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 paper, the authors consider modifications of general relativity characterized by a special noncovariant constraint on metric coefficients, which effectively generates a perfect-fluid type of matter stress tensor in Einstein equations.
Abstract: We consider modifications of general relativity characterized by a special noncovariant constraint on metric coefficients, which effectively generates a perfect-fluid type of matter stress tensor in Einstein equations. Such class of modified gravity models includes recently suggested generalized unimodular gravity (GUMG), its simplest version---unimodular gravity---and self-gravitating media theories. We make these gravity models covariant by introducing four Stueckelberg fields and show that in the case of generalized unimodular gravity three out of these fields dynamically decouple. This means that the covariant form of generalized unimodular gravity is dynamically equivalent a special form of $k$-essence theory with translationally noninvariant kinetic term in the Lagrangian which can be reconstructed from the parameters of GUMG theory. We provide the examples, where such reconstruction can be done explicitly, and briefly discuss theories beyond GUMG, related to self-gravitating media models. Also we compare GUMG $k$ inflation with cuscuton models of dynamically inert $k$-essence field and discuss motivation for GUMG coming from effective field theory.
8 citations
Cites background from "Null energy condition and superlumi..."
...Thus, contrary to k-essence, the equivalent perfect fluid possesses nonvanishing vorticity, see [44]....
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TL;DR: In this article, it was shown that the effective theory describing single component continuous media with a linear and constant equation of state of the form p = wρ is invariant under a 1-parameter family of continuous disformal transformations.
Abstract: We show that the effective theory describing single component continuous media with a linear and constant equation of state of the form p=wρ is invariant under a 1-parameter family of continuous disformal transformations. In the special case of w=1/3 (ultrarelativistic gas), such a family reduces to conformal transformations. As examples, perfect fluids, irrotational dust (mimetic matter) and homogeneous and isotropic solids are discussed.
8 citations
TL;DR: In this paper, an effective field theory that allows for stable null energy conditions with exactly luminal excitations only is presented, and it is shown that if the relevant null energy condition is inside the effective theory, then other solutions allow for superluminal signal propagation.
Abstract: In QFT, the null energy condition (NEC) for a classical field configuration is usually associated with that configuration's stability against small perturbations, and with the sub-luminality of these. Here, we exhibit an effective field theory that allows for stable NEC-violating solutions with exactly luminal excitations only. The model is the recently introduced `galileon', or more precisely its conformally invariant version. We show that the theory's low-energy S-matrix obeys standard positivity as implied by dispersion relations. However we also show that if the relevant NEC-violating solution is inside the effective theory, then other (generic) solutions allow for superluminal signal propagation. While the usual association between sub-luminality and positivity is not obeyed by our example, that between NEC and sub-luminality is, albeit in a less direct way than usual.
8 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 I SO(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 I SO(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.
8 citations
DOI•
01 Jan 2020
TL;DR: In this article, an effective field theory description for non-Abelian superfluids was derived for the spectrum of scaling dimensions and the OPE coefficients in a large charge expansion, both for theories invariant under Abelian and non-abelian symmetry groups.
Abstract: This thesis explores the application of semiclassical methods in the study of states with large quantum numbers for theories invariant under internal symmetries. In the first part of the thesis, we study zero-temperature superfluids. These provide a general description of many systems at finite charge density. In particular, we derive a universal effective field theory description for non-Abelian superfluids. Such construction illustrates the role of gapped Goldstones, Goldstone modes whose gap is fixed by the symmetry, and may be as large as the strong coupling scale of the system. The second and third part of the thesis are devoted to the study of operators with large internal charge in strongly coupled conformal field theories. Using effective field theory techniques, we derive universal results for the spectrum of scaling dimensions and the OPE coefficients in a large charge expansion, both for theories invariant under Abelian and non-Abelian symmetry groups. We also extend these results to operators with large spin as well as large internal charge. The last part of this thesis studies operators with large internal charge within the εexpansion. We show how, using a semiclassical approach, one can overcome the breakdown of diagrammatic perturbation theory for the multi-legged amplitudes associated with these operators. These results provide a concrete illustration of the systematic large charge expansion discussed in the previous parts.
8 citations
Additional excerpts
...17) provides a non-zero charge density J0 = F ′ 1(μ) ≡ n and we can obtain the energy density ρ and the pressure P as a function of μ inverting Tμν = (ρ+ P )uμuν + Pημν [65]; doing so on the background we recover the zero temperature thermodynamic identity ρ+ P = nμ [66]....
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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
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