Null energy condition and superluminal propagation
TL;DR: In this paper, the null energy condition is violated in a large class of situations, including isotropic solids and fluids relevant for cosmology, and the existence of superluminal modes is shown to imply the presence of instabilities.
Abstract: We study whether a violation of the null energy condition necessarily implies the presence of instabilities. We prove that this is the case in a large class of situations, including isotropic solids and fluids relevant for cosmology. On the other hand we present several counter-examples of consistent effective field theories possessing a stable background where the null energy condition is violated. Two necessary features of these counter-examples are the lack of isotropy of the background and the presence of superluminal modes. We argue that many of the properties of massive gravity can be understood by associating it to a solid at the edge of violating the null energy condition. We briefly analyze the difficulties of mimicking u H > 0 in scalar tensor theories of gravity.
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TL;DR: In this article, the authors showed that a generic massive gravity model with six degrees of freedom is perfectly viable for the unitary unitary gauge medium with stable phonon-like excitations and showed that under mild conditions, no ghost-like instability is present for any wavelength.
Abstract: Generic massive gravity models in the unitary gauge correspond to a self-gravitating medium with six degrees of freedom. It is widely believed that massive gravity models with six degrees of freedom have an unavoidable ghost-like instability; however, the corresponding medium has stable phonon-like excitations. The apparent contradiction is solved by the presence of a non-vanishing background pressure and energy density of the medium that opens up a stability window. The result is confirmed by looking at linear stability on an expanding Universe, recovering the flat space stability conditions in the small wavelength limit. Moreover, one can show that under rather mild conditions, no ghost-like instability is present for any wavelength. As a result, exploiting the medium interpretation, a generic massive gravity model with six degrees of freedom is perfectly viable.
10 citations
01 Jan 2013
TL;DR: In this paper, a nonsingular bouncing cosmological model was proposed to explain the early universe transition from a contraction phase into an expansion phase through a big bounce, and the stability of the bounce against inhomogeneities was investigated.
Abstract: This thesis studies the cosmological theory in which the universe transitions from a contraction phase into an expansion phase through a big bounce. Primordial uc- tuations that seed structure formation in the expansion phase arise from adiabatic perturbations in the preceding contraction phase. The purpose of this study is to un- derstand how the properties of the adiabatic perturbations are aected by the bounce. In particular, a nonsingular type of bounce is considered in which the universe ceases contraction and reverses to expansion at a nite size, fully described by known the- ories of classical gravity and eective eld theory. Two major aspects of such a nonsingular bounce are studied { the stability of the bounce against inhomogeneities, and the power spectrum of adiabatic perturbations after the bounce. Results show that a class of bouncing models based on ghost condensation are subject to unsta- ble growth of curvature and anisotropy, which alters the adiabatic perturbations and disrupts the nonsingular bounce. Another class of models with a ghost field are shown to have limited instability, though the contraction phase requires ne-tuning; suciently small perturbations can pass through the bounce and maintain a nearly scale-invariant power spectrum, consistent with observational constraints. Incorporating features of both models and resolving their problems, an ekpyrotic nonsingular bounce is proposed to support stable contraction and bouncing phases yet produce scale-invariant perturbations. Thus the nonsingular bouncing cosmology provides a possible explanation for the early universe.
10 citations
Cites background from "Null energy condition and superlumi..."
...Typically the violation of NEC would result in a gradient or ghost instability [70, 38]....
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TL;DR: In this paper, the authors performed a systematic study of various versions of massive gravity with and without violation of Lorentz symmetry in arbitrary dimension, and showed that these models are all associated with non-trivial dispersion laws, which easily allow superluminal propagation, ghosts, tachyons and essential irrationalities.
Abstract: We perform a systematic study of various versions of massive gravity with and without violation of Lorentz symmetry in arbitrary dimension. These theories are well known to possess very unusual properties, unfamiliar from studies of gauge and Lorentz invariant models. These peculiarities are caused by mixing of familiar transverse fields with revived longitudinal and pure gauge (Stueckelberg) fields and are all seen already in quadratic approximation. They are all associated with non-trivial dispersion laws, which easily allow superluminal propagation, ghosts, tachyons and essential irrationalities. Moreover, coefficients in front of emerging modes are small, what makes the theories essentially non-perturbative within a large Vainshtein radius. Attempts to get rid of unwanted degrees of freedom by giving them infinite masses lead to DVZ discontinuities in parameter (moduli) space, caused by un-permutability of different limits. Also, the condition m_{gh}=\infty can not be preserved already in non-trivial gravitational backgrounds and is unstable under any other perturbations of linearized gravity. At the same time an {\it a priori} healthy model of massive gravity in quadratic approximation definitely exists: provided by any mass level of Kaluza-Klein tower. It bypasses the problems because gravity field is mixed with other fields, and this explains why such mixing helps in other models. At the same time this can imply that the really healthy massive gravity can still require infinite number of extra fields beyond quadratic approximation.
10 citations
TL;DR: In this article, the authors studied the impact of spontaneous spacetime symmetry breaking during a quasi de-Sitter phase, in particular the 4-dimensional diffeomorphism invariance of GR is spontaneously broken down to $ISO(3)$.
Abstract: Inflation driven by a generic self-gravitating medium is an interesting alternative to study the impact of spontaneous spacetime symmetry breaking during a quasi de-Sitter phase, in particular the 4-dimensional diffeomorphism invariance of GR is spontaneously broken down to $ISO(3)$. The effective description is based on four scalar fields that describe the excitations of a supersolid. There are two phonon-like propagating scalar degrees of freedom that mix non-trivially both at early and late times and, after exiting the horizon, give rise to non-trivial correlations among the different scalar power spectra. The non-linear structure of the theory allows a secondary gravitational waves production during inflation, efficient enough to saturate the present experimental bound and with a blue-tilted spectral index.
10 citations
TL;DR: In this article, the authors explore wormholes in R2-gravity within the f(R, T) formalism by using hybrid shape functions, where R and T are the parameters of the hybrid shape function.
Abstract: In the present paper, we explore wormholes in R2-gravity within the f(R, T) formalism by using (hybrid shape function). The functional form f(R, T) = R + αR2 + λT is considered where R and T are th...
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01 Jan 1973
TL;DR: In this paper, the authors discuss the General Theory of Relativity in the large and discuss the significance of space-time curvature and the global properties of a number of exact solutions of Einstein's field equations.
Abstract: Einstein's General Theory of Relativity leads to two remarkable predictions: first, that the ultimate destiny of many massive stars is to undergo gravitational collapse and to disappear from view, leaving behind a 'black hole' in space; and secondly, that there will exist singularities in space-time itself. These singularities are places where space-time begins or ends, and the presently known laws of physics break down. They will occur inside black holes, and in the past are what might be construed as the beginning of the universe. To show how these predictions arise, the authors discuss the General Theory of Relativity in the large. Starting with a precise formulation of the theory and an account of the necessary background of differential geometry, the significance of space-time curvature is discussed and the global properties of a number of exact solutions of Einstein's field equations are examined. The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions. A discussion of the Cauchy problem for General Relativity is also included in this 1973 book.
8,932 citations
TL;DR: For a flat universe with a cosmological constant, the transition between the two epochs is constrained to be at z = 0.46 ± 0.13 as mentioned in this paper, and w = -1.02 ± (and w < -0.76 at the 95% confidence level) for an assumed static equation of state of dark energy.
Abstract: We have discovered 16 Type Ia supernovae (SNe Ia) with the Hubble Space Telescope (HST) and have used them to provide the first conclusive evidence for cosmic deceleration that preceded the current epoch of cosmic acceleration. These objects, discovered during the course of the GOODS ACS Treasury program, include 6 of the 7 highest redshift SNe Ia known, all at z > 1.25, and populate the Hubble diagram in unexplored territory. The luminosity distances to these objects and to 170 previously reported SNe Ia have been determined using empirical relations between light-curve shape and luminosity. A purely kinematic interpretation of the SN Ia sample provides evidence at the greater than 99% confidence level for a transition from deceleration to acceleration or, similarly, strong evidence for a cosmic jerk. Using a simple model of the expansion history, the transition between the two epochs is constrained to be at z = 0.46 ± 0.13. The data are consistent with the cosmic concordance model of ΩM ≈ 0.3, ΩΛ ≈ 0.7 (χ = 1.06) and are inconsistent with a simple model of evolution or dust as an alternative to dark energy. For a flat universe with a cosmological constant, we measure ΩM = 0.29 ± (equivalently, ΩΛ = 0.71). When combined with external flat-universe constraints, including the cosmic microwave background and large-scale structure, we find w = -1.02 ± (and w < -0.76 at the 95% confidence level) for an assumed static equation of state of dark energy, P = wρc2. Joint constraints on both the recent equation of state of dark energy, w0, and its time evolution, dw/dz, are a factor of ~8 more precise than the first estimates and twice as precise as those without the SNe Ia discovered with HST. Our constraints are consistent with the static nature of and value of w expected for a cosmological constant (i.e., w0 = -1.0, dw/dz = 0) and are inconsistent with very rapid evolution of dark energy. We address consequences of evolving dark energy for the fate of the universe.
4,236 citations
TL;DR: In this article, the first conclusive evidence for cosmic deceleration that preceded the current epoch of cosmic acceleration was provided by the discovery of 16 Type Ia supernovae with the Hubble Space Telescope (HST).
Abstract: We have discovered 16 Type Ia supernovae (SNe Ia) with the Hubble Space Telescope (HST) and have used them to provide the first conclusive evidence for cosmic deceleration that preceded the current epoch of cosmic acceleration. These objects, discovered during the course of the GOODS ACS Treasury program, include 6 of the 7 highest-redshift SNe Ia known, all at z>1.25, and populate the Hubble diagram in unexplored territory. The luminosity distances to these and 170 previous SNe Ia are provided. A purely kinematic interpretation of the SN Ia sample provides evidence at the > 99% confidence level for a transition from deceleration to acceleration or similarly, strong evidence for a cosmic jerk. Using a simple model of the expansion history, the transition between the two epochs is constrained to be at z=0.46 +/- 0.13. The data are consistent with the cosmic concordance model of Omega_M ~ 0.3, Omega_Lambda~0.7 (chi^2_dof=1.06), and are inconsistent with a simple model of evolution or dust as an alternative to dark energy. For a flat Universe with a cosmological constant. When combined with external flat-Universe constraints we find w=-1.02 + 0.13 - 0.19 (and $<-0.76 at the 95% confidence level) for an assumed static equation of state of dark energy, P = w\rho c^2. Joint constraints on both the recent equation of state of dark energy, $w_0$, and its time evolution, dw/dz, are a factor of ~8 more precise than its first estimate and twice as precise as those without the SNe Ia discovered with HST. Our constraints are consistent with the static nature of and value of w expected for a cosmological constant (i.e., w_0 = -1.0, dw/dz = 0), and are inconsistent with very rapid evolution of dark energy. We address consequences of evolving dark energy for the fate of the Universe.
3,528 citations
TL;DR: In this article, the authors propose a mechanism by which four-dimensional Newtonian gravity emerges on a 3-brane in 5D Minkowski space with an infinite size extra dimension.
3,247 citations