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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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TL;DR: In this paper, the authors characterize condensed matter systems as any state in a Poincare-invariant theory that spontaneously breaks Lorentz boosts while preserving at large distances some form of spatial translations, time-translations, and possibly spatial rotations.
Abstract: We classify condensed matter systems in terms of the spacetime symmetries they spontaneously break. In particular, we characterize condensed matter itself as any state in a Poincare-invariant theory that spontaneously breaks Lorentz boosts while preserving at large distances some form of spatial translations, time-translations, and possibly spatial rotations. Surprisingly, the simplest, most minimal system achieving this symmetry breaking pattern---the "framid"---does not seem to be realized in Nature. Instead, Nature usually adopts a more cumbersome strategy: that of introducing internal translational symmetries---and possibly rotational ones---and of spontaneously breaking them along with their space-time counterparts, while preserving unbroken diagonal subgroups. This symmetry breaking pattern describes the infrared dynamics of ordinary solids, fluids, superfluids, and---if they exist---supersolids. A third, "extra-ordinary", possibility involves replacing these internal symmetries with other symmetries that do not commute with the Poincare group, for instance the galileon symmetry, supersymmetry or gauge symmetries. Among these options, we pick the systems based on the galileon symmetry, the "galileids", for a more detailed study. Despite some similarity, all different patterns produce truly distinct physical systems with different observable properties. For instance, the low-energy $2\to 2$ scattering amplitudes for the Goldstone excitations in the cases of framids, solids and galileids scale respectively as $E^2$, $E^4$, and $E^6$. Similarly the energy momentum tensor in the ground state is "trivial" for framids ($\rho +p=0$), normal for solids ($\rho+p>0$) and even inhomogenous for galileids.

104 citations

Journal ArticleDOI
TL;DR: In this paper, the cosmological evolution of a mimetic matter model with arbitrary scalar potential is investigated, which is the method for constructing a model for an arbitrary evolution of the scale factor.
Abstract: We investigate the cosmological evolution of a mimetic matter model with arbitrary scalar potential. The cosmological reconstruction---which is the method for constructing a model for an arbitrary evolution of the scale factor---is explicitly performed for different choices of potential. The cases where the mimetic matter model shows the evolution as cold dark matter (CDM), the $w\mathrm{CDM}$ model, dark matter and dark energy with a dynamical $Om(z)$ [where $Om(z)\ensuremath{\equiv}[(H(z)/{H}_{0}{)}^{2}\ensuremath{-}1]/[(1+z{)}^{3}\ensuremath{-}1]$], and phantom dark energy with a phantom-nonphantom crossing are presented in detail. The cosmological perturbations for such evolutions are studied in the mimetic matter model. For instance, the evolution behavior of the matter density contrast (which is different than the usual one, i.e., $\stackrel{\ifmmode\ddot\else\textasciidieresis\fi{}}{\ensuremath{\delta}}+2H\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{\ensuremath{\delta}}\ensuremath{-}{\ensuremath{\kappa}}^{2}\ensuremath{\rho}\ensuremath{\delta}/2=0$) is investigated. The possibility of a peculiar evolution of $\ensuremath{\delta}$ in the model under consideration is shown. Special attention is paid to the behavior of the matter density contrast near the future singularity, where the decay of perturbations may occur much earlier than the singularity.

103 citations

Journal ArticleDOI
TL;DR: For interacting theories in more than two dimensions, it was shown in this article that the averaged null energy condition must be positive for all spin operators other than the stress tensor, leading to new inequalities for the coupling constants of spinning operators in conformal field theory.
Abstract: Unitary, Lorentz-invariant quantum field theories in flat spacetime obey microcausality: commutators vanish at spacelike separation. For interacting theories in more than two dimensions, we show that this implies that the averaged null energy, $\int du T_{uu}$, must be positive. 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 $\int du X_{uuu\cdots u} \geq 0$. 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.

103 citations


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

  • ...The connection between causality and null energy is well known in the gravitational context (see for example [19, 20] and the references above) and in AdS/CFT (see for example [21,22])....

    [...]

Journal ArticleDOI
TL;DR: In this paper, a simple braneworld model was investigated in which the universe contains only cold dark matter and a cosmological constant, but the effective dark energy is phantomlike because of extra-dimensional gravity effects.
Abstract: We investigate a simple braneworld model in which the universe contains only cold dark matter and a cosmological constant, but the effective dark energy is phantomlike because of extra-dimensional gravity effects. Modified gravity screens the cosmological constant {lambda}, allowing for a larger {lambda}. In practice, observations do not favor any significant screening. We use supernova data, the cosmic microwave background shift parameter, and the baryon oscillation peak in the galaxy distribution to constrain the model. We find the mean value of {omega}{sub m} with 68% confidence limits, and an upper limit on {omega}{sub {lambda}} at the 68% confidence level. The best-fit model is very close to a standard LCDM model, but the LCDM model provides a better fit since it has one less parameter.

103 citations

Journal ArticleDOI
TL;DR: In this article, the equivalence between a perfect barotropic fluid and a derivatively coupled scalar field with Lagrangian was used to derive the second-order metric during matter dominance in the comoving gauge directly as a function of the primordial inflationary perturbation ζ.
Abstract: We study nonlinear cosmological perturbations during post-inflationary evolution, using the equivalence between a perfect barotropic fluid and a derivatively coupled scalar field with Lagrangian . Since this Lagrangian is just a special case of k-inflation, this approach is analogous to the one employed in the study of non-Gaussianities from inflation. We use this method to derive the second-order metric during matter dominance in the comoving gauge directly as a function of the primordial inflationary perturbation ζ. Going to Poisson gauge, we recover the metric previously derived in the literature.

101 citations


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

  • ...so that √ X acts as a sort of conjugate variable with respect to n [9]....

    [...]

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