The van Dam-Veltman-Zakharov (vDVZ) discontinuity requires that the mass $m$ of the graviton is exactly zero, otherwise measurements of the deflection of starlight by the Sun and the precession of Mercury's perihelion would conflict with their theoretical values. This theoretical discontinuity is open to question for numerous reasons. In this paper we show from a phenomenological viewpoint that the $m>0$ hypothesis is in accord with Supernova Ia and CMB observations, and that the large scale structure of the universe suggests that $m \sim 10^{-30} $eV$/c^2$.
We introduce additional restriction into "general ether theory" - a generalization of Lorentz ether theory to gravity - which fixes the signs of the cosmological constants in this theory. This leads to an oscillating universe, thus, solves the cosmological horizon problem without inflation. We prove the equivalence of the Lagrangian of this theory with Logunov's "relativistic theory of gravity" with massive graviton and a variant of GR with four non-standard scalar fields and negative cosmological constant. We consider the remaining differences between these theories.
I consider a simple model where the graviton mass and the cosmological constant depend on a scalar field with appropriate couplings and I calculate the graviton propagator and the resulting effective potential for the scalar field in order to examine issues of stability and symmetry breaking.
Possible effects are considered which would be caused by a hypothetical superstrong interaction of photons or massive bodies with single gravitons of the graviton background. If full cosmological redshift magnitudes are caused by the interaction, then the luminosity distance in a flat non-expanding universe as a function of redshift is very similar to the specific function which fits supernova cosmology data by Riess et al. From another side, in this case every massive body, slowly moving relatively to the background, would experience a constant acceleration, proportional to the Hubble constan…
Relevant deformations of gravity present an exciting window of opportunity to probe the rigidity of gravity on cosmological scales. For a single-graviton theory, the leading relevant deformation constitutes a graviton mass term. In this paper, we investigate the classical and quantum stability of massive cosmological gravitons on generic Friedman backgrounds. For a Universe expanding towards a de Sitter epoch, we find that massive cosmological gravitons are self-protected against unitarity violations by a strong coupling phenomenon.
We show that the graviton acquires a mass in a de Sitter background given by $m_{g}^{2}=-{2/3}Λ.$ This is precisely the fine-tuning value required for the perturbed gravitational field to mantain its two degrees of freedom.
If the cosmological constant $Λ$ can not be neglected, we will show in this short report, that graviton should have a rest mass $m_g=\sqrt{2Λ}=\sqrt{2Λ}\hbar c^{-1}$ different from zero.
The spectrum and amplitude of the stochastic background of relic gravitons produced in a bouncing universe is calculated. The matter content of the model consists of dust and radiation fluids, and the bounce occurs due to quantum cosmological effects when the universe approaches the classical singularity in the contracting phase. The resulting amplitude is very small and it cannot be observed by any present and near future gravitational wave detector. Hence, as in the ekpyrotic model, any observation of these relic gravitons will rule out this type of quantum cosmological bouncing model.
Graviton fluctuations induce strong non-perturbative infrared renormalization effects for the cosmological constant. The functional renormalization flow drives a positive cosmological constant towards zero, solving the cosmological constant problem without the need to tune parameters. We propose a simple computation of the graviton contribution to the flow of the effective potential for scalar fields. Within variable gravity we find that the potential increases asymptotically at most quadratically with the scalar field. With effective Planck mass proportional to the scalar field, the solutions…
It is well known that gravitons can convert into photons, and vice versa, in the presence of cosmological magnetic fields. We study this conversion process in the context of atomic dark matter scenario. In this scenario, we can expect cosmological dark magnetic fields, which are free from the stringent constraint from the cosmic microwave observations. We find that gravitons can effectively convert into dark photons in the presence of cosmological dark magnetic fields. The graviton-dark photon conversion effect may open up a new window for ultra high frequency gravitational waves.
We discuss the production and evolution of cosmological gravitons showing how the cosmological background affects their dynamics. Besides, the detection of cosmological gravitons could constitute an extremely important signature to discriminate among different cosmological models. Here we consider the cases of scalar-tensor gravity and $f(R)$ gravity where it is demonstrated the amplification of graviton amplitude changes if compared with General Relativity. Possible observational constraints are discussed.
We study the imprint of a massive scalar particle on cosmological correlation functions, and suggest the way to determine the mass of the newly introduced particle, which is expected to be around 10^14 GeV. After reviewing the basic theory by Maldacena and the effective field theory (EFT) of inflation by Cheung et al., we apply these two theories to construct new couplings of a massive scalar field with primordial fluctuations including an arbitrary number of gravitons. We compute some correlation functions including these couplings in the soft-graviton limit. We show that when the number of s…
It has been suggested that the Dark Energy Coincidence Problem could be interpreted as a possible link between the cosmological constant and a massive graviton. We show that by using that link and models for the graviton mass a dark energy density can be obtained that is indeed very close to measurements by WMAP. As a consequence of the models, the cosmological constant was found to depend on the density of matter. A brief outline of the cosmological consequences such as the effect on the black hole solution is given.
In recent years, the calculation of the first non-vanishing order of the metric 2-point function or graviton propagator in a semiclassical limit has evolved as a standard test for the credibility of a proposed spin foam model. The existing results of spinfoam graviton propagator rely heavily on the so-called double scaling limit where spins $j$ are large and the Barbero-Immirzi parameter $γ$ is small such that the area $A\propto jγ$ is approximately constant. However, it seems that this double scaling limit is bound to break down in models including a cosmological constant. We explore this in …
Motivated by the interest raised by the problem of Lorenz-symmetry violating gauge theories in connetion with gravity models, this contribution sets out to provide a general method to systematically study the excitation spectrum of gravity actions which include a Lorentz-symmetry breaking Chern-Simons-type action term for the spin connection. A complete set of spin-type operators is found which accounts for the (Lorentz) violation parameter to all orders and graviton propagators are worked out in a number of different situations.
We revisit the proposal that the resolution of the Cosmological Constant Problem involves a sub-millimeter breakdown of the point-particle approximation for gravitons. No fundamental description of such a breakdown, which simultaneously preserves the point-particle nature of matter particles, is yet known. However, basic aspects of the self-consistency of the idea, such as preservation of the macroscopic Equivalence Principle while satisfying quantum naturalness of the cosmological constant, are addressed in this paper within a Soft Graviton Effective Theory. It builds on Weinberg's analysis o…
We study the effects of gravitationally-driven decoherence on tunneling processes associated with false vacuum decays, such as the Coleman--De~Luccia instanton. We compute the thermal graviton-induced decoherence rate for a wave function describing a perfect fluid of nonzero energy density in a finite region. When the effective cosmological constant is positive, the thermal graviton background sourced by a de Sitter horizon provides an unavoidable decoherence effect, which may have important consequences for tunneling processes in cosmological history. We discuss generalizations and consequenc…
In this thesis, we study three aspects of theories with massive gravitational waves. In the first part, we review to problems and issues of theories with massive gravitons before introducing models where Lorentz invariance is spontaneously broken by the vacuum expectation value of four scalar fields. In the second part, we discuss three aspects of these models: instantaneous interaction, spherically vacuum solutions and cosmological perturbations.
We consider the quantum Friedmann equations which include one-loop vacuum fluctuations due to gravitons and scalar field matter in a FLRW background with constant $ε=-{\dot{H}}/{H^2}$. After several field redefinitions, to remove the mixing between the gravitational and matter degrees of freedom, we can construct the one loop correction to the Friedmann equations. Due to cosmological particle creation, the propagators needed in such a calculation are typically infrared divergent. In this paper we construct the graviton and matter propagators, making use of the recent construction of the infrar…
Intrinsic properties of the space itself and quantum fluctuations of its geometry are sufficient to provide a mechanism for the acceleration of cosmological expansion (dark energy effect). Applying Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy approach to self-consistent equations of one-loop quantum gravity, we found exact solutions that yield acceleration. The permanent creation and annihilation of virtual gravitons is not in exact balance because of the expansion of the Universe. The excess energy comes from the spontaneous process of graviton creation and is trapped by the background. It p…
The problem of cosmological graviton creation for homogeneous and isotropic universes with elliptical ($\vae =+1$) and hyperbolical ($\vae =-1$) geometries is addressed. The gravitational wave equation is established for a self-gravitating fluid satisfying the barotropic equation of state $p=(γ-1)ρ$, which is the source of the Einstein's equations plus a cosmological $Λ$-term. The time dependent part of this equation is exactly solved in terms of hypergeometric functions for any value of $γ$ and spatial curvature $\vae$. An expression representing an adiabatic vacuum state is then obtained in …
We propose a multi-graviton theory with non-nearest-neighbor couplings in the theory space. The resulting four-dimensional discrete mass spectrum reflects the structure of a latticized extra dimension. For a plausible mass spectrum motivated by the discretized Randall-Sundrum brane-world, the induced cosmological constant turns out to be positive and may serve as a quite simple model for the dark energy of our accelerating universe.
The graviton is pictured as a bound state of a fermion and anti-fermion with the spacetime metric assumed to be a composite object of spinor fields, based on a globally Lorentz invariant action proposed by Hebecker and Wetterich. The additional degrees of freedom beyond those of the graviton are described by Goldstone boson gravitational degrees of freedom. If we assume that the fermion is a light neutrino with mass $m_nu\sim 10^{-3}$ eV, then we obtain the effective vacuum density ${\barρ}_λ\sim (10^{-3} eV)^4$, which agrees with the estimates for the cosmological constant from WMAP and SNIa …
It is shown that in some multi-supergraviton models, the contributions to the effective potential due to a non-trivial topology can be positive, giving rise in this way to a positive cosmological constant, as demanded by cosmological observations.
In this work, we explore some cosmological implications of the model proposed by M. Visser in 1998. In his approach, Visser intends to take in account mass for the graviton by means of an additional bimetric tensor in the Einstein's field equations. Our study has shown that a consistent cosmological model arises from Visser's approach. The most interesting feature is that an accelerated expansion phase naturally emerges from the cosmological model, and we do not need to postulate any kind of dark energy to explain the current observational data for distant type Ia supernovae (SNIa).
It was shown, that the presence of the so-called X-matter with an equation of state, which lies between limits of the strong and weak energy conditions, allows the variety of the cosmological scenarios in the relativistic theory of gravity. In spite of the fixed negative sign of the cosmological term in the field equations with massive graviton, it is possible to obtain the solutions with accelerated and complicated loitering expansion of the universe. The numerical estimation of the universe's age agrees with the modern observational data if the upper limit of the graviton's mass is 10^{-71} …
Primary features of a new cosmological model, which is based on conjectures about an existence of the graviton background and superstrong gravitational quantum interaction, are considered. An expansion of the universe is impossible in such the model because of deceleration of massive objects by the graviton background, which is similar to the one for the NASA deep space probes Pioneer 10, 11. Redshifts of remote objects are caused in the model by interaction of photons with the graviton background, and the Hubble constant depends on an intensity of interaction and an equivalent temperature of …
The existence of a non-zero cosmological constant $Λ$ gives rise to controversial interpretations. Is $Λ$ a universal constant fixing the geometry of an empty universe, as fundamental as the Planck constant or the speed of light in the vacuum? Its natural place is then on the left-hand side of the Einstein equation. Is it instead something emerging from a perturbative calculus performed on the metric $g\_{μν}$ solution of the Einstein equation and to which it might be given a material status of (dark or bright) "energy"? It should then be part of the content of the right-hand side of the Einst…
In the framework of the minimal quartet-metric gravity/systogravity, a scalar graviton/systolon is stated as a universal dark component, with supplementary manifestations in the different contexts either as dark matter or dark energy. An ensuing extension to the standard ΛCDM model is developed. A modification of the late expansion of the Universe, with an attractor of a scalar master equation defining an effective cosmological constant, which supersedes the true one, is proposed. A new partial solution to the cosmological constant problem is discussed.
In this paper we study the cosmological constant emerging from the Wheeler-DeWitt equation as an eigenvalue of the related Sturm-Liouville problem. We employ Gaussian trial functionals and we perform a mode decomposition to extract the transverse-traceless component, namely, the graviton contribution, at one loop. We implement a noncommutative-geometry- induced minimal length to calculate the number of graviton modes. As a result, we find regular graviton fluctuation energies for the Schwarzschild, de Sitter, and anti-de Sitter backgrounds. No renormalization scheme is necessary to remove infi…
The standard $Λ$-CDM predicts a growth of structures which tends to be higher than the values of redshift space distortion (RSD) measurements, if the cosmological parameters are fixed by the CMB data. In this paper we point out that this discrepancy can be resolved/understood if we assume that the graviton has a small but non-zero mass. In the context of the Minimal Theory of Massive Gravity (MTMG), due to infrared Lorentz violations measurable only at present cosmological scales, the graviton acquires a mass without being haunted by unwanted extra degrees of freedom. While the so-called self-…
Quantum Field Theory is plagued by divergences in the attempt to calculate physical quantities. Standard techniques of regularization and renormalization are used to keep under control such a problem. In this paper we would like to use a different scheme based on Modified Dispersion Relations (MDR) to remove infinities appearing in one loop approximation in contrast to what happens in conventional approaches. In particular, we apply the MDR regularization to the computation of the entropy of a Schwarzschild black hole from one side and the Zero Point Energy (ZPE) of the graviton from the other…
The basic cosmological conjecture about the Dopplerian nature of redshifts may be false if gravitons are super-strong interacting particles. A quantum mechanism of classical gravity and the main features of a new cosmological paradigm based on it are described here.
We analyze the physics of massive spin 2 fields in (A)dS backgrounds and exhibit that: The theory is stable only for masses m^2 >= 2Λ/3, where the conserved energy associated with the background timelike Killing vector is positive, while the instability for m^2<2Λ/3 is traceable to the helicity 0 energy. The stable, unitary, partially massless theory at m^2=2Λ/3 describes 4 propagating degrees of freedom, corresponding to helicities (+/-2,+/-1) but contains no 0 helicity excitation.
Beginning with the Pauli-Fierz theory, we construct a model for multi-graviton theory. Couplings between gravitons belonging to nearest-neighbor ``theory spaces'' lead to a discrete mass spectrum. Our model coincides with the Kaluza-Klein theory whose fifth dimension is latticized. We evaluate one-loop vacuum energy in models with a circular latticized extra dimension as well as with compact continuous dimensions. We find that the vacuum energy can take a positive value, if the dimension of the continuous space time is $6, 10,...$. Moreover, since the amount of the vacuum energy can be an arbi…
We compute the graviton one-loop correction to the expectation value of the local expansion rate in slow-roll inflation, with both slow-roll parameters finite. The calculation is based on a recent method to explicitly construct gauge-invariant observables in perturbative quantum gravity at all orders in perturbation theory, and it is particularly suited in cases of highly-symmetrical space-time backgrounds. Our analysis adds to recent calculations of that correction in de Sitter space-time and in single-field inflation with constant deceleration. In the former case a vanishing one-loop correct…
We overview a new mechanism whereby classical Riemannian geometry emerges out of the differential structure on quantum spacetime, as extension data for the classical algebra of differential forms. Outcomes for physics include a new formula for the standard Levi-Civita connection, a new point of view of the cosmological constant as a very small mass for the graviton of around $10^{-33}$ev, and a weakening of metric-compatibility in the presence of torsion. The same mechanism also provides a new construction for quantum bimodule connections on quantum spacetimes and a new approach to the quantum…
Alternatives to Einstein's theory of general relativity can be distinguished by measuring the parametrised post Newtonian parameters. Two such parameters $β$ and $γ$, equal to one in Einstein theory, can be obtained from static spherically symmetric solutions. For the graviton-dilaton system, as in Brans-Dicke or low energy string theory, we find that if $γ\ne 1$ for a charge neutral point star, then there exist naked singularities. Thus, if $γ$ is measured to be different from one, then it cannot be explained by these theories, without implying naked singularities. We also couple a cosmologic…
A new mechanism which leads to a linearized massless graviton localized on the brane is found in the $AdS$/CFT setting, {\it i.e.} in a single copy of $AdS_5$ spacetime with a singular brane on the boundary, within the Randall-Sundrum brane-world scenario. With an help of a recent development in path-integral techniques, a one-parameter family of propagators for linearized gravity is obtained analytically, in which a parameter $ξ$ reflects various kinds of boundary conditions that arise as a result of the half-line constraint. In the case of a Dirichlet boundary condition ($ξ= 0$) the graviton…
We give a simple proof of perturbative unitarity in gauge theories and quantum gravity using a special gauge that allows us to separate the physical poles of the free propagators, which are quantized by means of the Feynman prescription, from the poles that belong to the gauge-trivial sector, which are quantized by means of the fakeon prescription. The proof applies to renormalizable theories, including the ultraviolet complete theory of quantum gravity with fakeons formulated recently, as well as low-energy (nonrenormalizable) theories. We clarify a number of subtleties related to the study o…
Analysing the static, spherically symmetric graviton-dilaton solutions in low energy string and Brans-Dicke theory, we find the following. For a charge neutral point star, these theories cannot predict non trivial PPN parameters, $β$ and $γ$, without introducing naked singularities. We then couple a cosmological constant $Λ$ as in low energy string theory. We find that only in low energy string theory, a non zero $Λ$ leads to a curvature singularity, which is much worse than a naked singularity. Requiring its absence upto a distance $r_*$ implies a bound $| Λ| < 10^{- 102} (\frac{r_*}{\rm pc})…
The cosmological constant appearing in the Wheeler-De Witt equation is considered as an eigenvalue of the associated Sturm-Liouville problem. A variational approach with Gaussian trial wave functionals is used as a method to study such a problem. We approximate the equation to one loop in a Schwarzschild background and a zeta function regularization is involved to handle with divergences. The regularization is closely related to the subtraction procedure appearing in the computation of Casimir energy in a curved background. A renormalization procedure is introduced to remove the infinities tog…
We study topologically massive (2+1)-dimensional gravity with a negative cosmological constant. The masses of the linearized curvature excitations about AdS_3 backgrounds are not only shifted from their flat background values but, more surprisingly, split according to chirality. For all finite values of the topological mass, we find a single bulk degree of freedom with positive energy, and exhibit a complete set of normalizable, finite-energy wave packet solutions. This model can also be written as a sum of two higher-derivative SL(2,R) Chern--Simons theories, weighted by the central charges o…
Conversion of gravitational waves into electromagnetic radiation is discussed. The probability of transformations of gravitons into photons in presence of cosmological background magnetic field is calculated at the recombination epoch and during subsequent cosmological stages. The produced electromagnetic radiation is concentrated in the X-ray part of the spectrum. It is shown that if the early Universe was dominated by primordial black holes (PBHs) prior to Big Bang Nucleosynthesis (BBN), the relic gravitons emitted by PBHs would transform to an almost isotropic background of electromagnetic …
We make a number of remarks on linearized gravity with cosmological constant in any dimension, which, we argue, can be useful in a quantum gravity framework. For this purpose we assume that the background space-time metric corresponds to the de Sitter or anti-de Sitter space. Moreover, via the graviton mass and the cosmological constant correspondence, we make some interesting observations, putting special attention on the possible scenario of a graviton-tachyon connection. We compare our proposed formalism with the Novello and Neves approach.
Infrared gravitons are continually produced during inflation. Like all particles, their contribution to the vacuum energy comes not only from their bare kinetic energy but also from the interactions they have with other gravitons. These interactions can be substantial -- despite the particles being highly infrared -- because they occur over the enormous spatial volume of the universe. Furthermore, the interactions grow with time evolution because more and more such gravitons come into causal contact with one another. Since gravity is universally attractive, these interactions can act to slow a…
A nonlocal quantum gravity theory is presented which is finite and unitary to all orders of perturbation theory. Vertex form factors in Feynman diagrams involving gravitons suppress graviton and matter vacuum fluctuation loops by introducing a low-energy gravitational scale, Λ_{Gvac} < 2.4\times 10^{-3} eV. Gravitons coupled to non-vacuum matter loops and matter tree graphs are controlled by a vertex form factor with the energy scale, Λ_{GM} < 1-10 TeV.
A new approach to the cosmological constant problem is proposed by modifying Einstein's theory of general relativity, using instead a scalar-tensor theory of gravitation. This theory of gravity crucially incorporates the concept of quantum symmetry breaking. The role of the cosmological constant $λ$ as a graviton mass in the weak-field limit is necessarily utilized. Because $λ$ takes on two values as a broken symmetry, so does the graviton mass -- one of which cannot be zero. Gravity now exhibits both long- and short-range forces, by introducing hadron bags into strong interaction physics usin…
We use the Bogoliubov formalism to study both, particles and gravitons creation at the reheating epoch, after a phase transition from inflation to a radiation dominated universe. The modes of the inflaton field fluctuations and the scalar fluctuations of the metric at the end of inflation are obtained by using a recently introduced formalism related to the Induced Matter theory of gravity. The interesting result is that the number of created particles is bigger than $10^{90}$ on cosmological scales. Furthermore, the number of gravitons are nearly $10^{-17}$ times smaller than the number of cre…
We present the cosmological analysis of the Gauss-Bonnet quasi-dilaton massive gravity theory. This offers a gravitational theory with a non-zero graviton mass. We calculate the complete set of background equations of motion. Also, we obtain the self-accelerating background solutions and we present the constraints on parameters to indicate the correct sign of parameters. In addition, we analyse tensor perturbations and calculate the mass of graviton and find the dispersion relation of gravitational waves for two cases. Finally, we investigate the propagation of gravitational perturbation in th…
