We study a theory of minimally modified gravity called cuscuton/VCDM that propagates only two gravitational degrees of freedom. Despite being apparently different from general relativity (GR), it is in principle possible that this theory might be obtained via a field redefinition starting from the GR action. This would make the vacuum theory equivalent to GR and the theory would differ from GR only in the presence of matter. In this paper, studying the dispersion relation of gravitational waves and the dynamics of the Bianchi-I universe, we prove that such a field redefinition does not exist and that the theory differs from GR already in vacuum.
Traditional derivations of general relativity from the graviton degrees of freedom assume space-time Lorentz covariance as an axiom. In this essay, we survey recent evidence that general relativity is the unique spatially-covariant effective field theory of the transverse, traceless graviton degrees of freedom. The Lorentz covariance of general relativity, having not been assumed in our analysis, is thus plausibly interpreted as an accidental or emergent symmetry of the gravitational sector. From this point of view, Lorentz covariance is a necessary feature of low-energy graviton dynamics, not…
In this article we present results for tensor graviton modes (in seven dimensions and greater, $n\geq 3$) for greybody factors of Kerr-dS black holes and for Hawking radiation from simply rotating (n+4)-dimensional Kerr black holes. Although there is some subtlety with defining the Hawking temperature of a Kerr-dS black hole, we present some preliminary results for emissions assuming the standard Hawking normalization and a Bousso-Hawking-like normalization.
The solution to the linearized Einstein equation in de Sitter (dS) spacetime and the corresponding two-point function are explicitly written down in a gauge with two parameters `$a$' and `$b$'. The quantization procedure, independent of the choice of the coordinate system, is based on a rigorous group theoretical approach. Our result takes the form of a universal spin-two (transverse-traceless) sector and a gauge-dependent spin-zero (pure-trace) sector. Scalar equations are derived for the structure functions of each part. We show that the spin-two sector can be written as the resulting action…
We show that a partially massless graviton can propagate on a large set of spacetimes which are not Einstein spacetimes. Starting from a recently constructed theory for a massive graviton that propagates the correct number of degrees of freedom on an arbitrary spacetime, we first give the full explicit form of the scalar constraint responsible for the absence of a sixth degree of freedom. We then spell out generic conditions for the constraint to be identically satisfied, so that there is a scalar gauge symmetry which makes the graviton partially massless. These simplify if one assumes that sp…
The two-point function of linearized gravitons on de Sitter space is infrared divergent in the standard transverse traceless synchronous gauge defined by $k=0$ cosmological coordinates (also called conformal or Poincare coordinates). We show that this divergence can be removed by adding a linearized diffeomorphism to each mode function; i.e., by an explicit change of gauge. It follows that the graviton vacuum state is well-defined and de Sitter invariant in agreement with various earlier arguments.
We present a simple model in which a brane with anisotropic metric is embedded in an AdS bulk. We discuss the localization of the massless mode and the amplification of both the massless and the massive modes on the branes, paying particular attention to the normalization of the perturbed action and to the evaluation of the effective coupling constant that controls the amplitude of the spectrum. In the model under investigation there is no mass gap between massless and massive modes, and the massive modes can be amplified, with mass-dependent amplitudes.
We show, through an explicit calculation of the relevant Green's functions, that the transverse-traceless (TT) portion of the gravitational perturbations of Minkowski spacetime and of spatially flat cosmologies with a constant equation-of-state $w$ receive contributions from their isolated matter source(s) outside the past null cone of the observer. This implies the TT gravitational wave (GW) cannot be a standalone observable -- despite widespread (apparent) claims in the gravitational wave literature to the contrary. About a Minkowski background, all 4 of the gauge-invariant variables -- the …
We present a general model of interacting metric fields with the sum of massless non-interacting spin 2 fields as the linear limit. In the non-interacting limit the model is reduced to a sum of general relativity actions, with the usual Einstein-Hilbert kinetic term for each metric field. Until now the accepted view was that such theories are inconsistent since it has been proven that ghost terms and/or discontinuity in the number of degrees of freedom at the zero interaction limit, are unavoidable. We do not refute these results, but instead prove by construction that they do not necessarily …
We study a novel class of higher derivative theories for interacting massless gravitons in Minkowski spacetime. These theories were first discussed by Wald decades ago, and are characterized by scattering amplitudes essentially different from general relativity and many of its modifications. We discuss various aspects of these higher derivative theories, including the Lagrangian construction, violation of asymptotic causality, scattering amplitudes, non-renormalization, and possible implications on emergent gravitons from condensed matter systems.
We use a simplified formalism to re-compute the single graviton loop contribution to the self-mass of a massless, conformally coupled scalar on de Sitter background which was originally made by Boran, Kahya and Park [1-3]. Our result resolves the problem with the flat space correspondence limit that was pointed out by Fröb [4]. We discuss how this computation will be used in a long-term project to purge the linearized effective field equation of gauge dependence.
We study the constraint structure of Fierz -Pauli action in both flat and curved space in the framework of Hamiltonian formalism. We observe an abrupt change in the constraint algebra and the characteristics of the constraints when the mass term is turned off. As is well-known, for de Sitter background with a special tuning of the mass, we will have a gauge symmetry and one degree of freedom less. We will show how this abrupt change in the behavior of the system is reflected on the properties of the constraint algebra. We also obtain the generating functional of gauge transformations both for …
In the holographic picture, the Brout-Englert-Higgs (BEH) mechanism in d-dimensional Yang-Mills theories is conjectured to provide a Higgs-like mechanism for gravity in d+1 dimensions, resulting in massive (or massless) gravitons in IR (or UV) completions. Accordingly, one could imagine dual (magnetic-type) fields of massive gravitons in the IR (low-energy) limit that are coupled to the curl of their own energy-momentum, as well as to the rotation of matter fields on large scales. This hypothesis, which might solve cosmological issues currently ascribed to dark matter and dark energy, needs to…
We construct an n-dimensional Born-Infeld type gravity theory that has the same properties as Einstein's gravity in terms of the vacuum and particle content: Namely, the theory has a unique viable vacuum (maximally symmetric solution) and a single massless unitary spin-2 graviton about this vacuum. The BI gravity, in some sense, is the most natural, minimal generalization of Einstein's gravity with a better UV behavior, and hence, is a potentially viable proposal for low energy quantum gravity. The Gauss-Bonnet combination plays a non-trivial role in the construction of the theory. As an extre…
We construct Born-Infeld (BI) type gravity theories which describe tree-level unitary (non-ghost and non-tachyonic) massless spin-2 modes around their maximally symmetric vacua in four dimensions. Building unitary BI actions around flat vacuum is straightforward; but, this is a complicated task around (anti)-de Sitter backgrounds. In this work, we solve the issue and give details of constructing perturbatively viable determinantal BI theories. It is interesting that the Gauss-Bonnet combination, which is a total derivative in four dimensions, plays an important role in the construction of viab…
The quasinormal modes of a massless Dirac field in the de Rham-Gabadadze-Tolley (dRGT) massive gravity theory with asymptotically de Sitter spacetime are investigated using the Wentzel- Kramers-Brillouin (WKB) approximation. The effective potential for the massless Dirac field due to the dRGT black hole is derived. It is found that the shape of the potential depends crucially on the structure of the graviton mass and the behavior of the quasinormal modes is controlled by the graviton mass parameters. Higher potentials give stronger damping of the quasinormal modes. We compare our results to th…
The striking GW170817 event indicated that the graviton is nearly massless, since the gamma rays emitted from the two neutron stars merging arrived almost simultaneously with the gravitational waves. Thus, the graviton must also be massless during the inflationary and post-inflationary era, since there is no obvious reason to believe otherwise. In this letter we shall investigate the theoretical implications of the constraint that the graviton is massless to an Einstein-Gauss-Bonnet theory with linear coupling of the scalar field to the four dimensional Gauss-Bonnet invariant. As we show, the …
We consider a braneworld model in which an anisotropic brane is embedded in a dilatonic background. We solve the background solutions and study the behavior of the perturbations when the universe evolves from an inflationary Kasner phase to a Minkowski phase. We calculate the massless mode spectrum, and find that it does not differ from what expected in standard four-dimensional cosmological models. We then evaluate the spectrum of both light (ultrarelativistic) and heavy (nonrelativistic) massive modes, and find that, at high energies, there can be a strong enhancement of the Kaluza-Klein spe…
We obtain the fully covariant linearized field equations for the metric perturbation in the de Rham-Gabadadze-Tolley (dRGT) ghost free massive gravities. For a subset of these theories, we show that the non dynamical metric that appears in the dRGT setup can be completely eliminated leading to the theory of a massive graviton moving in a single metric. This has a mass term which contains non trivial contributions of the space-time curvature. We show further how 5 covariant constraints can be obtained including one which leads to the tracelessness of the graviton on flat space-time and removes …
Solutions of massless spin-2 field equations are written in terms of massless spin-$\frac{3}{2}$ Rarita-Schwinger fields and twistor spinors. It is shown that the proposed massless spin-2 fields satisfy the tracelessness and divergencelessness conditions and are in the kernel of the Laplace-Beltrami operator. A spin lowering procedure for special cases and a symmetry operator for massless spin-2 fields are also obtained. Description of massless spin-2 fields in terms of lower spin fields are found.
We formulate Positivity Bounds for scattering amplitudes including exchange of massless particles. We generalize the standard construction through dispersion relations to include the presence of a branch cut along the real axis in the complex plane for the Maldestam variable $s$. In general, validity of these bounds require the cancellation of divergences in the forward limit of the amplitude, proportional to $t^{-1}$ and $\log(t)$. We show that this is possible in the case of gravitons if one assumes a Regge behavior of the amplitude at high energies below the Planck scale, as previously sugg…
Quantum creation processes during the very rapid early expansion of the universe are believed to give rise to temperature anisotropies and polarization patterns in the CMB radiation. These have been observed by satellites such as COBE, WMAP, and PLANCK, and by bolometric instruments placed near the South Pole by the BICEP collaborations. The expected temperature anisotropies are well-confirmed. The B-mode polarization patterns in the CMB are currently under measurement jointly by the PLANCK and BICEP groups to determine the extent to which the B-modes can be attributed to gravitational waves f…
Recent nonlinear completions of Fierz-Pauli theory for a massive spin-2 field include nonlinear massive gravity and bimetric theories. The spectrum of black-hole solutions in these theories is rich, and comprises the same vacuum solutions of Einstein's gravity enlarged to include a cosmological constant. It was recently shown that Schwarzschild (de Sitter) black holes in these theories are generically unstable against spherical perturbations. Here we show that a notable exception is partially massless gravity, where the mass of the graviton is fixed in terms of the cosmological constant by μ^2…
Many studies have been carried out in the literature to evaluate the number of polarization modes of gravitational waves in modified theories, in particular in $f(R)$ theories. In the latter ones, besides the usual two transverse-traceless tensor modes present in general relativity, there are two additional scalar ones: a massive longitudinal mode and a massless transverse mode (the so-called breathing mode). This last mode has often been overlooked in the literature, due to the assumption that the application of the Lorenz gauge implies transverse-traceless wave solutions. We however show tha…
In addition to the usual linear gravitational waves in transverse-traceless coordinates, higher-order gravitational field equations, as well as their corresponding solutions, are explicitly obtained. It is found that higher-order waves do not represent corrections to the first-order wave. In contrast, all higher than second-order solutions do represent corrections to the second-order wave, a property that makes the first-order gravitational wave to stand apart from higher-order waves. Furthermore, although the first-order solution is transverse and traceless, all higher-order solutions are not…
In this paper, the two-point function of linearized gravitons on de Sitter (dS) space is presented. Technically, respecting the dS ambient space notation, the field equation is given by the coordinate-independent Casimir operators of the de Sitter group. Analogous to the quantization of the electromagnetic field in Minkowski space, the field equation admits gauge solutions. The notation allows us to exhibit the formalism of Gupta-Bleuler triplets for the present field in exactly the same manner as it occurs for the electromagnetic field. In this regard, centering on the spin-two part (the trac…
We relax the assumption of time translation and Lorentz boost symmetry in theories involving massless spin 2 gravitons, while maintaining a basic notion of locality that there is no instantaneous signaling at a distance. We project out longitudinal modes, leaving only two degrees of freedom of the graviton. Our previous work, which assumed time translation symmetry, found that the Lorentz boost symmetry is required to ensure locality at leading order. In this work, without assuming time translations or Lorentz boosts, we show that locality of the exchange action between matter sources demands …
In the report, the theory of unimodular bimode gravity built on principles of unimodular gauge invariance/relativity and general covariance is exposed. Besides the massless tensor graviton of General Relativity, the theory includes an (almost) massless scalar graviton treated as the gravitational dark matter. A spherically symmetric vacuum solution, describing the coherent scalar-graviton field for the soft-core dark halos with the asymptotically flat rotation curves, is demonstrated.
We review some recent work by Carone, Erlich and Vaman on composite gravitons in metric-independent quantum field theories, with the aim of clarifying a number of basic issues. Focusing on a theory of scalar fields presented previously in the literature, we clarify the meaning of the tunings required to obtain a massless graviton. We argue that this formulation can be interpreted as the massless limit of a theory of massive composite gravitons in which the graviton mass term is not of Pauli-Fierz form. We then suggest closely related theories that can be defined without such a limiting procedu…
The impact of the existence of gravitons with non-vanishing masses on the B modes of the Cosmic Microwave Background (CMB) is investigated. We also focus on putative modifications to the speed of the gravitational waves. We find that a change of the graviton speed shifts the acoustic peaks of the CMB and then could be easily constrained. For the case of massive gravity, we show analytically how the B modes are sourced in a manner differing from the massless case leading to a plateau at low $l$ in the CMB spectrum. We also study the case when there are more than one graviton, and when pressure …
We study a family of higher-derivative conformal operators $P_{2k}^{(2)}$ acting on transverse-traceless symmetric 2-tensors on generic Einstein spaces. They are a natural generalization of the well-known construction for scalars. We first provide the alternative description in terms of a bulk Poincaré-Einstein metric by making use of the AdS/CFT dictionary and argue that their holographic dual generically consists of bulk massive gravitons. At one-loop quantum level, we put forward a holographic formula for the functional determinant of the higher-derivative conformal operators $P_{2k}^{(2)}$…
Pauli-Fierz approach to description of a massless spin-2 particle is investigated in the framework of 30-component first order relativistic wave equation theory on a curved space-time background. It is shown that additional gauge symmetry of massless equations established by Pauli-Fierz can be extended only to curved space-time regions where Ricci tensor vanishes. In all such space-time models the generally covariant S=2 massless wave equation exhibits gauge symmetry property, otherwise it is not so.
We discuss the cosmological amplification of tensor perturbations in a simple example of brane-world scenario, in which massless gravitons are localized on a higher-dimensional Kasner-like brane embedded in a bulk AdS background. Particular attention is paid to the canonical normalization of the quadratic action describing the massless and massive vacuum quantum fluctuations, and to the exact mass-dependence of the amplitude of massive fluctuations on the brane. The perturbation equations can be separated. In contrast to de Sitter models of brane inflation, we find no mass gap in the spectrum …
Theories with massive gravitons have peculiarity called the van Dam-Veltman-Zakharov discontinuity in that the massive theory propagator does not go to the massless graviton propagator in the zero graviton mass limit. This results in large deviation in Newtons law for massive graviton theories even when the graviton mass vanishes. We test the vDVZ in massive graviton theories for single graviton vertex process namely the gravitational radiation from a classical source. We calculate the gravitational radiation from compact binaries using the perturbative Feynman diagram method. We perform this …
Classical soft graviton theorem gives the gravitational wave-form at future null infinity at late retarded time $u$ for a general classical scattering. The large $u$ expansion has three known universal terms: the constant term, the term proportional to $1/u$ and the term proportional to $\ln u/u^2$, whose coefficients are determined solely in terms of the momenta of incoming and the outgoing hard particles, including the momenta carried by outgoing gravitational and electromagnetic radiation produced during scattering. For the constant term, also known as the memory effect, the dependence on t…
We show that higher spin systems specific to cosmological spaces are subject to the same problems as models with Poincar'e limits. In particular, we analyse partially massless (PM) spin 2 and find that both its gravitational coupling and nonlinear extensions suffer from the usual [background- and self-coupling] difficulties: Consistent free field propagation does not extend beyond background Einstein geometries. Then, using conformal Weyl gravity (CG), which consists of relative ghost PM and graviton excitations, we find that avoiding graviton-ghosts restricts CG-generated PM self-couplings to…
Non-linear partially massless (PM) gravity, if it exists, is a theory of massive gravity in which the graviton has four propagating degrees of freedom. In PM gravity, a scalar gauge symmetry removes one of the five modes of the massive graviton. This symmetry ties the value of the cosmological constant to the mass of the graviton, which in turn can be kept small in a technically natural way. Thus PM gravity could offer a compelling solution to the old cosmological constant problem. In this work we look for such a theory among the known ghost-free massive gravity models with a de Sitter referen…
Recent astrophysical data indicate that our universe might currently be in a de Sitter (dS) phase. The importance of dS space has been primarily ignited by the study of the inflationary model of the universe and the quantum gravity. As we know Einstein's theory of gravitation (with a nonzero cosmological constant) can be interpreted as a theory of a metric field; that is, a symmetric tensor field of rank-2 on a fixed de Sitter background. It has been shown that the massless spin-2 Fierz-Pauli wave equation (or the linearized Einstein equation) is not conformally invariant. This result is in co…
In Einstein's general relativity (GR), gravity is described by a massless spin-2 metric field, and the extension of GR to include a mass term for the graviton has profound implication for gravitation and cosmology. Besides the gravity experiments carried out in the Solar System and those recently with gravitational waves (GWs), pulsar timing observations provide a complementary means to test the masslessness of graviton. In this contribution, I overview three methods in probing the mass of graviton from precision timing of binary pulsars via the modified gravitational radiation (hence, the obs…
We propose an unified theory for spinor fields on extended Weyl manifolds taking into account self-interactions to obtain the Relativistic dynamics on a general curved Riemannian background as continuation of the Relativistic Quantum Geometry program, recently introduced. We focuss our attention separately on both, massless and matter fields. We study an example of confined gravitons on a de Sitter (dS) background at Planckian scales.
We have computed the number of polarization modes of gravitational waves propagating in the Minkowski background in $f(R)$ gravity. This is three of two from transverse-traceless tensor modes and one from a massive trace mode, which confirms the results found in the literature. There is no massless breathing mode and the massive trace mode corresponds to the Ricci scalar. A newly defined metric tensor in $f(R)$ gravity satisfies the transverse-traceless (TT) condition as well as the TT wave equation.
In this work we shall introduce a theoretical framework comprised by a non-minimal coupled canonical scalar field, a non-minimal coupling to the Gauss-Bonnet invariant and a non-minimal kinetic coupling. This theoretical framework is basically a non-minimally coupled Einstein-Gauss-Bonnet theory with extra corrections of the form of a non-minimal kinetic coupling. In order to comply with the GW170817 event, we shall impose a constraint on the propagation speed of the primordial tensor perturbations that it is equal to that of light's in vacuum, and this constraint basically specifies the way t…
We obtain the equation that describe the conditions of quantization for neutral massless bosons on an arbitrary curved space-time, obtained using a particular theoretical formalism developed in a previous work\cite{MM}. In particular, we study the emission of neutral massless $(1, 2)\hbar$-spin bosons during pre-inflation using the recently introduced unified spinor field theory. We conclude that during pre-inflation (which is governed by an vacuum equation of state), is emitted gravitational radiation, which could be detected in the future, as primordial gravitational radiation.
We calculate the one loop graviton vacuum polarization induced by a massless, nonminimally coupled scalar field on Minkowski background. We make use of the Schwinger-Keldysh formalism, which allows us to study time dependent phenomena. As an application we compute the leading quantum correction to the Newtonian potential of a point particle. The novel aspect of the calculation is the use of the Schwinger-Keldysh formalism, within which we calculate the time transients induced by switching on of the graviton-scalar coupling.
A special class of higher curvature theories of gravity, Ricci Cubic Gravity (RCG), in general d dimensional space-time has been investigated in this paper. We have used two different approaches, the linearized equations of motion and auxiliary field formalism to study the massive and massless graviton propagating modes of the AdS background. Using the auxiliary field formalism, we have found the renormalized boundary stress tensor to compute the mass of Schwarzschild AdS and Lifshitz black holes in RCG theory.
We provide evidence that general relativity is the unique spatially covariant effective field theory of the transverse, traceless graviton degrees of freedom. The Lorentz covariance of general relativity, having not been assumed in our analysis, is thus plausibly interpreted as an accidental or emergent symmetry of the gravitational sector.
We discuss the creation of massless particles in a Universe, which transits from a radiation-dominated era to any other expansion law. We calculate in detail the generation of gravitons during the transition to a matter dominated era. We show that the resulting gravitons generated in the standard radiation/matter transition are negligible. We use our result to constrain one or more previous matter dominated era, or any other expansion law, which may have taken place in the early Universe. We also derive a general formula for the modification of a generic initial graviton spectrum by an early m…
