It is shown that nonlinear terms in equations of gravitons on the background of curved space-time of the expanding Universe can solve the problem of the negative square of the effective mass formally arising in linear approximation for gravitons. Similar to well known spontaneous breaking of symmetry in Goldstone model one must take another vacuum so that nonzero vacuum expectation value of the quantized graviton field leads to change of spectrum for gravitons. There appears two graviton fields, one with the positive mass, another with the zero mass. Energy density and the density of particles created by gravitation of the expanding Universe are calculated for some special cases of the scale factor. Numerical results are obtained for the dust universe case.
It is shown that nonlinear terms in equations of gravitons on the background of curved space-time of the expanding Universe can solve the problem of the negative square of the effective mass formally arising in linear approximation for gravitons. Similar to well known spontaneous breaking of symmetry in Goldstone model one must take another vacuum so that nonzero vacuum expectation value of the quantized graviton field leads to change of spectrum for gravitons. There appears two graviton fields, one with the positive mass, another with the zero mass. Energy density and the density of particles…
We consider some aspects of spontaneous breaking of Lorentz Invariance in field theories, discussing the possibility that the certain tensor operators may condensate in the ground state in which case the tensor Goldstone particles would appear. We analyze their dynamics and discuss to which extent such a theory could imitate the gravity. We are also interested if the universality of coupling of such `gravitons' with other particles can be achieved in the infrared limit. Then we address the more complicated models when such tensor Goldstones coexist with the usual geometrical gravitons. At the …
We complement investigations of the gauge structure of general relativity with an analysis of the physical consequences of the spontaneous breaking of diffeomorphism invariance which manifests itself in e.g. the socalled Einstein hole problem. We analyze the nature of the gravitons as Goldstone excitations both in the classical and the quantum case. We show that the metrical field and the classical space-time manifold play the role of an order parameter field and order parameter manifold as macroscopic super structures living in an underlying presumed quantum space-time. We furthermore relate …
We formulate the graviton propagator on de Sitter background in a 2-parameter family of simple gauges which break de Sitter invariance. Explicit results are derived for the first order perturbations in each parameter. These results should be useful in computations to check for gauge dependence of graviton loop corrections.
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.
A direct consequence of quantization of gravity would be the existence of gravitons. Therefore, spontaneous transition of an atom from an excited state to a lower-lying energy state accompanied with the emission of a graviton is expected. In this paper, we take the gravitons emitted by hydrogen and helium in the Universe after recombination as a possible source of high frequency background gravitational waves, and calculate the energy density spectrum. Explicit calculations show that the most prominent contribution comes from the $3d-1s$ transition of singly ionized helium $\mathrm{He}^{+}$, w…
A spontaneous symmetry breaking mechanism is used in quantum gravity to obtain a convergent positive definite density-matrix as the most general quantum state of Euclidean wormholes
We propose a model of bimetric gravity in which the mixing of metrics naturally gives a mass to a graviton by the compactification with flux of two gauge fields in extra dimensions. We assume that each metric in the solution for the background geometry describes the four-dimensional Minkowski spacetime with an $S^2$ extra space, though the two radii of $S^2$ for two metrics take different values in general. The solution is derived by the effective potential method in the presence of the magnetic fluxes on the extra spheres. We find that the a massive graviton is governed by the Fierz-Pauli Lag…
Spontaneous breaking of local Lorentz symmetry is of interest as a possible mechanism originating from physics at the Planck scale. If such breaking occurs, however, it raises the questions of what the fate of the Nambu-Goldstone modes is, whether a Higgs mechanism can occur, and whether additional massive modes (analogous to the Higgs particle) can appear. A summary of some recent work looking at these questions is presented here.
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.
We point out that a spontaneous scalarized inspiring double neutron star (DNS) system can provide us a natural laboratory to investigate the generation mechanism of masses for gravitons. Because of the appearance of a gravitational scalar background field, with small fluctuations, converged by iterative interplay of the mass dimensional external scalar fields, the binary system suffers from a spontaneous Lorentz symmetry breaking. The two scalarized NSs dip in a Higgs-like gravitational scalar potential, where the massless scalar background fluctuation field plays the role of Higgs field. Cons…
Treating the gravitational field as a dynamical field, we study the spontaneous symmetry breaking induced by a scalar field under its self-interaction and non-minimal interaction with gravity in four dimensional space-time. In particular, we explore the feasibility of inducing spontaneous symmetry breaking after introducing the non-minimal coupling, and discuss briefly the cosmological constant problem corresponding to the phase transition associated with the spontaneous symmetry breaking.
We construct effective field theories in which gravity is modified via spontaneous breaking of local Lorentz invariance. This is a gravitational analogue of the Higgs mechanism. These theories possess additional graviton modes and modified dispersion relations. They are manifestly well-behaved in the UV and free of discontinuities of the van Dam-Veltman-Zakharov type, ensuring compatibility with standard tests of gravity. They may have important phenomenological effects on large distance scales, offering an alternative to dark energy. For the case in which the symmetry is broken by a vector fi…
We give a detailed analysis of the particle spectrum and the perturbative unitarity of the recently introduced Weyl-invariant version of the new massive gravity in 2+1 dimensions. By computing the action up to second order in the fluctuations of the metric, the gauge and the scalar fields around the anti-de Sitter (AdS) and flat vacua, we find that the theory describes unitary (tachyon and ghost-free) massive spin-2, massive (or massless) spin-1 and massless spin-0 excitations for certain ranges of the dimensionless parameters. The theory is not unitary in de Sitter space. Scale invariance is …
Lorentz-violating operators involving Standard Model fields are tightly constrained by experimental data. However, bounds are more model-independent for Lorentz violation appearing in purely gravitational couplings. The spontaneous breaking of Lorentz invariance by the vacuum expectation value of a vector field selects a universal rest frame. This affects the propagation of the graviton, leading to a modification of Newton's law of gravity. We compute the size of the long-range preferred-frame effect in terms of the coefficients of the two-derivative operators in the low-energy effective theor…
We explore the possibility of the spontaneous symmetry breaking in 5D conformally invariant gravity, whose action consists of a scalar field nonminimally coupled to the curvature with its potential. Performing dimensional reduction via ADM decomposition, we find that the model allows an exact solution giving rise to the 4D Minkowski vacuum. Exploiting the conformal invariance with Gaussian warp factor, we show that it also admits a solution which implement the spontaneous breaking of conformal symmetry. We investigate its stability by performing the tensor perturbation and find the resulting s…
Gravitational theories with fixed background fields break local Lorentz and diffeomorphism invariance either explicitly or spontaneously. In the case of explicit breaking it is known that conflicts can arise between the dynamics and geometrical constraints, while spontaneous breaking evades this problem. It is for this reason that in the gravity sector of the Standard-Model Extension (SME) it is assumed that the background fields (SME coefficients) originate from spontaneous symmetry breaking. However, in other examples, such as Chern-Simons gravity and massive gravity, diffeomorphism invarian…
We propose a new scenario to implement spontaneous symmetry breaking in the space-time of an arbitrary dimension (D>2) by introducing the non-minimal coupling between the scalar field and the gravity. In this scenario, the usage of the familiar lambda Phi ^4 term, which is non-renormalizable for D >= 5, can be avoided altogether.
A very simple mechanism is proposed that stabilizes the orbifold geometry within the context of the Randall-Sundrum proposal for solving the hierarchy problem. The electroweak TeV scale is generated from the Planck scale by spontaneous breaking of the orbifold symmetry
We explicitly work out the de Sitter breaking contributions to the recent solution for the de Donder gauge graviton propagator on de Sitter. We also provide explicit power series expansions for the two structure functions, which are suitable for implementing dimensional regularization. And we evaluate the coincidence limit of the propagator.
Spontaneous Lorentz invariance violation (SLIV) realized through a nonlinear tensor field constraint H_{}^2=\pm M^2 (M is the proposed scale for Lorentz violation) is considered in tensor field gravity theory, which mimics linearized general relativity in Minkowski space-time. We show that such a SLIV pattern, due to which the true vacuum in the theory is chosen, induces massless tensor Goldstone modes some of which can naturally be associated with the physical graviton. When expressed in terms of the pure Goldstone modes, this theory looks essentially nonlinear and contains a variety of Loren…
It has long been known that photons and gravitons may appear as vector and tensor Goldstone modes caused \ by spontaneous Lorentz invariance violation (SLIV). Usually this approach is considered for photons and gravitons separately. We develop the emergent electrogravity theory consisting of the ordinary QED and the tensor field gravity model which mimics the linearized general relativity in Minkowski spacetime. In this theory, Lorentz symmetry appears incorporated into higher global symmetries of the length-fixing constraints put on the vector and tensor fields involved, $A_{μ}^{2}=\pm M_{A}^…
Tunneling in quantum field theory is well understood in the case of a single scalar field. However, in theories with spontaneous symmetry breaking, one has to take into account the additional zero modes which appear due to the Goldstone phenomenon. We calculate the false vacuum decay rate in this case. The result may differ significantly from the tunneling rates in the absence of symmetry breaking.
