On the gravitational seesaw in higher-derivative gravity

Abstract

Local gravitational theories with more than four derivatives are superrenormalizable. They also may be unitary in the Lee-Wick sense. Thus it is relevant to study the low-energy properties of these theories, especially to identify observables which might be useful for experimental detection of higher derivatives. Using an analogy with the neutrino physics, we explore the possibility of a gravitational seesaw mechanism in which several dimensional parameters of the same order of magnitude produce a hierarchy in the masses of propagating particles. Such a mechanism could make a relatively light degree of freedom detectable in low-energy laboratory and astrophysical observations, such as torsionbalance experiments and the bending of light. We demonstrate that such a seesaw mechanism in the six-and morederivative theories is unable to reduce the lightest mass more than in the simplest four-derivative model. Adding more derivatives to the four-derivative action of gravity makes heavier masses even greater, while the lightest massive ghost is not strongly affected. This fact is favorable for protecting the theory from instabilities but makes the experimental detection of higher derivatives more difficult.

Gravitational Friedel oscillations in higher-derivative and infinite-derivative gravity?

“…In this essay, we pursued a somewhat different direction by focussing on the linearized theory at mesoscopic distances, M r ∼ O(1), where both the gravitational potential as well we the local energy density exhibits fluctuations, the latter one assuming negative values in some regions. For values of M m Planck these oscillations might become observable at some point in the future [16,17,18].…”

Weak-field limit and regular solutions in polynomial higher-derivative gravities

“…We conclude that r −1 q(r 2 − t 2 ) is bounded for general polynomial gravity models, which implies in the existence of the mass gap for the formation of mini black holes. The size of the gap depends on the scale λ = max i {m −1 i } defined by the massive excitations of the model; such scale could be affected by a gravitational seesaw-like mechanism as discussed in [13] (see also [10,70] for experimental bounds on λ).…”

“…In this regard, two models have been the subject of interesting investigations in recent years. The first one we mention is the Lee-Wick gravity [11,12]-see, e.g., [10,[13][14][15][16] for further developments and applications. This theory is defined by the Einstein-Hilbert action enlarged by curvature-squared terms which contain polynomial functions of the d'Alembert operator, such as R µν F 1 (✷)R µν and RF 2 (✷)R. A general action of this type can be called polynomial higher-derivative gravity and was introduced in [5]; the Lee-Wick gravity assumes, furthermore, that the polynomials F i are such that all the massive poles of the propagator which correspond to ghost modes are complex.…”

Scalar model of effective field theory in curved space

“…At the same time, in quantum gravity such a fundamental theory is not known. This becomes a problem if we recognize that all known approaches, including string theory, have the same level of difficulties concerning higher derivatives and ghosts [7,8]. Thus, it looks like we need to have to worry about ultimate quantum gravity, even if are interested only in the IR effective approaches.…”