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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

AbstractWe 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.

Topics: Null (mathematics) (59%), Energy condition (59%), Massive gravity (53%), Superluminal motion (52%), General relativity (51%)

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Citations
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Journal ArticleDOI
Abstract: In the Dvali-Gabadadze-Porrati (DGP) model, the "self-accelerating" solution is plagued by a ghost instability, which makes the solution untenable. This fact, as well as all interesting departures from general relativity (GR), are fully captured by a four-dimensional effective Lagrangian, valid at distances smaller than the present Hubble scale. The 4D effective theory involves a relativistic scalar pi, universally coupled to matter and with peculiar derivative self-interactions. In this paper, we study the connection between self-acceleration and the presence of ghosts for a quite generic class of theories that modify gravity in the infrared. These theories are defined as those that at distances shorter than cosmological, reduce to a certain generalization of the DGP 4D effective theory. We argue that for infrared modifications of GR locally due to a universally coupled scalar, our generalization is the only one that allows for a robust implementation of the Vainshtein effect-the decoupling of the scalar from matter in gravitationally bound systems-necessary to recover agreement with solar-system tests. Our generalization involves an internal Galilean invariance, under which pi's gradient shifts by a constant. This symmetry constrains the structure of the pi Lagrangian so much so that in 4D there exist only five terms that can yield sizable nonlinearities without introducing ghosts. We show that for such theories in fact there are "self-accelerating" de Sitter solutions with no ghostlike instabilities. In the presence of compact sources, these solutions can support spherically symmetric, Vainshtein-like nonlinear perturbations that are also stable against small fluctuations. We investigate a possible infrared completion of these theories at scales of order of the Hubble horizon, and larger. There are however some features of our theories that may constitute a problem at the theoretical or phenomenological level: the presence of superluminal excitations; the extreme subluminality of other excitations, which makes the quasistatic approximation for certain solar-system observables unreliable due to Cherenkov emission; the very low strong-interaction scale for pi pi scatterings.

1,937 citations


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

  • ...In a broad technical sense we may define a modification of gravity as a field theory possessing solutions over which new degrees of freedom affect the propagation of gravity while the background is not producing any sizable energy momentum tensor [7]....

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Journal ArticleDOI
Abstract: We study the effective field theory of inflation, i.e. the most general theory describing the fluctuations around a quasi de Sitter background, in the case of single field models. The scalar mode can be eaten by the metric by going to unitary gauge. In this gauge, the most general theory is built with the lowest dimension operators invariant under spatial diffeomorphisms, like g00 and Kμν, the extrinsic curvature of constant time surfaces. This approach allows us to characterize all the possible high energy corrections to simple slow-roll inflation, whose sizes are constrained by experiments. Also, it describes in a common language all single field models, including those with a small speed of sound and Ghost Inflation, and it makes explicit the implications of having a quasi de Sitter background. The non-linear realization of time diffeomorphisms forces correlation among different observables, like a reduced speed of sound and an enhanced level of non-Gaussianity.

1,099 citations


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

  • ...It would also be interesting to use our approach for the study of fluctuations in fluids like in radiation or matter dominance [8]....

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  • ...In appendix A we prove (1)Indeed, as shown for example in [8], non-vorticous excitations of a perfect fluid may be described by a derivatively coupled scalar....

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  • ...This is an example of the well studied relationship between violation of the null energy condition, which in a FRW Universe is equivalent to Ḣ < 0, and the presence of instabilities in the system [17, 8]....

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Journal ArticleDOI
Luca Amendola1, Stephen Appleby2, Anastasios Avgoustidis3, David Bacon4, Tessa Baker5, Marco Baldi6, Marco Baldi7, Marco Baldi8, Nicola Bartolo9, Nicola Bartolo6, Alain Blanchard10, Camille Bonvin11, Stefano Borgani6, Stefano Borgani12, Enzo Branchini6, Enzo Branchini13, Clare Burrage3, Stefano Camera, Carmelita Carbone6, Carmelita Carbone14, Luciano Casarini15, Luciano Casarini16, Mark Cropper17, Claudia de Rham18, J. P. Dietrich19, Cinzia Di Porto, Ruth Durrer11, Anne Ealet, Pedro G. Ferreira5, Fabio Finelli6, Juan Garcia-Bellido20, Tommaso Giannantonio19, Luigi Guzzo6, Luigi Guzzo14, Alan Heavens18, Lavinia Heisenberg21, Catherine Heymans22, Henk Hoekstra23, Lukas Hollenstein, Rory Holmes, Zhiqi Hwang24, Knud Jahnke25, Thomas D. Kitching17, Tomi S. Koivisto26, Martin Kunz11, Giuseppe Vacca27, Eric V. Linder28, M. March29, Valerio Marra30, Carlos Martins31, Elisabetta Majerotto11, Dida Markovic32, David J. E. Marsh33, Federico Marulli8, Federico Marulli6, Richard Massey34, Yannick Mellier35, Francesco Montanari36, David F. Mota15, Nelson J. Nunes37, Will J. Percival32, Valeria Pettorino38, Valeria Pettorino39, Cristiano Porciani, Claudia Quercellini, Justin I. Read40, Massimiliano Rinaldi41, Domenico Sapone42, Ignacy Sawicki43, Roberto Scaramella, Constantinos Skordis43, Constantinos Skordis44, Fergus Simpson45, Andy Taylor22, Shaun A. Thomas, Roberto Trotta18, Licia Verde45, Filippo Vernizzi38, Adrian Vollmer, Yun Wang46, Jochen Weller19, T. G. Zlosnik47 
Abstract: Euclid is a European Space Agency medium-class mission selected for launch in 2020 within the cosmic vision 2015–2025 program. The main goal of Euclid is to understand the origin of the accelerated expansion of the universe. Euclid will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and red-shifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky. Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss five broad topics: dark energy and modified gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis. This review has been planned and carried out within Euclid’s Theory Working Group and is meant to provide a guide to the scientific themes that will underlie the activity of the group during the preparation of the Euclid mission.

1,036 citations


Journal ArticleDOI
Abstract: We study the effective field theory of inflation, i.e. the most general theory describing the fluctuations around a quasi de Sitter background, in the case of single field models. The scalar mode can be eaten by the metric by going to unitary gauge. In this gauge, the most general theory is built with the lowest dimension operators invariant under spatial diffeomorphisms, like g^{00} and K_{mu nu}, the extrinsic curvature of constant time surfaces. This approach allows us to characterize all the possible high energy corrections to simple slow-roll inflation, whose sizes are constrained by experiments. Also, it describes in a common language all single field models, including those with a small speed of sound and Ghost Inflation, and it makes explicit the implications of having a quasi de Sitter background. The non-linear realization of time diffeomorphisms forces correlation among different observables, like a reduced speed of sound and an enhanced level of non-Gaussianity.

999 citations


Journal ArticleDOI
Abstract: We argue that certain apparently consistent low-energy effective field theories described by local, Lorentzinvariant Lagrangians, secretly exhibit macroscopic non-locality and cannot be embedded in any UV theory whose S-matrix satisfies canonical analyticity constraints. The obstruction involves the signs of a set of leading irrelevant operators, which must be strictly positive to ensure UV analyticity. An IR manifestation of this restriction is that the “wrong” signs lead to superluminal fluctuations around non-trivial backgrounds, making it impossible to define local, causal evolution, and implying a surprising IR breakdown of the effective theory. Such effective theories can not arise in quantum field theories or weakly coupled string theories, whose S-matrices satisfy the usual analyticity properties. This conclusion applies to the DGP brane-world model modifying gravity in the IR, giving a simple explanation for the difficulty of embedding this model into controlled stringy backgrounds, and to models of electroweak symmetry breaking that predict negative anomalous quartic couplings for the W and Z. Conversely, any experimental support for the DGP model, or measured negative signs for anomalous quartic gauge boson couplings at future accelerators, would constitute direct evidence for the existence of superluminality and macroscopic non-locality unlike anything previously seen in physics, and almost incidentally falsify both local quantum field theory and perturbative string theory.

914 citations


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

  • ...Conversely, as soon as superluminal modes are allowed, the null energy condition is lost, even in the absence of instabilities within the matter dynamics [12], and CTC’s can in principle appear with respect to the gravitational metric gμν as well....

    [...]

  • ...While our arguments do not directly apply to theories in which the vacuum spontaneously breaks Lorentz invariance, such as Higgs phases of gravity [6, 7, 8] or the models studied in [12], it would be interesting to ask whether there are any analogous constraints to those we have discussed....

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  • ...Notice that a violation of the Null Energy Condition under very broad assumptions leads either to instabilities at arbitrarily short time-scales or to superluminal propagation in the matter sector [12]....

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  • ...It is a remarkable fact that if the matter dynamics do not feature either instabilities or superluminal modes then the energy momentum tensor corresponding to the effective metric satisfies the null energy condition [12]....

    [...]


References
More filters

Book
01 Jan 1973
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.

8,650 citations


Book
01 Jan 1984

8,120 citations


Journal ArticleDOI
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.

4,027 citations


Journal ArticleDOI
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.

3,399 citations


Journal ArticleDOI
Abstract: We suggest a mechanism by which four-dimensional Newtonian gravity emerges on a 3-brane in 5D Minkowski space with an infinite size extra dimension. The worldvolume theory gives rise to the correct 4D potential at short distances whereas at large distances the potential is that of a 5D theory. We discuss some phenomenological issues in this framework.

3,196 citations