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Journal ArticleDOI

Null energy condition and superluminal propagation

07 Mar 2006-Journal of High Energy Physics (IOP Publishing)-Vol. 2006, Iss: 3, pp 025-025
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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Citations
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Journal ArticleDOI
TL;DR: In this paper, a wide class of models which realise a bounce in a spatially flat Friedmann universe in standard General Relativity were presented. But the main ingredient of the models is a noncanonical, minimally coupled scalar field belonging to the class of theories with Kinetic Gravity Braiding / Galileon-like self-couplings.
Abstract: We present a wide class of models which realise a bounce in a spatially flat Friedmann universe in standard General Relativity The key ingredient of the theories we consider is a noncanonical, minimally coupled scalar field belonging to the class of theories with Kinetic Gravity Braiding / Galileon-like self-couplings In these models, the universe smoothly evolves from contraction to expansion, suffering neither from ghosts nor gradient instabilities around the turning point The end-point of the evolution can be a standard radiation-domination era or an inflationary phase We formulate necessary restrictions for Lagrangians needed to obtain a healthy bounce and illustrate our results with phase portraits for simple systems including the recently proposed Galilean Genesis scenario

309 citations

Journal ArticleDOI
TL;DR: This article developed a cosmological model where primordial inflation is driven by a "solid", defined as a system of three derivatively coupled scalar fields obeying certain symmetries and spontaneously breaking a certain subgroup of these.
Abstract: We develop a cosmological model where primordial inflation is driven by a 'solid', defined as a system of three derivatively coupled scalar fields obeying certain symmetries and spontaneously breaking a certain subgroup of these The symmetry breaking pattern differs drastically from that of standard inflationary models: time translations are unbroken This prevents our model from fitting into the standard effective field theory description of adiabatic perturbations, with crucial consequences for the dynamics of cosmological perturbations Most notably, non-gaussianities in the curvature perturbations are unusually large, with f_NL ~ 1/(\epsilonc_s^2), and have a novel shape: peaked in the squeezed limit, with anisotropic dependence on how the limit is approached Other unusual features include the absence of adiabatic fluctuation modes during inflation---which does not impair their presence and near scale-invariance after inflation---and a slightly blue tilt for the tensor modes

298 citations


Cites background or methods from "Null energy condition and superlumi..."

  • ...10)—whose structure is protected by the volume-preserving diff symmetry— features vanishing propagation speed for the transverse phonons [8, 9], as can be checked explicitly in (2....

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  • ...Cosmological systems of this sort have been considered briefly in [8]....

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  • ...On the other hand however, because of powerful conservation laws for vorticity, classically one can consistently set to zero the transverse excitations—the vortices—and be left with an EFT for the compressional modes only [8]....

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  • ...Here instead we will review the equivalent construction of [8, 9] (see also [10]), whose notation we will follow....

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  • ...But our EFT conforms to the hypotheses of the general theorem of [8], which links NEC violations to such pathologies as ghost- or gradient-instabilities and superluminality....

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Journal ArticleDOI
TL;DR: In this article, the authors consider the low-energy effective field theory describing the infrared dynamics of non-dispative fluids, and they extend previous work to accommodate conserved charges, and clarify the matching between field-theory variables and thermodynamical ones.
Abstract: We consider the low-energy effective field theory describing the infrared dynamics of nondissipative fluids. We extend previous work to accommodate conserved charges, and we clarify the matching between field-theory variables and thermodynamical ones. We discuss the systematics of the derivative expansion, for which field theory offers a conceptually clear and technically neat scheme. As an example, we compute the correction to the sound-wave dispersion relation coming from a sample second-order term. This formalism forms the basis for a study of anomalies in hydrodynamics via effective field theory, which is initiated in a companion paper.

273 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that the averaged null energy of a spin operator in more than two dimensions must be non-negative, i.e., it cannot be a non-local operator.
Abstract: Unitary, Lorentz-invariant quantum field theories in flat spacetime obey mi-crocausality: commutators vanish at spacelike separation. For interacting theories in more than two dimensions, we show that this implies that the averaged null energy, ∫ duT uu , must be non-negative. This non-local operator appears in the operator product expansion of local operators in the lightcone limit, and therefore contributes to n-point functions. We derive a sum rule that isolates this contribution and is manifestly positive. The argument also applies to certain higher spin operators other than the stress tensor, generating an infinite family of new constraints of the form ∫ duX uuu···u ≥ 0. These lead to new inequalities for the coupling constants of spinning operators in conformal field theory, which include as special cases (but are generally stronger than) the existing constraints from the lightcone bootstrap, deep inelastic scattering, conformal collider methods, and relative entropy. We also comment on the relation to the recent derivation of the averaged null energy condition from relative entropy, and suggest a more general connection between causality and information-theoretic inequalities in QFT.

255 citations

Journal ArticleDOI
TL;DR: In this article, a cosmological scenario is proposed, in which standard inflation is replaced by an expanding phase with a drastic violation of the Null Energy Condition (NEC): \dot H >> H^2.
Abstract: We propose a novel cosmological scenario, in which standard inflation is replaced by an expanding phase with a drastic violation of the Null Energy Condition (NEC): \dot H >> H^2. The model is based on the recently introduced Galileon theories, that allow NEC violating solutions without instabilities. The unperturbed solution describes a Universe that is asymptotically Minkowski in the past, expands with increasing energy density until it exits the regime of validity of the effective field theory and reheats. This solution is a dynamical attractor and the Universe is driven to it, even if it is initially contracting. The study of perturbations of the Galileon field reveals some subtleties, related to the gross violation of the NEC and it shows that adiabatic perturbations are cosmologically irrelevant. The model, however, suggests a new way to produce a scale invariant spectrum of isocurvature perturbations, which can later be converted to adiabatic: the Galileon is forced by symmetry to couple to the other fields as a dilaton; the effective metric it yields on the NEC violating solution is that of de Sitter space, so that all light scalars will automatically acquire a nearly scale-invariant spectrum of perturbations.

251 citations


Cites background from "Null energy condition and superlumi..."

  • ...It is worth emphasizing that the NEC is usually taken for granted not due to lack of imagination, but because of its exceptional robustness—it is especially hard to construct consistent effective field theories that violate it [1]....

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  • ...For these theories the usual relation between the violation of the NEC and the presence of pathological instabilities [1] is avoided, due to the presence of higher derivative interactions....

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References
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Book
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

Book
01 Jan 1984

8,137 citations

Journal ArticleDOI
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

Journal ArticleDOI
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

Journal ArticleDOI
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