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 numerical evolutions in spherical symmetry. We find that these solutions are stable under large initial perturbations, as long as they do not cause gravitational collapse. When gravitational collapse is triggered, the characteristic speeds of the scalar evolution equation diverge, even before apparent black-hole or sound horizons form. This casts doubts on whether the dynamical evolution of screened stars may be predicted in these effective field theories.
In this work, we illustrate through a simple example the possibility of testing the chameleon screening mechanism in the Solar System using the forthcoming LISA Pathfinder mission around gravitational saddle points. We find distinctive tidal stress signatures for such models and consider the potential for constraints.
We study nonlinear effects of perturbations around a cosmological background in projected massive gravity, which admits self-accelerating solutions in an open FLRW universe. Using the zero-curvature scaling limit, we derive nonlinear equations containing all the relevant terms on subhorizon scales. We find that the solution for a scalar graviton vanishes completely for all scales, which agrees with the linear perturbation analysis in the previous study. In addition, the effects on the gravitational potential due to the next order perturbation are strongly suppressed within the horizon. Therefo…
Extending general relativity by adding extra degrees of freedom is a popular approach for explaining the accelerated expansion of the Universe and to build high energy completions of the theory of gravity. The presence of such new degrees of freedom is, however, tightly constrained from several observations and experiments that aim to test general relativity in a wide range of scales. The viability of a given modified theory of gravity, therefore, strongly depends on the existence of a screening mechanism that suppresses the extra degrees of freedom. We perform simulations, and find that waves…
Scalar fields are crucial components in high energy physics and extensions of General Relativity. The fact they are not observed in the solar system may be due to a mechanism which screens their presence in high dense regions. We show how observations of the ellipticity of galaxy clusters can discriminate between models with and without scalar fields and even between different screening mechanisms. Using nowadays X-ray observations we put novel constraints on the different models.
We discuss a possible mechanism to screen a cosmological constant in non-local gravity. We find that in a simple model of of non-local gravity with the Lagrangian of the form, $R+f(\Box^{-1}R)-2Λ$ where $f(X)$ is a quadratic function of $X$, there is a flat spacetime solution despite the presence of the cosmological constant $Λ$. Unfortunately, however, we also find that this solution contains a ghost in general. Then we discuss the condition to avoid a ghost and find that one can avoid it only for a finite range of `time'. Nevertheless our result suggests the possibility of solving the cosmol…
Modified gravity theories with an effective Newton constant that varies over cosmological timescales generally predict a different gravitational wave luminosity distance than General Relativity. While this holds for a uniform variation, we show that if locally screened at the source and at the observer as required to pass stringent astrophysical tests of gravity, the General Relativistic distance is restored. In the absence of such a screening, the same effect must modify electromagnetic luminosity distances inferred from supernovae Type Ia, to the extent that the effects can cancel in the com…
The Brans-Dicke theory of gravity is one of the oldest ideas to extend general relativity by introducing a non-minimal coupling between the scalar field and gravity. The Solar System tests put tight constraints on the theory. In order to evade these constraints, various screening mechanisms have been proposed. These screening mechanisms allow the scalar field to couple to matter as strongly as gravity in low density environments while suppressing it in the Solar System. The Vainshtein mechanism, which is found in various modified gravity models such as massive gravity, braneworld models and sc…
A case of non-minimal couplings between gravity and electromagnetic fields is presented. The field equations are worked out in the language of exterior differential forms. An exact charge screening class of solutions is given with a specific discussion on the polarisation and magnetisation of spacetime. The consequences of non-minimal couplings to gravity are examined.
We offer predictions of symmetron modified gravity in the neighborhood of realistic dark matter halos. The predictions for the fifth force are obtained by solving the nonlinear symmetron equation of motion in the spherical NFW approximation. In addition, we compare the three major known screening mechanisms: Vainshtein, Chameleon, and Symmetron around such dark matter sources, emphasizing the significant differences between them and highlighting observational tests which exploit these differences. Finally, we demonstrate the host halo environmental screening effect ("blanket screening") on sma…
Scalar forces "screened" by the Vainshtein mechanism may hold the key to understanding the cosmological expansion of our universe, while predicting new and exciting features in the interaction between massive bodies. Here we explore the dynamics of the Vainshtein screening mechanism, focusing on the decoupling limit of the DGP braneworld scenario and dRGT massive gravity. We show that there is a vast set of initial conditions whose evolution is well defined and which are driven to the static, screening solutions of these theories. Screening solutions are stable and behave coherently under smal…
It is shown that extensions to General Relativity, which introduce a strongly coupled scalar field, can be viable if the interaction has a non-conformal form. Such disformal coupling depends upon the gradients of the scalar field. Thus, if the field is locally static and smooth, the coupling becomes invisible in the solar system: this is the disformal screening mechanism. A cosmological model is considered where the disformal coupling triggers the onset of accelerated expansion after a scaling matter era, giving a good fit to a wide range of observational data. Moreover, the interaction leaves…
We investigate cosmological dynamics and screening mechanism of the Dirac-Born-Infeld (DBI) Galileon model. The model has been divided into two regimes, one has positive signs in front of scalar field kinetic terms so-called the DBI galileon, another one has negative signs and it is dubbed as the DBIonic galileon. We find de Sitter solution and evolution of the Universe starting from radiation dominated era to late-time accelerated expansion in the DBI galileon model without the presence of potential term. In one of the attractors, the ghost and Laplacian instabilities vanishes for the whole e…
We study a new model of Energy-Momentum Squared Gravity (EMSG), called Energy-Momentum Log Gravity (EMLG), constructed by the addition of the term $f(T_{μν}T^{μν})=α\ln(λ\,T_{μν}T^{μν})$, envisaged as a correction, to the Einstein-Hilbert action with cosmological constant $Λ$. The choice of this modification is made as a specific way of including new terms in the right-hand side of the Einstein field equations, resulting in constant effective inertial mass density and, importantly, leading to an explicit exact solution of the matter energy density in terms of redshift. We look for viable cosmo…
We investigate de Sitter solutions in non-local gravity as well as in non-local gravity with Lagrange constraint multiplier. We examine a condition to avoid a ghost and discuss a screening scenario for a cosmological constant in de Sitter solutions. Furthermore, we explicitly demonstrate that three types of the finite-time future singularities can occur in non-local gravity and explore their properties. In addition, we evaluate the effective equation of state for the universe and show that the late-time accelerating universe may be effectively the quintessence, cosmological constant or phantom…
The distinction between modified gravity and quintessence or dynamical dark energy is difficult. Many models of modified gravity are equivalent to models of coupled quintessence by virtue of variable transformations. This makes an observational differentiation between modified gravity and dark energy very hard. For example, the additional scalar degree of freedom in $f(R)$-gravity or non-local gravity can be interpreted as the cosmon of quintessence. Nevertheless, modified gravity can shed light on questions of interpretation, naturalness and simplicity. We present a simple model where gravity…
We review finite-time future singularities in modified gravity. We reconstruct an explicit model of modified gravity realizing a crossing of the phantom divide and show that the Big Rip singularity appears in the modified gravitational theory. It is also demonstrated that the (finite-time) Big Rip singularity in the modified gravity is transformed into the infinite-time singularity in the corresponding scalar field theory obtained through the conformal transformation. Furthermore, we study several models of modified gravity which produce accelerating cosmologies ending at the finite-time futur…
In modified gravity, the one-loop matter power spectrum exhibits an ultraviolet divergence as shown in the framework of the degenerate higher-order scalar-tensor theory. To address this problem, we extend the effective field theory of large scale structure to modified gravity theories. We find that new counterterms appear and renormalize the ultraviolet divergence as a natural consequence of non-linearity in the modified Poisson equation. The renormalized one-loop matter power spectrum is useful to test modified gravity theories by comparing to observations.
The second law and the generalized second law of thermodynamics in cosmology in the framework of the modified Gauss-Bonnet theory of gravity are investigated. The conditions upon which these laws hold are derived and discussed.
Screened modified gravity (SMG) and Brans-Dicke (BD) gravity are typical examples of scalar-tensor theories with and without screening mechanisms, which can suppress the scalar field in dense regions. In this paper, we investigate the tests of time-varying gravitational constant $G$, gravitational dipole radiation, and Nordtvedt effect in BD and SMG theories, respectively. We place new constraints on these theories by combining Cassini experiment, lunar laser ranging (LLR) measurements, and pulsar observations from PSRs J1738$+$0333 and J0348$+$0432. We find that screening mechanism has import…
We propose a simple and computationally fast method for performing N-body simulations for a large class of modified gravity theories with a screening mechanism such as chameleons, symmetrons and galileons. By combining the linear Klein-Gordon equation with a screening factor, calculated from analytical solutions of spherical symmetric configurations, we obtain a modified field equation whose solution is exact in the linear regime while at the same time takes screening into account on non-linear scales. The resulting modified field equation remains linear and can be solved just as quickly as th…
We consider nonlocal modified Einstein gravity without matter, where nonlocal term has the form $P(R) F(\Box) Q(R)$. For this model, in this paper we give the derivation of the equations of motion in detail. This is not an easy task and presented derivation should be useful to a researcher who wants to investigate nonlocal gravity. Also, we present the second variation of the related Einstein-Hilbert modified action and basics of gravity perturbations.
The symmetron model is a scalar-tensor theory of gravity with a screening mechanism that suppresses the effect of the symmetron field at high densities characteristic of the solar system and laboratory scales but allows it to act with gravitational strength at low density on the cosmological scale. We elucidate the screening mechanism by showing that in the quasi-static Newtonian limit there are precise analogies between symmetron gravity and electrostatics for both strong and weak screening. For strong screening we find that large dense bodies behave in a manner analogous to perfect conductor…
We consider some cosmological aspects of nonlocal modified gravity with $Λ$ term, where nonlocality is of the type $R \mathcal{F}(\Box) R$. Using ansatz of the form $\Box R = r R +s,$ we find a few a(t) nonsingular bounce cosmological solutions for all three values of spatial curvature parameter k. We also discuss this modified gravity model from F(R) theory point of view.
We systematically review some standard issues and also the latest developments of modified gravity in cosmology, emphasizing on inflation, bouncing cosmology and late-time acceleration era. Particularly, we present the formalism of standard modified gravity theory representatives, like $F(R)$, $F(\mathcal{G})$ and $F(T)$ gravity theories, but also several alternative theoretical proposals which appeared in the literature during the last decade. We emphasize on the formalism developed for these theories and we explain how these theories can be considered as viable descriptions for our Universe.…
We study the stability of the Vainshtein screening solution of the massive/bi-gravity based on the massive nonlinear sigma model as the effective action inside the Vainshtein radius. The effective action is obtained by taking the $Λ_2$ decoupling limit around a curved spacetime. First we derive a general consequence that any Ricci flat Vainshtein screening solution is unstable when we take into account the excitation of the scalar graviton only. This instability suggests that the nonlinear excitation of the scalar graviton is not sufficient to obtain a successful Vainshtein screening in massiv…
In this paper we study long range modifications of gravity in the consistent framework of bigravity, which introduces a second massive spin-2 field and allows to continuously interpolate between the regime of General Relativity (mediated by a massless spin-2 field) and massive gravity (mediated by a massive spin-2 field). In particular we derive for the first time the equations for light deflection in this framework and study the effect on the lensing potential of galaxy clusters. By comparison of kinematic and lensing mass reconstructions, stringent bounds can be set on the parameter space of…
Viable modifications of gravity on cosmological scales predominantly rely on screening mechanisms to recover Einstein's Theory of General Relativity in the Solar System, where it has been well tested. A parametrisation of the effects of such modifications in the spherical collapse model is presented here for the use of modelling the modified nonlinear cosmological structure. The formalism allows an embedding of the different screening mechanisms operating in scalar-tensor theories through large values of the gravitational potential or its first or second derivatives as well as of linear suppre…
We review thermodynamic properties of modified gravity theories such as $F(R)$ gravity and $f(T)$ gravity, where $R$ is the scalar curvature and $T$ is the torsion scalar in teleparallelism. In particular, we explore the equivalence between the equations of motion for modified gravity theories and the Clausius relation in thermodynamics. In addition, thermodynamics of the cosmological apparent horizon is investigated in $f(T)$ gravity. We show both equilibrium and non-equilibrium descriptions of thermodynamics. It is demonstrated that the second law of thermodynamics in the universe can be met…
We investigate the Hamiltonian structure of a class of gravitational theories whose actions are linear in the lapse function. We derive the necessary and sufficient condition for a theory in this class to have two or less local physical degrees of freedom. As an application we then find several concrete examples of modified gravity theories in which the total number of local physical degrees of freedom in the gravity sector is two.
We investigate the efficiency of screening mechanisms in the hybrid metric-Palatini gravity. The value of the field is computed around spherical bodies embedded in a background of constant density. We find a thin shell condition for the field depending on the background field value. In order to quantify how the thin shell effect is relevant, we analyze how it behaves in the neighborhood of different astrophysical objects (planets, moons or stars). We find that the condition is very well satisfied except only for some peculiar objects. Furthermore we establish bounds on the model using data fro…
We test the subclasses of Horndeski gravity without Vainshtein mechanism in the strong field regime of binary pulsars. We find the rate of energy losses via the gravitational radiation predicted by such theories and compare our results with observational data from quasi-circular binaries PSR J1738+0333, PSR J0737-3039, PSR J1012+5307. In addition, we consider few specific cases: the hybrid metric-Palatini f(R)-gravity and massive Brans-Dicke theory.
Screened modified gravity (SMG) is a kind of scalar-tensor theory with screening mechanisms, which can suppress the fifth force in dense regions and allow theories to evade the solar system and laboratory tests. In this paper, we investigate how the screening mechanisms in SMG affect the gravitational radiation damping effects, calculate in detail the rate of the energy loss due to the emission of tensor and scalar gravitational radiations, and derive their contributions to the change in the orbital period of the binary system. We find that the scalar radiation depends on the screened paramete…
We investigate the environment dependence of dark matter halos in the symmetron modified gravity scenario. The symmetron is one of three known mechanisms for screening a fifth-force and thereby recovering General Relativity in dense environments. The effectiveness of the screening depends on both the mass of the object and the environment it lies in. Using high-resolution N-body simulations we find a significant difference, which depends on the halos mass and environment, between the lensing and dynamical masses of dark matter halos similar to the f(R) modified gravity. The symmetron can howev…
We explicitly show that the equations of motion for modified gravity theories of $F(R)$-gravity, the scalar-Gauss-Bonnet gravity, $F(\mathcal{G})$-gravity and the non-local gravity are equivalent to the Clausius relation in thermodynamics. In addition, we discuss the relation between the expression of the entropy and the contribution from the modified gravity as well as the matter to the definition of the energy flux (heat).
This paper scrutinises the tenability of a strict conceptual distinction between space(time) and matter via the lens of the debate between modified gravity and dark matter. In particular, we consider Berezhiani and Khoury's novel 'superfluid dark matter theory' (SFDM) as a case study. Two families of criteria for being matter and being spacetime, respectively, are extracted from the literature. Evaluation of the new scalar field postulated by SFDM according to these criteria reveals that it is as much (dark) matter as anything could possibly be, but also$-$below the critical temperature for su…
In the frameworks of the effective field theory of metric supplemented by some distinct dynamical coordinates parametrized, in turn, by a scalar quartet -- the so-called quartet-metric gravity -- the extension of tensor gravity through a massive scalar graviton in addition to the massless tensor one is consistently exposed. The field equations for the two realizations of such an extension originating from the classically equivalent prototype theories - General Relativity (GR) and its Weyl transverse (WTDiff) alternative - are derived and argued to be, generally, non-equivalent, with the pure-g…
We propose a generalization of Chern-Simons (CS) modified gravity in first-order formalism. CS modified gravity action has a term that comes from the chiral anomaly which is Pontryagin invariant. First-order CS modified gravity is a torsional theory and in a space-time with torsion the chiral anomaly includes a torsional topological term called Nieh-Yan invariant. We generalize the CS modified gravity by adding the Nieh-Yan term to the action and find the effective theory. We compare the generalized theory with the first-order CS modified gravity and comment on the similarities and differences…
Long range scalar fields with a coupling to matter appear to violate known bounds on gravitation in the solar system and the laboratory. This is evaded thanks to screening mechanisms. In this short review, we shall present the various screening mechanisms from an effective field theory point of view. We then investigate how they can and will be tested in the laboratory and on astrophysical and cosmological scales.
We provide a cosmological test of modified gravity with two tensorial degrees of freedom and no extra propagating scalar mode. The theory of gravity we consider admits a cosmological model that is indistinguishable from the $Λ$CDM model at the level of the background evolution. The model has a single modified-gravity parameter $β$, the effect of which can be seen in linear perturbations, though no extra scalar mode is propagating. Using the Boltzmann code modified to incorporate the present model, we derive the constraints $-0.047 < β< -0.028$ at 68$\%$ confidence from Planck CMB data. Since o…
We consider a nonminimally coupled curvature-matter gravity theory at the Solar System scale. Both a fifth force of Yukawa type and a further non-Newtonian extra force that arises from the nonminimal coupling are present in the solar interior and in the solar atmosphere up to interplanetary space. The extra force depends on the spatial gradient of space-time curvature R. The conditions under which the effects of such forces can be screened by the chameleon mechanism and be made consistent with Cassini measurement of PPN parameter $γ$ are examined. This consistency analysis requires a specific …
We construct a generalization of the standard $Λ$CDM model, wherein we simultaneously replace the spatially flat Robertson-Walker metric with its simplest anisotropic generalization (LRS Bianchi I metric), and couple the cold dark matter to the gravity in accordance with the energy-momentum squared gravity (EMSG) of the form $f(T_{μν}T^{μν})\propto T_{μν}T^{μν}$. These two modifications -- namely, two new stiff fluid-like terms of different nature -- can mutually cancel out, i.e., the shear scalar can be screened completely, and reproduce mathematically exactly the same Friedmann equation of t…
We develop Hamiltonian formalism for Lagrange Multiplier Modified Gravity. We further calculate the Poisson brackets between constraints and we show that they coincide with the algebra of constraints in Hamiltonian formulation of General Relativity.
Inspired by Verlinde's idea, some modified versions of entropic gravity have appeared in the literature. Extending them in a unified formalism, we derive the generalized gravitational equations accordingly. From gravitational equations, the energy-momentum conservation law and cosmological equations are investigated. The covariant conservation law of energy-momentum tensor severely constrains viable modifications of entropic gravity. A discrepancy arises when two independent methods are applied to the homogeneous isotropic universe, posing a serious challenge to modified models of entropic gra…
Many theories of modified gravity, including the well studied Horndeski models, are characterized by a screening mechanism that ensures that standard gravity is recovered near astrophysical bodies. In a recently introduced class of gravitational theories that goes beyond Horndeski, it has been found that new derivative interactions lead to a partial breaking of the Vainshtein screening mechanism inside any gravitational source, although not outside. We study the impact of this new type of deviation from standard gravity on the density profile of a spherically symmetric matter distribution, in …
We study all four types of finite-time future singularities emerging in late-time accelerating (effective quintessence/phantom) era from $\mathcal{F}(R,G)$-gravity, where $R$ and $G$ are the Ricci scalar and the Gauss-Bonnet invariant, respectively. As an explicit example of $\mathcal{F}(R,G)$-gravity, we also investigate modified Gauss-Bonnet gravity, so-called $F(G)$-gravity. In particular, we reconstruct the $F(G)$-gravity and $\mathcal{F}(R,G)$-gravity models where accelerating cosmologies realizing the finite-time future singularities emerge. Furthermore, we discuss a possible way to cure…
Gravitational instability in classical Jeans theory, General Relativity, and modified gravity is considered. The background density increase leads to a faster growth of perturbations in comparison with the standard theory. The transition to the Newtonian gauge in the case of coordinate dependent background metric functions is studied. For modified gravity a new high frequency stable solution is found.
We show that field equations of some typical modified gravity theories can be recast as thermodynamic first law on dynamical holographic screens. The thermodynamic second law are also presented.
We present a general parallelized and easy-to-use code to perform numerical simulations of structure formation using the COLA (COmoving Lagrangian Acceleration) method for cosmological models that exhibit scale-dependent growth at the level of first and second order Lagrangian perturbation theory. For modified gravity theories we also include screening using a fast approximate method that covers all the main examples of screening mechanisms in the literature. We test the code by comparing it to full simulations of two popular modified gravity models, namely $f(R)$ gravity and nDGP, and find go…
We explore a new horizon of modified gravity from the viewpoint of the particle physics. As a concrete example, we take the $F(R)$ gravity to raise a question: can a scalar particle ("scalaron") derived from the $F(R)$ gravity be a dark matter candidate? We place the limit on the parameter in a class of $F(R)$ gravity model from the constraint on the scalaron as a dark matter. The role of the screening mechanism and compatibility with the dark energy problem are addressed.
In the recent years, a host of modified gravity models have been proposed as alternatives to the dark energy. A quantum theory of gravity also requires to modify `General Theory of Relativity'. In the present article, we consider five different modified theories of gravity, and compare inflationary parameters with recent data sets released by two Planck collaboration teams. Our analysis reveals that the scalar-tensor theory of gravity is the best alternative.
We consider the modified gravity whose action represents itself as a sum of the usual Einstein-Hilbert action and the gravitational Chern-Simons term and show that the Gödel metric solves the modified equations of motion, thus proving that the closed timelike curves whose presence is characteristic for the Gödel solution are not forbidden in the case of the Chern-Simons modified gravity as well.
In this work, we have considered the Ricci dark energy model, where the energy density of the universe is proportional to the Ricci scalar curvature, in the dynamic Chern-Simons modified gravity. We show that in this context the evolution of the scale factor is similar to that displayed by the modified Chaplygin gas.
In this work, we study the large scale structure formation in the modified gravity in the framework of Palatini formalism and compare the results with the equivalent smooth dark energy models as a tool to distinguish between these models. Through the inverse method, we reconstruct the dynamics of universe, modified gravity action and the structure formation indicators like the screened mass function and gravitational slip parameter. Consequently, we extract the matter density power spectrum for these two models in the linear regime and show that the modified gravity and dark energy models pred…
While quantum gravity is not solved yet, a screening mass for the graviton remains theoretically possible. If such a mass would screen gravity at distances of the order of the cluster galaxy radius, it could account for the universe expansion. The modified Newtonian dynamics model also could be related to a screening graviton mass at inter-galactic scales. Moreover, massive spin-2 theories constitute a very active theoretical topic. We briefly show how the very recent LIGO gravitational wave observation GW150914, emitted by a binary black hole merger distant $\sim 1.3 \times 10^9$ ly from the …
The Horndeski theory of gravity is known as the most general scalar-tensor theory with second-order field equations. Recently, it was demonstrated by Gleyzes et al. that the Horndeski theory can further be generalized in such a way that although field equations are of third order, the number of propagating degrees of freedom remains the same. We study small-scale gravity in the generalized Horndeski theory, focusing in particular on an impact of the new derivative interaction beyond Horndeski on the Vainshtein screening mechanism. In the absence of the quintic galileon term and its generalizat…
The modified gravity (MOG) theory is applied to the gravitational wave binary merger GW190814 to demonstrate that the modified Tolman-Oppenheimer-Volkoff equation for a neutron star can produce a mass $M=2.6 -2.7 M_\odot$, allowing for the binary secondary component to be identified as a heavy neutron star in the hypothesized mass gap $2.5 - 5 M_\odot$.
The cosmological phenomenology of gravity is typically studied in two limits: relativistic perturbation theory (on large scales) and Newtonian gravity (required for smaller, non-linear, scales). Traditional approaches to model-independent modified gravity are based on perturbation theory, so do not apply on non-linear scales. Future surveys such as Euclid will produce significant data on both linear and non-linear scales, so a new approach is required to constrain model-independent modified gravity by simultaneously using all of the data from these surveys. We use the higher order equations fr…
