The phantom menaced: Constraints on low-energy effective ghosts

Abstract

It has been suggested that a scalar field with negative kinetic energy, or "ghost," could be the source of the observed late-time cosmological acceleration. Naively, such theories should be ruled out by the catastrophic quantum instability of the vacuum. We derive phenomenological bounds on the Lorentz-violating ultraviolet cutoff Λ which must apply to low-energy effective theories of ghosts, in order to keep the instability at unobservable levels. Assuming only that ghosts interact at least gravitationally, we show that Λ < ∼ 3 MeV for consistency with the cosmic gamma ray background. We also show that theories of ghosts with a Lorentz-conserving cutoff are completely excluded. PACS numbers: 98.80.Cq, 98.70.Vc The present accelerated expansion of the universe seems to be an experimental fact, now that data from distant type Ia supernovae [1] have been corroborated by those from the cosmic microwave background [2]. Although the simplest explanation is a cosmological constant Λ of order (10 −3 eV) 4 , this tiny energy scale is so far below the expected "natural" size for a cosmological constant, that alternative explanations have been vigorously pursued. A common approach has been to assume that the true value of Λ is zero, due to an unknown mechanism, and to propose new physics which would explain why the present-day vacuum energy differs from zero by the small observed amount.The most popular idea has been quintessence, in which the universe is gradually approaching the zero of the vacuum energy by the slow rolling of an extremely weakly coupled scalar field. More recently, some less conventional alternatives have been considered, including "phantom matter," which is essentially quintessence with a wrong-sign kinetic term [3]. These models are motivated by the supernova data, which suggest that the dark energy equation of state violates the weak energy condition by having p < −ρ [4].A serious problem with phantom matter, which is overlooked in the literature that attempts to apply it to cosmology, is that such theories are not quantum mechanically viable, either because they violate conservation of probability, or they have unboundedly negative energy density and lead to the absence of a stable vacuum state. Whether a ghost carries negative norm and positive energy, or vice versa, is a choice which is made during the quantization procedure. This choice exists because the iǫ prescription for defining the propagator near its poles is not unique, and not specified by the Lagrangian itself. The momentum space propagator for a ghost can have either of the two formsIn the first form in (1), the imaginary part of the propagator has the opposite sign relative to that of a positive norm particle. This will cause the optical theorem to be violated, leading to a nonunitary theory. That is, this choice gives a theory with no probabilistic interpretation. It is therefore unphysical and should be dismissed.On the other hand, if the second form in (1) is chosen, unitarity is maintained. The price to be paid is that the pole...

Oxidised cosmic acceleration

“…In the case of two-derivative field theories, there are good reasons to believe that NEC violation goes hand-in-hand with pathologies such as superluminal signal propagation, unitarity violations, and instabilities [33,34,35,36]. There are mechanisms by which the NEC can be violated in theories of physical interest.…”

“…In the classic Kaluza-Klein reduction, shape and size parameters (moduli) of the underlying theory, and it seems likely that most "well-behaved" theories should satisfy the NEC. There are some rigorous formulations of this belief, where NEC violation is shown to lead to superluminal propagation, instabilities, and violations of unitarity or causality [30,31,32,33,34,35,36]. Certainly the NEC forbids a number of solutions to Einstein's equations with strange properties: traversable wormholes [37,38], superluminal "warp drives" [39,40,41,42,43,44], time machines [45,46], universes with big rip singularities [47,48], and pathologies with gravitational thermodynamics [49,50,51,52,53] are possible with NECviolating "exotic" matter.…”

Об Изотропном Энергетическом Условии И Космологии

“…Поэтому обыч-ные частицы могут распасться на более тяжелые частицы и фантомы. Это обсуж-дается в [3], [4].…”

Could dark energy be vector-like?

“…Scalar tachyons 3 indeed have been widely considered in the literature. Other forms of instability are more worrisome, like the quantum-mechanical instability of the vacuum in the presence of a phantom [12,13]. By simple analogy, any form of instability associated with a tachyonic vector is not expected to be of this second kind, as the vectors have a conventional kinetic term.…”

“…Because of that, phantom dark energy is quantum-mechanically unstable upon decay of the vacuum into (positive energy) gravitons and (negative energy) phantom particles [12,13]. Hence, if future preciser observations confirm the current trend and favor a dark energy equation of state smaller than minus one [1,14], alternative (viable) models are needed to account for such a value 1 [16].…”