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 show that for a wide range of initial conditions, the tachyonic field gets stabilized with the appropriate values well before the onset of the ekpyrotic phase.
Abstract: New ekpyrotic cosmology is an alternative scenario of early universe cosmology in which the universe existed before the big bang. The simplest model relies on two scalar fields, whose entropy perturbation leads to a scale-invariant spectrum of density fluctuations. The ekpyrotic solution has a tachyonic instability along the entropy field direction which, a priori, appears to require fine-tuning of the initial conditions. In this paper, we show that these can be achieved naturally by adding a small positive mass term for the tachyonic field and coupling to light fermions. Then, for a wide range of initial conditions, the tachyonic field gets stabilized with the appropriate values well before the onset of the ekpyrotic phase. Furthermore, we show that ekpyrotic theory is successful in solving the flatness, horizon and homogeneity problems of standard big bang cosmology. Motivated by the analysis of the tachyonic instability, we propose a simplification of the model in terms of new field variables. Instead of requiring two exponential potentials, one for each scalar field, it suffices to consider a single nearly exponential potential for one of the fields and a tachyonic mass term along the orthogonal direction in field space. All other terms in the potential are essentially arbitrary. This greatly widens the class of ekpyrotic potentials and allows substantial freedom in determining the spectral index and possible non-Gaussianity. We present a generalized expression for the spectral index which is easily consistent with the observed red tilt. We also argue that for a wide range of potentials non-Gaussianity can be substantial, within the reach of current observations.
75 citations
Posted Content•
TL;DR: In this paper, the authors derive the low-energy effective action governing the infrared dynamics of relativistic superfluids at finite temperature in terms of infrared degrees of freedom and symmetries.
Abstract: We derive the low-energy effective action governing the infrared dynamics of relativistic superfluids at finite temperature. We organize our derivation in an effective field theory fashion-purely in terms of infrared degrees of freedom and symmetries. Our degrees of freedom are the superfluid phase \psi, and the comoving coordinates for the volume elements of the normal fluid component. The presence of two sound modes follows straightforwardly from Taylor-expanding the action at second order in small perturbations. We match our description to more conventional hydrodynamical ones, thus linking the functional form of our Lagrangian to the equation of state, which we assume as an input. We re-derive in our language some standard properties of relativistic superfluids in the high-temperature and low-temperature limits. As an illustration of the efficiency of our methods, we compute the cross-section for a sound wave (of either type) scattering off a superfluid vortex at temperatures right beneath the critical one.
74 citations
Cites background from "Null energy condition and superlumi..."
...The normal component has the usual long-wavelength degrees of freedom of ordinary hydrodynamics, which for field theoretical purposes are conveniently parameterized by three scalar fields φ(~x, t), with I = 1, 2, 3 [8, 9]....
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...Their dynamics should be invariant under the following internal symmetries [8, 9]:...
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TL;DR: In this paper, the authors investigated the black hole solutions within the single scalar field consistent truncations of the dual field theory, and constructed black hole solution that have spherical, toroidal, and hyperbolic horizon topologies.
73 citations
Cites background from "Null energy condition and superlumi..."
...Since the null energy condition is valid for our solutions, there are no violations that lead to superluminal propagation and instabilities in the bulk [32] and so we expect that the boundary theory is well defined (see, e....
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TL;DR: The Cheng-Weyl vector field as discussed by the authors couples only to a scalar field and the gravitational field naturally and does not interact with other known matter in the standard model of particle physics.
Abstract: Weyl's idea on scale invariance was resurrected by Cheng in 1988. The requirement of local scale invariance leads to a completely new vector field, which we call the 'Cheng-Weyl vector field'. The Cheng-Weyl vector field couples only to a scalar field and the gravitational field naturally. It does not interact with other known matter in the standard model of particle physics. In the present work, the ( generalized) Cheng-Weyl vector field coupled with the scalar field and its cosmological application are investigated. A mixture of the scalar field and a so-called 'cosmic triad' of three mutually orthogonal Cheng-Weyl vector fields is regarded as the dark energy in the universe. The cosmological evolution of this 'mixed' dark energy model is studied. We find that the effective equation-of-state parameter of the dark energy can cross the phantom divide w(de) = -1 in some cases; the first and second cosmological coincidence problems can be alleviated at the same time in this model.
70 citations
TL;DR: In this paper, the authors construct a theory that admits a time-dependent solution smoothly interpolating between a null energy condition (NEC)-satisfying phase at early times and a NEC-violating phase at late times.
Abstract: We construct a theory that admits a time-dependent solution smoothly interpolating between a null energy condition (NEC)-satisfying phase at early times and a NEC-violating phase at late times. We first review earlier attempts to violate the NEC and an argument of Rubakov, presented in [V. A. Rubakov, Phys. Rev. D 88, 044015 (2013)], which forbids the existence of such interpolating solutions in a single-field dilation-invariant theory. We then construct a theory which, in addition to possessing a Poincar\'e-invariant vacuum, does admit such a solution. For a wide range of parameters, perturbations around this solution are at all times stable, comfortably subluminal and weakly coupled. The theory requires us to explicitly break dilation invariance, so it is unlikely that the theory is fully stable under quantum corrections, but we argue that the existence of a healthy interpolating solution is quantum-mechanically robust.
69 citations
Cites background from "Null energy condition and superlumi..."
...The theorem of [63] relies heavily on the standard organization of effective field theory, i....
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...pathologies [63], including ghosts, gradient instabilities, superluminality, absence of a Lorentzinvariant vacuum, etc....
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...The no-go theorem of [63] is thus evaded by relying on higher-derivative spatial gradient terms....
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...More generally, it was shown in [63, 75] that violating the NEC in theories of the form L(φI , ∂φI) (i....
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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