational radiation and modified Alfvén-Rao modes. The threshold value of the gravitational wave amplitude associated with convective stabilization is particularly small if the gravitational frequency is close to twice the modified Alfvén w…
The Laser Interferometer Gravitational-Wave Observatory (LIGO) detection of gravitational waves that take away 5% of the total mass of two merging black holes points out on the importance of considering varying gravitational mass of a system. Using an assumption that the energy-momentum pseudo-tensor of gravitational waves is not considered as a source of gravitational field, we analyse a perturbation of the Friedmann-Robertson-Walker metric caused by the varying gravitational mass of a system. This perturbation leads to a modified Friedmann equation that contains a term similar to the 'cosmol…
The purpose of the classical Einstein and Landau-Lifshitz pseudotensors is for determining the gravitational energy. Neither of them can guarantee a positive energy in holonomic frames. In the small sphere approximation, it has been required that the quasilocal expression for the gravitational energy-momentum density should be proportional to the Bel-Robinson tensor $B_{αβμν}$. However, we propose a new tensor $V_{αβμν}$ which is the sum of certain tensors $S_{αβμν}$ and $K_{αβμν}$, it has certain properties so that it gives the same gravitational "energy-momentum" content as $B_{αβμν}$ does. …
A consequence of adopting a modified gravitational theory (MOG) for the aLIGO GW190521 gravitational wave detection involving binary black hole sources is to fit the aLIGO strain and chirp data with lower mass, compact coalescing binary systems such as neutron star-neutron star (NS-NS), black hole - neutron star (BH-NS), and black hole-black hole (BH-BH) systems. In MOG BH - BH component masses can be smaller than the component masses $m_1=85M_\odot$ and $m_2=66M_\odot$ inferred from the aLIGO GW190521 gravitational wave event. This reduces the mass of the final remnant mass $M_f=150M_\odot$ a…
Motivated by the dark energy issue, a minisuperspace approach to the stability for modified gravitational models in a four dimensional cosmological setting are investigated. Specifically, after revisiting the $f(R)$ case, $R$ being the Ricci curvature, we present a stability condition around a de Sitter solution valid for modified gravitational models of generalized Gauss-Bonnet type $F(R,G,Q)$, $G$ and $Q$ being the Gauss-Bonnet and quadratic Riemann invariants respectively. A generalization to higher order invariants is mentioned.
We study the gravitational waves in modified Gauss-Bonnet gravity. Applying the metric perturbation around a cosmological background, we obtain explicit expressions for the wave equations. It is shown that the speed of the traceless mode is equal to the speed of light. An additional massive scalar mode appears in the propagation of the gravitational waves. To find phenomena beyond the general relativity the scalar mode mass is calculated as a function of the background curvature in some typical models.
We have taken a modified version of the Einstein Hilbert action, $ f(R, T^ϕ) $ gravity under consideration, where $T^ϕ$ is the energy-momentum tensor trace for the scalar field under consideration. The structural behaviour of the scalar field considered varies with the form of the potential. The number of polarization modes of gravitational waves in modified theories has been studied extensively for the corresponding fields. There are two additional scalar modes, in addition to the usual two transverse-traceless tensor modes found in general relativity: a massive longitudinal mode and a massle…
In this paper, we describe the extension to study the thermodynamics of the structure formation in the large scale Universe in the nonlocal gravity formalism using standard statistical mechanics. From the derivation of the grand partition function in a modified version of the Yang-Lee theory, we obtained the corresponding thermodynamics properties that can be in consistency with a Bose-Einstein dark matter framework and derive its gravitational phase transition.
General Relativity has so far passed almost all the ground-based and solar-system experiments. Any reasonable extended gravity models should consistently reduce to it at least in the weak field approximation. In this work we derive the gravitational potential for the Palatini formulation of the modified gravity of the L(R) type which admits a de Sitter vacuum solution. We conclude that the Newtonian limit is always obtained in those class of models and the deviations from General Relativity is very small for a slowly moving source.
This paper is devoted to investigate the gravitational perfect fluid collapse in the framework of Chern-Simon modified gravity. For this purpose, we assume the spherically symmetric metric as an interior region and the Schwarzchild spacetime is considered as an exterior region of the star. The Israel junction conditions are used to match the interior and exterior spacetimes. For the sake of simplicity, we take the external field $Θ$ as a function of time parameter $t$ and obtain the solution of the field equations of Chern-Simon modified gravity. Junction conditions have been used to calculate…
In this paper, we seek to find a modified theory of gravity that accounts for the back-reaction of QED on curved spacetime. It is already known that vacuum fluctuations induce interactions between gravity and photons. An effective action for electromagnetism, which encodes the details of such quantum process, is utilized to get a set of modified Maxwell's equation and a new Lagrangian for the dynamics of gravity. Imposition of Cauchy predictability on these modified Maxwell's equations lead us to a new effective metric, from which the Lagrangian can be calculated. The new Lagrangian for gravit…
We analyze the propagation of gravitational waves in a medium containing bounded subsystems ("molecules"), able to induce significant Macroscopic Gravity effects. We establish a precise constitutive relation between the average quadrupole and the amplitudes of a vacuum gravitational wave, via the geodesic deviation equation. Then we determine the modified equation for the wave inside the medium and the associated dispersion relation. A phenomenological analysis shows that anomalous polarizations of the wave emerge with an appreciable experimental detectability if the medium is identified with …
It is shown that the theoretical arguments for the unavoidable collapse of massive stars, which are valid within standard general relativity, are not valid in extended gravity. In particular a calculation is reported of neutron stars within a theory obtained from an Einstein-Hilbert action involving a function of $R^{2}-1/2R_{μν}R^{μν}$ added to the Ricci scalar $R$. The calculation suggests that within that theory there are stable neutron stars with arbitrarily high baryon number.
In the non-standard model of relic gravitational waves (RGWs) generated in the early universe, the theoretical spectrum of is mainly described by an amplitude $r$ and a spectral index $β$, the latter usually being determined by the slope of the inflation potential. Pulsar timing arrays (PTAs) data have imposed constraints on the amplitude of strain spectrum for a power-law form as a phenomenological model. Applying these constraints to a generic, theoretical spectrum with $r$ and $β$ as independent parameters, we convert the PTAs constraint into an upper bound on the index $β$, which turns out…
A possible deviation from the precession of the Gravity Probe-B gyroscope predicted by general relativity is obtained in the nonsymmetric gravity theory. The time delay of radio signals emitted by spacecraft at planetary distances from the Sun, in nonsymmetric gravity theory is the same as in general relativity. A correction to the precession of the gyroscope would provide a possible experimental signature for the Gravity Probe-B gyroscope experiment. The Lense-Thirring frame-dragging effect is predicted to be the same as in GR.
We investigate the scalar induced gravitational waves (SIGWs) in the Chern-Simons (CS) modified gravity during the radiation dominated era. The SIGWs are circularly polarized, which provide us a tool to test the possible parity violation in the early universe. We derive the semianalytic expressions to evaluate the fractional energy density of the SIGWs, $Ω_{\mathrm{GW}}$, which receives contributions from the general relativity (GR) and the correction due to the parity-violating term, respectively. We find that the degree of the circular polarization of the SIGWs can be as large as of order un…
Action-level characterization of gravitational-wave propagation in dynamical Barbero--Immirzi gravity
State Key Laboratory of Radio Astronomy and Technology, Xinjiang Astronomical Observatory, Chinese Academy of Sciences（中国科学院新疆天文台射电天文与技术重点实验室）；Shanxi Province Intelligent Optoelectronic Sensing Application Technology Innovation Center, Yuncheng University（运城学院山西省智能光电传感应用技术创新中心）；Departamento de Física Teórica, IF-UERJ（里约热内卢州立大学理论物理研究所）；College of Mechanical and Electrical Engineering, Tarim University（塔里机械与电气工程学院）；Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University（北京师范大学天文与前沿物理研究所）；School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院）
We consider modified theories of gravity with a direct coupling between matter and geometry, denoted by an arbitrary function in terms of the Ricci scalar. Due to such a coupling, the matter stress tensor is no longer conserved and there is an energy transfer between the two components. By solving the conservation equation, we argue that the matter system should gain energy in this interaction, as demanded by the second law of thermodynamics. In a cosmological setting, we show that although this kind of interaction may account for cosmic acceleration, this latter together with direction of the…
Gravitational-wave sources can serve as standard sirens to probe cosmology by measuring their luminosity distance and redshift. Such standard sirens are also useful to probe theories beyond general relativity with a modified gravitational-wave propagation. Many of previous studies on the latter assume multi-messenger observations so that the luminosity distance can be measured with gravitational waves while the redshift is obtained by identifying sources' host galaxies from electromagnetic counterparts. Given that gravitational-wave events of binary neutron star coalescences with associated el…
The physically realistic model of compact stars undergoing gravitational collapse in $ f(R) $ gravity has been developed. We consider a more general model $ R + f(R) = R + k R^m $ and describe the interior space-time of gravitationally collapsing stars with separable-form of metric admitting homothetic killing vector. We then investigate the junction conditions to match the interior space-time with exterior space-time. Considering all junction conditions, we find analytical solutions describing interior space-time metric, energy density, pressures, and heat flux density of the compact stars un…
It is well known that two types of gravitational wave memory exist in general relativity (GR): the linear memory and the non-linear, or Christodoulou memory. These effects, especially the latter, depend on the specific form of Einstein equation. It can then be speculated that in modified theories of gravity, the memory can differ from the GR prediction, and provides novel phenomena to study these theories. We support this speculation by considering scalar-tensor theories, for which we find two new types of memory: the T memory and the S memory, which contribute to the tensor and scalar compone…
One of the predictions from simple inflation models is a stochastic background of gravitational waves (or literally what is called the Primordial Gravitational Waves (\textbf{PGW})) with a nearly scale--invariant spectrum. In this work, we consider these waves arising from perturbing the Anisotropic background (Bianchi type--I) metric by focus on their power spectrums.The intended frameworks are the Einstein's and modified gravity frames. The investigations indicate that in the modified gravity context, the results have more ability to adapt to physical conditions or constraints. Especially, t…
The family of metrics corresponding to the plane-fronted gravitational waves with parallel propagation, commonly referred to as the family of pp-wave metrics, is studied in the context of various modified gravitational models in a self-contained and coherent manner by using a variant of the null coframe formulation of Newman and Penrose and the exterior algebra of differential forms on pseudo-Riemannian manifolds.
Implementing Poincaré's `geometric conventionalism' a scalar Lorentz-covariant gravity model is obtained based on gravitationally modified Lorentz transformations (or GMLT). The modification essentially consists of an appropriate space-time and momentum-energy scaling ("normalization") relative to a nondynamical flat background geometry according to an isotropic, nonsingular gravitational `affecting' function Phi(r). Elimination of the gravitationally `unaffected' S_0 perspective by local composition of space-time GMLT recovers the local Minkowskian metric and thus preserves the invariance of …
Modified gravity (MOG) is a covariant, relativistic, alternative gravitational theory whose field equations are derived from an action that supplements the spacetime metric tensor with vector and scalar fields. Both gravitational (spin 2) and electromagnetic waves travel on null geodesics of the theory's one metric. Despite a recent claim to the contrary, MOG satisfies the weak equivalence principle and is consistent with observations of the neutron star merger and gamma ray burster event GW170817/GRB170817A.
Recent gravitational wave observations have allowed stringent new constraints on modifications to General Relativity (GR) in the extreme gravity regime. Although these observations were consistent with compact binaries with no orbital eccentricity, gravitational waves emitted in mildly eccentric binaries may be observed once detectors reach their design sensitivity. In this paper, we study the effect of eccentricity in gravitational wave constraints of modified gravity, focusing on Jordan-Brans- Dicke-Fierz theory as an example. Using the stationary phase approximation and the post-circular ap…
We investigate how the production of gravitational waves (GWs) is affected by the GW velocity $(c_T)$ during preheating after inflation. For instance, we simulate the production of GWs after $λϕ^4$ chaotic inflation, and find that GW spectrum is enhanced for $c_T<1$, but distorted (suppressed at low frequency, but enhanced at high frequency) for $c_T>1$.
Modified gravitational wave propagation is a smoking gun of modifications of gravity at cosmological scales, and can be the most promising observable for testing such theories. The observation of gravitational waves (GW) in recent years has allowed us to start probing this effect, and here we briefly review two promising ways of testing it. We will show that, already with the current network of detectors, it is possible to reach an interesting accuracy in the estimation of the $Ξ_0$ parameter (that characterizes modified gravitational wave propagation, with $Ξ_{0, {\rm GR}} = 1$) and with next…
The direct discovery of gravitational waves has finally opened a new observational window on our Universe, suggesting that the population of coalescing binary black holes is larger than previously expected. These sources produce an unresolved background of gravitational waves, potentially observables by ground-based interferometers. In this paper we investigate how modified theories of gravity, modeled using the ppE formalism, affect the expected signal, and analyze the detectability of the resulting stochastic background by current and future ground-based interferometers. We find the constrai…
We consider the nondynamical Chern-Simons (nCS) modified gravity, which is regarded as a parity-odd theory of massive gravity in four dimensions. We first find polarization modes of gravitational waves for $θ=x/μ$ in nCS modified gravity by using the Newman-Penrose formalism where the null complex tetrad is necessary to specify gravitational waves. We show that in the Newman-Penrose formalism, the number of polarization modes is one in addition to an unspecified $Ψ_4$, implying three degrees of freedom for $θ=x/μ$. This compares with two for a canonical embedding of $θ=t/μ$. Also, if one intro…
Teleparallel theory of gravity and its modifications have been studied extensively in literature. However, gravitational waves has not been studied enough in the framework of teleparallelism. In the present study, we discuss gravitational waves in general theories of teleparallel gravity containing the torsion scalar $T$, the boundary term $B$ and a scalar field $ϕ$. The goal is to classify possible new polarizations generalizing results presented in Ref.[15]. We show that, if the boundary term is minimally coupled to the torsion scalar and the scalar field, gravitational waves have the same p…
We reexamined the gravitational time delay of light, allowing for various models of modified gravity. We clarify the dependence of the time delay (and induced frequency shift) on modified gravity models and investigate how to distinguish those models, when light propagates in static spherically symmetric spacetimes. Thus experiments by radio signal from spacecrafts at very different distances from Sun and future space-borne laser interferometric detectors could be a probe of modified gravity in the solar system.
In this work we shall exhaustively study the effects of modified gravity on the energy spectrum of the primordial gravitational waves background. S. Weinberg has also produced significant works related to the primordial gravitational waves with the most important one being the effects of neutrinos on primordial gravitational waves. With this sort review, our main aim is to gather all the necessary information for studying the effects of modified gravity on primordial gravitational waves in a concrete and quantitative way and in a single paper. After reviewing all the necessary techniques for e…
We suggest the modified gravity where some arbitrary function of Gauss-Bonnet (GB) term is added to Einstein action as gravitational dark energy. It is shown that such theory may pass solar system tests. It is demonstrated that modified GB gravity may describe the most interesting features of late-time cosmology: the transition from deceleration to acceleration, crossing the phantom divide, current acceleration with effective (cosmological constant, quintessence or phantom) equation of state of the universe.
A Hamiltonian system with a modified Henon-Heiles potential is investigated. This describes the motion of free test particles in vacuum gravitational pp-wave spacetimes with both quadratic ("homogeneous") and cubic ("non-homogeneous") terms in the structural function. It is shown that, for energies above a certain value, the motion is chaotic in the sense that the boundaries separating the basins of possible escapes become fractal. Similarities and differences with the standard Henon-Heiles and the monkey saddle systems are discussed. The box-counting dimension of the basin boundaries is also …
Modified gravitational wave (GW) propagation is a generic phenomenon in modified gravity. It affects the reconstruction of the redshift of coalescing binaries from the luminosity distance measured by GW detectors, and therefore the reconstruction of the actual masses of the component compact stars from the observed (`detector-frame') masses. We show that, thanks to the narrowness of the mass distribution of binary neutron stars, this effect can provide a clear signature of modified gravity, particularly for the redshifts explored by third generation GW detectors such as Einstein Telescope and …
It has been recently shown that quadruply lensed gravitational-wave (GW) events due to coalescing binaries can be localized to one or just a few galaxies, even in the absence of an electromagnetic counterpart. We discuss how this can be used to extract information on modified GW propagation, which is a crucial signature of modifications of gravity at cosmological scales. We show that, using quadruply lensed systems, it is possible to constrain the parameter $Ξ_0$ that characterizes modified GW propagation, without the need of imposing a prior on $H_0$. A LIGO/Virgo/Kagra network at target sens…
In this proceedings, we are interested in dark gravitational wave standard sirens and their use for cosmology and for constraining modified gravity theories. Due to the extra friction term introduced in their propagation equation those theories predict different luminosity distances for electromagnetic and gravitational waves (GWs). This effect can be parametrized by the two variables $Ξ_0$ and $n$, that can be measured from gravitational wave observations, and specifically from the binary black hole (BBH) mergers detected by LIGO and Virgo. By fitting jointly BBH population models in mass and…
Exotic objects such as the Ellis wormhole are expected to act as gravitational lenses. Much like their nonexotic counterparts, information about these lenses can be found by considering the strong and weak lensing fields they induce. In this work, we consider how weak gravitational lensing flexion can provide information beyond that of shear. We find that directional flexion can distinguish between the case of a positive or negative convergence where directional shear cannot, and therefore can provide a unique lensing signature for objects with an Ellis wormhole-type metric. We also consider c…
Modified gravity theories generically predict a violation of Lorentz invariance, which may lead to a modified dispersion relation for propagating modes of gravitational waves. We construct a parametrized dispersion relation that can reproduce a range of known Lorentz-violating predictions and investigate their impact on the propagation of gravitational waves. A modified dispersion relation forces different wavelengths of the gravitational wave train to travel at slightly different velocities, leading to a modified phase evolution observed at a gravitational-wave detector. We show how such corr…
The finding of Gravitational Waves by the aLIGO scientific and VIRGO collaborations opens opportunities to better test and understand strong interactions, both nuclear-hadronic and gravitational. Assuming General Relativity holds, one can constrain hadron physics at a neutron star. But precise knowledge of the Equation of State and transport properties in hadron matter can also be used to constrain the theory of gravity itself. I review a couple of these opportunities in the context of modified f(R) gravity, the maximum mass of neutron stars, and progress in the Equation of State of neutron ma…
The spectrum of thermal gravitational waves is obtained by including the high frequency thermal gravitons created from extra-dimensional effect and is a new feature of the spectrum. The amplitude and spectral energy density of gravitational waves in thermal vacuum state are found enhanced. The amplitude of the waves get modified in the frequency range (10$^{-16}$ -10 $^{8}$ Hz) but the corresponding spectral energy density is less than the upper bound of various estimated results. With the addition of higher frequency thermal waves, the obtained spectral energy density of the wave in thermal v…
Recent work has shown that modified gravitational wave (GW) propagation can be a powerful probe of dark energy and modified gravity, specific to GW observations. We use the technique of Gaussian processes, that allows the reconstruction of a function from the data without assuming any parametrization, to measurements of the GW luminosity distance from simulated joint GW-GRB detections, combined with measurements of the electromagnetic luminosity distance by simulated DES data. For the GW events we consider both a second-generation LIGO/Virgo/Kagra (HVLKI) network, and a third-generation detect…
In the weak-field limit of General Relativity, gravitational waves obey linear equations and propagate at the speed of light. These properties of General Relativity are supported by the observation of ultra high energy cosmic rays as well as by LIGO's recent detection of gravitation waves. We argue that two existing relativistic generalizations of Modified Newtonian Dynamics, namely Generalized Einstein-Aether theory and BIMOND, display fatal inconsistencies with these observations.
We present an inflationary model preceded by a bounce in a metric theory a lá $f(R)$ where $R$ is the scalar curvature of the space-time. The model is asymptotically de Sitter such that the gravitational action tends asymptotically to a Hilbert-Einstein action, therefore modified gravity affects only the early stages of the universe. We then analyse the spectrum of the gravitational waves through the method of the Bogoliubov coefficients by two means: taking into account the gravitational perturbations due to the modified gravitational action in the $f(R)$ setup and by simply considering those…
A recent theory about the origin of the gravity suggests that the gravity is originally an entropic force. In this work, we discuss the effects of generalized uncertainty principle (GUP) which is proposed by some approaches to quantum gravity such as string theory, black hole physics and doubly special relativity theories (DSR), on the area law of the entropy. This leads to a $\sqrt{Area}$-type correction to the area law of entropy which imply that the number of bits $N$ is modified. Therefore, we obtain a modified Newton's law of gravitation. Surprisingly, this modification agrees with differ…
We have investigated the geodetic precession and the strong gravitational lensing in the slowly-rotating black hole in the dynamical Chern-Simons modified gravity theory. We present the formulas of the orbital period $T$ and the geodetic precession angle $ΔΘ$ for the timelike particles in the circular orbits around the black hole, which shows that the change of the geodetic precession angle with the Chern-Simons coupling parameter $ξ$ is converse to the change of the orbital period with $ξ$ for fixed $a$. We also discuss the effects of the Chern-Simons coupling parameter on the strong gravitat…
It has been shown in the literature that detections of gravitational waves (GWs) emitted by binary sources can provide measurements of luminosity distance. The events followed by electromagnetic counterparts are, then, suitable for probing the distance-redshift relation and doing cosmological parameter estimation, as well as investigating modified gravity (MG) models. In the context of effective approaches to MG equivalent to Horndeski, this GW distance differs from the standard electromagnetic luminosity distance due to the presence of a modified friction in the wave propagation. Here, we inv…
The emergent area of gravitational wave astronomy promises to provide revolutionary discoveries in the areas of astrophysics, cosmology, and fundamental physics. One of the most exciting possibilities is to use gravitational-wave observations to test alternative theories of gravity. In this contribution we describe how to use observations of extreme-mass-ratio inspirals by the future Laser Interferometer Space Antenna to test a particular class of theories: Chern-Simons modified gravity.
