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 study the connection between self-acceleration and the presence of ghosts for a quite generic class of theories that modify gravity in the infrared, defined as those that at distances shorter than cosmological, reduce to a certain generalization of the Dvali-Gabadadze-Porrati (DGP) effective theory.
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.
2,086 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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Heidelberg University1, Korea Institute for Advanced Study2, University of Nottingham3, Institute of Cosmology and Gravitation, University of Portsmouth4, University of Oxford5, INAF6, Istituto Nazionale di Fisica Nucleare7, University of Bologna8, University of Padua9, University of Toulouse10, University of Geneva11, University of Trieste12, Roma Tre University13, University of Milan14, University of Oslo15, Federal University of Rio Grande do Norte16, University College London17, Imperial College London18, Ludwig Maximilian University of Munich19, Autonomous University of Madrid20, ETH Zurich21, University of Edinburgh22, Leiden University23, Sun Yat-sen University24, Max Planck Society25, Royal Institute of Technology26, University of Milano-Bicocca27, University of California, Berkeley28, University of Pennsylvania29, Universidade Federal do Espírito Santo30, University of Porto31, University of Portsmouth32, King's College London33, Durham University34, Institut d'Astrophysique de Paris35, Helsinki Institute of Physics36, University of Lisbon37, Université Paris-Saclay38, Paris Diderot University39, University of Surrey40, University of Trento41, University of Chile42, Academy of Sciences of the Czech Republic43, University of Cyprus44, University of Barcelona45, California Institute of Technology46, Perimeter Institute for Theoretical Physics47
TL;DR: Euclid is a European Space Agency medium-class mission selected for launch in 2020 within the cosmic vision 2015-2025 program as discussed by the authors, which will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and red-shift of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky.
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.
1,211 citations
TL;DR: The effective field theory of inflation as discussed by the authors is the most general theory describing the fluctuations around a quasi de Sitter background, in the case of single field models, in which the scalar mode can be eaten by the metric by going to unitary gauge.
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.
1,183 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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TL;DR: In this paper, it was shown that low-energy effective field theories described by local, Lorentz invariant Lagrangians, secretly exhibit macroscopic non-locality and cannot be embedded in any UV theory whose S-matrix satisfies canonical analyticity constraints.
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.
1,127 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....
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...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]....
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TL;DR: The effective field theory of inflation as mentioned in this paper is the most general theory describing the fluctuations around a quasi de Sitter background, in the case of single field models, in which the scalar mode can be eaten by the metric by going to unitary gauge.
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.
1,103 citations
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TL;DR: In this paper, a new class of solutions of the Einstein field equations is presented, which describe wormholes that, in principle, could be traversed by human beings, and it is essential in these solutions that the wormhole possess a throat at which there is no horizon.
Abstract: Rapid interstellar travel by means of spacetime wormholes is described in a way that is useful for teaching elementary general relativity. The description touches base with Carl Sagan’s novel C o n t a c t, which, unlike most science fiction novels, treats such travel in a manner that accords with the best 1986 knowledge of the laws of physics. Many objections are given against the use of black holes or Schwarzschild wormholes for rapid interstellar travel. A new class of solutions of the Einstein field equations is presented, which describe wormholes that, in principle, could be traversed by human beings. It is essential in these solutions that the wormhole possess a throat at which there is no horizon; and this property, together with the Einstein field equations, places an extreme constraint on the material that generates the wormhole’s spacetime curvature: In the wormhole’s throat that material must possess a radial tension τ0 with the enormous magnitude τ0∼ (pressure at the center of the most massive of neutron stars)×(20 km)2/(circumference of throat)2. Moreover, this tension must exceed the material’s density of mass‐energy, ρ0 c 2. No known material has this τ0>ρ0 c 2property, and such material would violate all the ‘‘energy conditions’’ that underlie some deeply cherished theorems in general relativity. However, it is not possible today to rule out firmly the existence of such material; and quantum field theory gives tantalizing hints that such material might, in fact, be possible.
2,169 citations
TL;DR: In this article, the basic theory of k-essence and dynamical attractors based on evolving scalar fields with nonlinear kinetic energy terms in the action is presented, and guidelines for constructing concrete examples and show that there are two classes of solutions.
Abstract: We recently introduced the concept of ``k-essence'' as a dynamical solution for explaining naturally why the universe has entered an epoch of accelerated expansion at a late stage of its evolution. The solution avoids fine-tuning of parameters and anthropic arguments. Instead, k-essence is based on the idea of a dynamical attractor solution which causes it to act as a cosmological constant only at the onset of matter domination. Consequently, k-essence overtakes the matter density and induces cosmic acceleration at about the present epoch. In this paper, we present the basic theory of k-essence and dynamical attractors based on evolving scalar fields with nonlinear kinetic energy terms in the action. We present guidelines for constructing concrete examples and show that there are two classes of solutions, one in which cosmic acceleration continues forever and one in which the acceleration has finite duration.
1,794 citations
TL;DR: The holographic principle as mentioned in this paper asserts that the fundamental degrees of freedom involved in a unified description of spacetime and matter must be manifest in an underlying quantum theory of gravity, and it has yet to be explained.
Abstract: There is strong evidence that the area of any surface limits the information content of adjacent spacetime regions, at $1.4\ifmmode\times\else\texttimes\fi{}{10}^{69}$ bits per square meter. This article reviews the developments that have led to the recognition of this entropy bound, placing special emphasis on the quantum properties of black holes. The construction of light sheets, which associate relevant spacetime regions to any given surface, is discussed in detail. This article explains how the bound is tested, and its validity is demonstrated in a wide range of examples. A universal relation between geometry and information is thus uncovered. It has yet to be explained. The holographic principle asserts that its origin must lie in the number of fundamental degrees of freedom involved in a unified description of spacetime and matter. It must be manifest in an underlying quantum theory of gravity. This article surveys some successes and challenges in implementing the holographic principle.
1,706 citations
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TL;DR: In this paper, the authors present an alternative explanation which allows scalar fields to evolve cosmologically while having couplings to matter of order unity in the solar system, where the mass of the fields depends on the local matter density.
Abstract: The evidence for the accelerated expansion of the universe and the time-dependence of the fine-structure constant suggests the existence of at least one scalar field with a mass of order H_0 If such a field exists, then it is generally assumed that its coupling to matter must be tuned to unnaturally small values in order to satisfy the tests of the Equivalence Principle (EP) In this paper, we present an alternative explanation which allows scalar fields to evolve cosmologically while having couplings to matter of order unity In our scenario, the mass of the fields depends on the local matter density: the interaction range is typically of order 1 mm on Earth (where the density is high) and of order 10-10^4 AU in the solar system (where the density is low) All current bounds from tests of General Relativity are satisfied Nevertheless, we predict that near-future experiments that will test gravity in space will measure an effective Newton's constant different by order unity from that on Earth, as well as EP violations stronger than currently allowed by laboratory experiments Such outcomes would constitute a smoking gun for our scenario
1,388 citations
TL;DR: In this article, the authors study the stability of dynamical models exhibiting a negative kinetic term and show that these models might be phenomenologically viable if thought of as effective field theories valid only up to a certain momentum cutoff.
Abstract: Models of dark energy are conveniently characterized by the equation-of-state parameter $w=p/\ensuremath{\rho},$ where $\ensuremath{\rho}$ is the energy density and p is the pressure. Imposing the dominant energy condition, which guarantees stability of the theory, implies that $wg~\ensuremath{-}1.$ Nevertheless, it is conceivable that a well-defined model could (perhaps temporarily) have $wl\ensuremath{-}1 ,$ and indeed such models have been proposed. We study the stability of dynamical models exhibiting $wl\ensuremath{-}1$ by virtue of a negative kinetic term. Although naively unstable, we explore the possibility that these models might be phenomenologically viable if thought of as effective field theories valid only up to a certain momentum cutoff. Under our most optimistic assumptions, we argue that the instability time scale can be greater than the age of the universe, but only if the cutoff is at or below ${10}^{\ensuremath{-}3}\mathrm{eV}.$ We conclude that it is difficult, although not necessarily impossible, to construct viable models of dark energy with $wl\ensuremath{-}1;$ observers should keep an open mind, but the burden is on theorists to demonstrate that any proposed new models are not ruled out by rapid vacuum decay.
1,224 citations