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Register a new userEmergence of ghosts in Horndeski theory
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Eugeny Babichev
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We show that starting from initial conditions with stable perturbations, evolution of a galileon scalar field results in the appearance of a ghost later on. To demonstrate this, we consider a theory with k-essence and cubic galileon Lagrangians on a fixed Minkowski background. Explicit analytical solutions of simple waves are constructed, on top of which a healthy scalar degree of freedom is shown to be converted onto a ghost. Such a transformation is smooth and moreover perturbations remain hyperbolic all the time (until a caustic forms). We discuss a relation between the ghost and the appearance of closed causal curves for such solutions.
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We study the metric-affi
We consider anisotropic cosmologies in a particular shift-symmetric Horndeski theory containing the $G^{mu u}partial_muphi partial_ uphi$ coupling, where $G^{mu u}$ is the Einstein tensor. This theory admits stable in the future self-accelerating cosmologies whose tensor perturbations propagate with the velocity very close to the speed of light such that the theory agrees with the gravity wave observations. Surprisingly, we find that the anisotropies within the Bianchi I homogeneous spacetime model are screened at early time by the scalar charge, whereas at late times they are damped in the usual way. Therefore, contrary to what one would normally expect, the early state of the universe in the theory cannot be anisotropic and (locally) homogeneous in the absence of spatial curvature. The early universe cannot be isotropic either, because it should then be unstable with respect to inhomogeneous perturbations. As a result, the early universe should be inhomogeneous. At the same time, we find that in the spatially curved Bianchi IX case the anisotropies can be strong at early times even in the presence of a scalar charge.
We present a new understanding of the unstable ghost-like resonance which appears in theories such as quadratic gravity and Lee-Wick type theories. Quantum corrections make this resonance unstable, such that it does not appear in the asymptotic spectrum. We prove that these theories are unitary to all orders. Unitarity is satisfied by the inclusion of only cuts from stable states in the unitarity sum. This removes the need to consider this as a ghost state in the unitarity sum. However, we often use a narrow-width approximation where we do include cuts through unstable states, and ignore cuts through the stable decay products. If we do this with the unstable ghost resonance at one loop, we get the correct answer only by using a contour which was originally defined by Lee and Wick. The quantum effects also provide damping in both the Feynman and the retarded propagators, leading to stability under perturbations.
In this paper, we investigate the AC charge transport in the holographic Horndeski gravity and identify a metal-semiconductor like transition that is driven by the Horndeski coupling. Moreover, we fit our numeric data by the Drude formula in slow relaxation cases.
We discuss aspects of non-perturbative unitarity in quantum field theory. The additional ghost degrees of freedom arising in truncations of an effective action at a finite order in derivatives could be fictitious degrees of freedom. Their contributions to the fully-dressed propagator -- the residues of the corresponding ghost-like poles -- vanish once all operators compatible with the symmetry of the theory are included in the effective action. These fake ghosts do not indicate a violation of unitarity.
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