Gravitational waves (GWs) are direct probes of cosmological gravity, sensitive to space-time inhomogeneities along their propagation. The presence of massive objects breaks homogeneity and isotropy, allowing for new interactions between different GW polarizations, and opening up the intriguing opportunity to test modified gravity theories. This setup generalizes the notion of gravitational deflection and lensing, revealing novel phenomena in modified theories. Any non-minimal theory introduces effective mass terms for GWs, causing \textit{lens-induced dispersion} (LID), a frequency-dependent phase shift on the waveform. We compute GW dispersion in Einstein's general relativity (GR) for a spherical matter distribution, finding a small but non-zero phasing that is potentially accessible to next-generation detectors. We then extend our analysis to scalar-tensor theories, focusing on symmetron gravity as an example of screened theory, combining cosmological deviations and consistency with local gravity tests. We find enhanced GW dispersion in a large region of the symmetron parameter space, compared to both GR and Brans-Dicke theory. We argue that dispersion, associated to an effective mass for the metric fluctuations, can in some cases prevent the propagation of GWs through some astrophysical bodies, turning them into reflectors. Our analysis shows that the Earth becomes an efficient GW shield for a hitherto unconstrained region of the symmetron parameter space, leading to a $\sim 50\%$ fraction of events becoming unobservable or at least displaying a dramatic modification of the detector antenna response. The richness and universality of dispersive phenomena in non-minimal theories open a new avenue to test theories of dynamical dark-energy, relevant in light of recent observational results challenging the $Λ$CDM paradigm.
In a fully inhomogeneous, anisotropic cosmological simulation performed by solving Einstein's equations with numerical relativity, we find a local measurement of the effective Hubble parameter differs by less than 1\% compared to the global value. This variance is consistent with predictions from Newtonian gravity. We analyse the averaged local expansion rate on scales comparable to Type 1a supernova surveys, and find that local variance cannot resolve the tension between the \citet{riess2018b} and \citet{planck2018a} measurements.
We perform three-dimensional numerical relativity simulations of homogeneous and inhomogeneous expanding spacetimes, with a view towards quantifying non-linear effects from cosmological inhomogeneities. We demonstrate fourth-order convergence with errors less than one part in 10^6 in evolving a flat, dust Friedmann-Lemaitre-Roberston-Walker (FLRW) spacetime using the Einstein Toolkit within the Cactus framework. We also demonstrate agreement to within one part in 10^3 between the numerical relativity solution and the linear solution for density, velocity and metric perturbations in the Hubble …
In the framework of spatially averaged inhomogeneous cosmologies in classical general relativity, effective Einstein equations govern the dynamics of averaged scalar variables in a scale--dependent way. A particular cosmology may be characterized by a cosmic equation of state, closing the hierarchy of effective equations. In this context a natural candidate is provided by the Chaplygin gas, standing for a unified description of dark energy and dark matter. In this paper, we suppose that the inhomogeneous properties of matter and geometry obey the Chaplygin equation of state. The most extreme i…
In this paper, we have searched the existence of the similarity solution for plane symmetric inhomogeneous cosmological models in general relativity. The matter source consists of perfect fluid with proportionality relation between expansion scalar and shear scalar. The isovector fields of Einstein's field equation for the models under consideration are derived. A new class of exact solutions of Einstein's field equation have been obtained for inhomogeneous space-time. The physical behaviors and geometric aspects of the derived models have been discussed in detail.
The parameterised post-Newtonian (PPN) formalism has enabled stringent tests of static weak-field gravity in a theory-independent manner. Here we incorporate screening mechanisms of modified gravity theories into the framework by introducing an effective gravitational coupling and defining the PPN parameters as functions of position. To determine these functions we develop a general method for efficiently performing the post-Newtonian expansion in screened regimes. For illustration, we derive all the PPN functions for a cubic galileon and a chameleon model. We also analyse the Shapiro time del…
We present a new approach to coarse-graining of variables describing dust flow in GR. It is based on assigning quasi-local shear, twist and expansion to 2-dimensional surfaces with the help of isometric embeddings into the 3-dimensional Euclidean space and deriving the time evolution equations for them. In contrast to the popular Buchert's scheme it allows to coarse-grain tensorial quantities in a coordinate-independent way. The framework can be used to estimate backreaction in inhomogeneous cosmological models.
In this paper we investigate a class of solutions of Einstein equations for the plane-symmetric perfect fluid case with shear and vanishing acceleration. If these solutions have shear, they must necessarily be non-static. We examine the integrable cases of the field equations systematically. Among the cases with shear we find three classes of solutions.
A new class of solutions of Einstein field equations has been investigated for inhomogeneous cylindrically symmetric space-time with string source. To get the deterministic solution, it has been assumed that the expansion ($θ$) in the model is proportional to the eigen value $σ^{1}_{1}$ of the shear tensor $σ^{i}_{j}$. Certain physical and geometric properties of the models are also discussed.
We bring together two popular formalisms which generically parameterise deviations from General Relativity on astrophysical and cosmological scales, namely the parameterised post-Newtonian (PPN) formalism and the effective field theory (EFT) of dark energy and modified gravity. These separate formalisms are successfully applied to independently perform tests of gravity in their respective regimes of applicability on vastly different length scales. Nonlinear screening mechanisms indeed make it imperative to probe General Relativity across a wide range of scales. For a comprehensive interpretati…
The gravitational instability of inhomogeneities in the expanding universe is studied by the relativistic second-order approximation. Using the tetrad formalism we consider irrotational dust universes and get equations very similar to those given in the Lagrangian perturbation theory in Newtonian cosmology. Neglecting the cosmological constant and assuming a flat background model we give the solutions of the nonlinear dynamics of cosmological perturbations. We present the complete second-order solutions, which extend and improve earlier works.
For general relativistic spacetimes filled with an irrotational perfect fluid a generalized form of Friedmann's equations governing the expansion factor of spatially averaged portions of inhomogeneous cosmologies is derived. The averaging problem for scalar quantities is condensed into the problem of finding an `effective equation of state' including kinematical as well as dynamical `backreaction' terms that measure the departure from a standard FLRW cosmology. Applications of the averaged models are outlined including radiation-dominated and scalar field cosmologies (inflationary and dilaton/…
For general relativistic spacetimes filled with irrotational `dust' a generalized form of Friedmann's equations for an `effective' expansion factor $a_D (t)$ of inhomogeneous cosmologies is derived. Contrary to the standard Friedmann equations, which hold for homogeneous-isotropic cosmologies, the new equations include the `backreaction effect' of inhomogeneities on the average expansion of the model. A universal relation between `backreaction' and average scalar curvature is also given. For cosmologies whose averaged spatial scalar curvature is proportional to $a_D^{-2}$, the expansion law go…
While the use of numerical general relativity for modeling astrophysical phenomena and compact objects is commonplace, the application to cosmological scenarios is only just beginning. Here, we examine the expansion of a spacetime using the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formalism of numerical relativity in synchronous gauge. This work represents the first numerical cosmological study that is fully relativistic, non-linear and without symmetry. The universe that emerges exhibits an average Friedmann-Lemaïtre-Robertston-Walker (FLRW) behavior, however this universe also exhibits loca…
We modify Einstein General Relativity by adding non-dynamical scalar fields to account simultaneously for both dark matter and dark energy. The dark energy in this case can be distributed in-homogeneously even within horizon scales. Its inhomogeneities can contribute to the late time integrated Sachs-Wolfe effect, possibly removing some of the low multipole anomalies in the temperature fluctuations of the CMB spectrum. The presence of the inhomogeneous dark matter also influences structure formation in the universe.
In general, modified gravity theories are modifications or extensions of Einstein's general relativity. Some of them give rise to additional scalar degrees of freedom in Nature. If these scalar fields exist and are light enough, they should cause a gravity-like fifth force that could, in principle, exceed gravity in its strength. However, there are tight constraints on fifth forces from Solar System-based tests. Screening mechanisms are popular means for avoiding these constraints by suppressing a fifth force in regions of high environmental mass density but allowing for phenomenologically int…
We analyze the compatibility between the geometrodynamics and thermodynamics of a binary mixture of perfect fluids which describe inhomogeneous cosmological models. We generalize the thermodynamic scheme of general relativity to include the chemical potential of the fluid mixture with non-vanishing entropy production. This formalism is then applied to the case of Szekeres and Stephani families of cosmological models. The compatibility conditions turn out to impose symmetry conditions on the cosmological models in such a way that only the limiting case of the Friedmann-Robertson-Walker model re…
Gravitational wave (GW) observations provide insight into the gravity regime. These observations relies on the comparison of the data to the GWs model, which depends on the orbital evolution of the binary systems. In this paper, we study the orbital evolution of eccentric compact binaries within screened modified gravity, which is a kind of scalar-tensor theory with screening mechanisms. According to the Noether's theorem, from the theory's GW action, we compute the angular momentum flux both as a function of the fields in the theory and as a function of the multipole moments of a N-body syste…
We investigate effective equations governing the volume expansion of spatially averaged portions of inhomogeneous cosmologies in spacetimes filled with an arbitrary fluid. This work is a follow-up to previous studies focused on irrotational dust models (Paper I) and irrotational perfect fluids (Paper II) in flow-orthogonal foliations of spacetime. It complements them by considering arbitrary foliations, arbitrary lapse and shift, and by allowing for a tilted fluid flow with vorticity. As for the first studies, the propagation of the spatial averaging domain is chosen to follow the congruence o…
Adding a light scalar degree of freedom to General Relativity often induces a fifth force whose magnitude is strongly constrained by laboratory experiments and solar system tests. The Vainshtein screening mechanism ensures that the effects of this supplementary force are suppressed in dense environments. However, the field solution of theories exhibiting Vainshtein screening is only known in spherically symmetric situations. In this article we examine in different configurations the two-body potential energy of pointlike particles in a specific $P(X)$ theory with Vainshtein screening. We use i…
Testing gravity by binary pulsars nowadays becomes a key issue. Screened modified gravity is a kind of scalar-tensor theory with screening mechanism in order to satisfy the tight Solar System tests. In this paper, we investigate how the screening mechanism affects the orbital dynamics of binary pulsars, and calculate in detail the five post-Keplerian (PK) parameters in this theory. These parameters differ from those of general relativity (GR), and the differences are quantified by the scalar charges, which lead to the dipole radiation in this theory. We combine the observables of PK parameters…
In this work numerical methods for solving Einstein's equations are developed and applied to the study of inhomogeneous cosmological models. A two-dimensional computer code is described which implements two advanced numerical methods: LeVeque's multi-dimensional high-resolution integration scheme which allows accurate evolution of solutions containing discontinuities or steep gradients, and an adaptive mesh refinement (AMR) algorithm which enables the local resolution of a simulation to vary dynamically in response to the behaviour of the evolved solution. A family of hyperbolic formulations o…
We perturbatively construct asymptotically $\mathbb{R}^{1,3}\times\mathbb{T}^2$ black branes with multiple inhomogeneous directions and show that some of them are thermodynamically preferred over uniform branes in both the microcanonical and canonical ensembles. This demonstrates that, unlike five-dimensional black strings, the instability of some unstable black branes has a plausible endpoint that does not require a violation of cosmic censorship.
A new definition of coarse-grained quantities describing the dust flow in General Relativity is proposed. It assigns the coarse--grained expansion, shear and vorticity to finite-size comoving domains of fluid in a covariant, coordinate-independent manner. The coarse--grained quantities are all quasi-local functionals, depending only on the geometry of the boundary of the considered domain. They can be thought of as relativistic generalizations of simple volume averages of local quantities in a flat space. The procedure is based on the isometric embedding theorem for S^2 surfaces and thus requi…
Vacuum energy remains the simplest model of dark energy which could drive the accelerated expansion of the Universe without necessarily introducing any new degrees of freedom. Inhomogeneous vacuum energy is necessarily interacting in general relativity. Although the four-velocity of vacuum energy is undefined, an interacting vacuum has an energy transfer and the vacuum energy defines a particular foliation of spacetime with spatially homogeneous vacuum energy in cosmological solutions. It is possible to give a consistent description of vacuum dynamics and in particular the relativistic equatio…
We consider cosmological models where dark matter is charged under a dark Abelian gauge field. This new interaction is repulsive and competes with gravity on large scales and in the dynamics of galaxies and clusters. We focus on non-linear models of dark electrodynamics where the effects of the new force are screened within a K-mouflage radius that helps avoiding traditional constraints on charged dark matter models. We discuss the background cosmology of these models in a Newtonian approach and show the equivalence with relativistic Lemaître models where an inhomogeneous pressure due to the e…
We examine in this paper the possibility of finding exact solutions for Teleparallel Gravity (TG) of the type of spherically symmetric Lema\^ıtre-Tolman-Bondi (LTB) dust models. We apply to the LTB metric, as obtained from the Schwarzschild solution in General Relativity, the formalism of Teleparallel Gravity in its extension to $f(T,B)$ models. An exact LTB solution is obtained that is compatible with a specific $f(T,B)$ model that seems to be appropriate to fit observations when applied to standard spatially flat Robertson-Walker geometry.
Scalar-tensor gravity, with the screening mechanisms to avoid the severe constraints of the fifth force in the Solar System, can be described with a unified theoretical framework, the so-called screened modified gravity (SMG). Within this framework, in this paper we calculate the waveforms of gravitational-waves (GWs) emitted by inspiral compact binaries, which include four polarization modes, the plus $h_{+}$, cross $h_{\times}$, breathing $h_{b}$, and longitudinal $h_{L}$ modes. The scalar polarizations $h_b$ and $h_L$ are both caused by the scalar field of SMG, and satisfy a simple linear r…
Gravitational theories differing from General Relativity may explain the accelerated expansion of the Universe without a cosmological constant. However, to pass local gravitational tests, a "screening mechanism" is needed to suppress, on small scales, the fifth force driving the cosmological acceleration. We consider the simplest of these theories, i.e. a scalar-tensor theory with first-order derivative self-interactions, and study isolated (static and spherically symmetric) non-relativistic and relativistic stars. We produce screened solutions and use them as initial data for non-linear numer…
The screened modified gravity (SMG) is a unified theoretical framework, which describes the scalar-tensor gravity with screening mechanism. Based on the gravitational-wave (GW) waveform derived in our previous work \citep{liu2018waveforms}, in this article we investigate the potential constraints on SMG theory through the GW observation of the future space-borne GW detectors, including LISA, TianQin and Taiji. We find that, for the EMRIs consisting of a massive black hole and a neutron star, if the EMRIs are at Virgo cluster, the GW signals can be detected by the detectors at quite high signif…
When do the nonlinear effects of general relativity matter in astrophysical situations? They are obviously relevant for very compact sources of the gravitational field, such as neutron stars or black holes. In this paper I discuss another, less obvious situation, in which large relativistic effects may arise due to a complicated, multiscale structure of the matter distribution. I present an exact solution with an inhomogeneous energy density distribution in the form of a hierarchy of nested voids and overdensities of various sizes, extending from the homogeneity scale down to arbitrary small s…
The applications of numerical relativity to cosmology are on the rise, contributing insight into such cosmological problems as structure formation, primordial phase transitions, gravitational-wave generation, and inflation. In this paper, I present the infrastructure for the computation of inhomogeneous dust cosmologies which was used recently to measure the effect of nonlinear inhomogeneity on the cosmic expansion rate. I illustrate the code's architecture, provide evidence for its correctness in a number of familiar cosmological settings, and evaluate its parallel performance for grids of up…
This review was given at the 65th birthday meeting of D.W. Sciama, The Renaissance of General Relativity and Cosmology, to be published by Cambridge University Press. It presents progress in the understanding of non-standard relativistic cosmologies during Sciama's career, organized by the areas of application rather than the mathematical types of the models.
In this paper we explore the possibility to find exact solutions for Teleparallel Gravity (TG) of the type of spherically symmetric Lema\^ıtre-Tolman-Bondi (LTB) dust models. We apply to the LTB metric the formalism of Teleparallel Gravity in its extension to $f(T,B)$ models, which can be seen it as the analagous from the Schwarzschild solution in General Relativity. An exact LTB solution is obtained which is compatible with a specific $f(T,B)$ model whose observational constraints are cosmological viable in a standard spatially flat Robertson-Walker geometry.
The splashback radius $r_\mathrm{sp}$ has been identified in cosmological $N$-body simulations as an important scale associated with gravitational collapse and the phase-space distribution of recently accreted material. We employ a semi-analytical approach to study the spherical collapse of dark matter haloes in symmetron gravity and provide insights into how the phenomenology of splashback is affected. The symmetron is a scalar-tensor theory of gravity which exhibits a screening mechanism whereby higher-density regions are screened from the effects of a fifth force. In this model, we find tha…
A new family of spherically symmetric inhomogeneous solutions of Brans-Dicke gravity is generated using the Fonarev solution of general relativity as a seed and a map from the Einstein to the Jordan conformal frame. The Brans-Dicke scalar field self-interacts with a power-law or inverse power-law potential in the Jordan frame. This 4-parameter family of geometries, which is dynamical and asymptotically Friedmann-Lemaitre-Robertson-Walker, contains as special cases two previously known classes of solutions and solves also the field equations of $f(R)=R^n$ gravity
We investigate the existence of inhomogeneous Szekeres spacetimes in Einstein-æther theory. We show that inhomogeneous solutions which can be seen as extension of the Szekeres solutions existing in Einstein-æther gravity only for a specific relation between the dimensionless coefficients which defines the coupling between the æther filed with gravity. The two Szekeres classes of solutions are derived. Also a class of inhomogeneous FLRW-like spacetimes is allowed by the theory for arbitrary values of the dimensionless coefficients of the æther field. The stability of the solutions obtained is p…
The dark energy universe equation of state (EOS) with inhomogeneous,Hubble parameter dependent term is considered. The motivation to introduce such a term comes from time-dependent viscosity considerations and modifications of general relativity. For several explicit examples of such EOS it is demonstrated how the type of future singularity changes, how the phantom epoch emerges and how crossing of phantom barrier occurs. Similar cosmological regimes are considered for the universe with two interacting fluids and for universe with implicit EOS. For instance, the crossing of phantom barrier is …
Scalar-tensor theories leaving significant modifications of gravity at cosmological scales rely on screening mechanisms to recover General Relativity (GR) in high-density regions and pass stringent tests with astrophysical objects. Much focus has been placed on the signatures of such modifications of gravity on the propagation of gravitational waves (GWs) through cosmological distances while typically assuming their emission from fully screened regions with the wave generation strictly abiding by GR. Here, we closely analyse the impact of screening mechanisms on the inspiral GW waveforms from …
We present exact non-singular bounce solutions of general relativity in the presence of a positive cosmological constant and an electromagnetic field, without any exotic matter. The solutions are distinguished by being spatially inhomogeneous in one direction, while they can also contain non-trivial electromagnetic field lines. The inhomogeneity may be substantial, for instance, there can be one bounce in one region of the universe and two bounces elsewhere. Since the bounces are followed by a phase of accelerated expansion, the metrics described here also permit the study of (geodesically com…
We consider a Lemaitre - Tolman - Bondi type space-time in Einstein gravity with the Gauss-Bonnet combination of quadratic curvature terms, and present exact solution in closed form. It turns out that the presence of the coupling constant of the Gauss-Bonnet terms alpha > 0 completely changes the causal structure of the singularities from the analogous general relativistic case. The gravitational collapse of inhomogeneous dust in the five-dimensional Gauss-Bonnet extended Einstein equations leads to formation of a massive, but weak, timelike singularity which is forbidden in general relativity…
Why is the Universe so homogeneous and isotropic? We summarize a general study of a $γ$-law perfect fluid alongside an inhomogeneous, massless scalar gauge field (with homogeneous gradient) in anisotropic spaces with General Relativity. The anisotropic matter sector is implemented as a $j$-form (field-strength level), where $j\,\in\,\{1,3\}$, and the spaces studied are Bianchi space-times of solvable type. Wald's no-hair theorem is extended to include the $j$-form case. We highlight three new self-similar space-times: the Edge, the Rope and Wonderland. The latter solution is so far found to ex…
The evolution of inhomogeneous space-times composed of uncharged fermions is studied for Szekeres metrics which have no Killing vectors, in general. Using the Einstein-Cartan theory to include the effects of (intrinsic) matter spin in General Relativity, the dynamics of a perfect fluid with non-null spin degrees of freedom is considered. It is shown that, if the matter is composed by effective dust and certain constraints on the initial data are verified, a singularity will not form. Various special cases are discussed, such as Lemaître-Tolman-Bondi and Bianchi I space-times, where the results…
$f(R)$ is a paradigmatic modified gravity theory that typifies extensions to General Relativity with new light degrees of freedom and hence screened fifth forces between masses. These forces produce observable signatures in galaxy morphology, caused by a violation of the weak equivalence principle due to a differential impact of screening among galaxies' mass components. We compile statistical datasets of two morphological indicators -- offsets between stars and gas in galaxies and warping of stellar disks -- and use them to constrain the strength and range of a thin-shell-screened fifth force…
Additional scalar fields from scalar-tensor, modified gravity or higher dimensional theories beyond general relativity may account for dark energy and the accelerating expansion of the Universe. These theories have lead to proposed models of screening mechanisms, such as chameleon and symmetron fields, to account for the tight experimental bounds on fifth-force searches. Cold atom systems have been very successfully used to constrain the parameters of these screening models, and may in future eliminate the interesting parameter space of some models entirely. In this paper, we show how to manip…
Bending of light rays by gravitational sources is one of the first evidences of the general relativity. When the gravitational souce is a stationary massive object such as a black hole, the bending angle has an integral representation, from which various series expansions in terms of the parameters of orbit and the background spacetime has been derived. However, it is not clear that it has any analytic expansion. In this paper, we show that such an analytic expansion can be obtained for the case of a Schwarzschild black hole by solving an inhomogeneous Picard-Fuchs equation, which has been app…
Self-similar models are important in general relativity and other fundamental theories. In this paper we shall discuss the ``similarity hypothesis'', which asserts that under a variety of physical circumstances solutions of these theories will naturally evolve to a self-similar form. We will find there is good evidence for this in the context of both spatially homogenous and inhomogeneous cosmological models, although in some cases the self-similar model is only an intermediate attractor. There are also a wide variety of situations, including critical pheneomena, in which spherically symmetric…
We obtain the equations of motions of the $f(T)$ theory considering the Lemaître-Tolman-Bondi's metric for a set of diagonal and non-diagonal tetrads. In the case of diagonal tetrads the equations of motion of the $f(T)$ theory impose a constant torsion or the same equations of the General Relativity, while in the case of non-diagonal set the equations are quite different from that obtained in GR. We show a simple example of an universe dominated by the matter for the two cases. The comparison of the mass in the non-diagonal case shows a sort of increased with respect to the diagonal one. We a…
We present some results regarding metric perturbations in general relativity and other metric theories of gravity. In particular, using the Newman Penrose variables, we write down and discuss the equations which govern tensor field perturbations of ranks $0, \pm 1$ and $\pm 2$ (scalar,vector,tensor bosonic perturbations) over certain space-times that admit specific background metrics expressible in isotropic coordinates. Armed with these equations, we are able to develop the Hadamard series which can be associated with the fundamental solution of the equations, wherein we introduce an inhomoge…
We present and discuss two different possibilities to construct position space version for Magueijo-Smolin (MS) doubly special relativity proposal. The first possibility is to start from ordinary special relativity and then to define conserved momentum in special way. It generates MS invariant as well as nonlinear MS transformations on the momentum space, leading to consistent picture for one-particle sector of the theory. The second possibility is based on the following observation. Besides the nonlinear MS transformations, the MS energy-momentum relation is invariant also under some inhomoge…
The presence and evolution of apparent horizons in a two-parameter family of spherically symmetric, time-dependent solutions of Brans-Dicke gravity are analyzed. These solutions were introduced to model space- and time-varying gravitational couplings and are supposed to represent central objects embedded in a spatially flat universe. We find that the solutions possess multiple evolving apparent horizons, both black hole horizons covering a central singularity and cosmological ones. It is not uncommon for two of these horizons to merge, leaving behind a naked singularity covered only by a cosmo…
The Bianchi IX model has been used often to investigate the structure close to singularities of general relativity. Its classical chaos is expected to have, via the BKL scenario, implications even for the approach to general inhomogeneous singularities. Thus, it is a popular model to test consequences of modifications to general relativity suggested by quantum theories of gravity. This paper presents a detailed proof that modifications coming from loop quantum gravity lead to a non-chaotic effective behavior. The way this is realized, independently of quantization ambiguities, suggests a new l…
