34 research outputs found
Casimir effect for nonlocal field theories with continuum massive modes
In this paper, we study the Casimir force for a class of Lorentzian nonlocal field theories. These theories include a continuum of massive excitations. In this regard, the effect of continuum massive modes on Casimir force is of interest. We focus on the simplest case of two absorbing parallel planes in 1+1 dimensions, and we show that, unlike local field theories, the thickness of the absorbing " walls " changes the value of Casimir force
Generalized Causal Set d'Alembertians
We introduce a family of generalized d'Alembertian operators in D-dimensional
Minkowski spacetimes which are manifestly Lorentz-invariant, retarded, and
non-local, the extent of the nonlocality being governed by a single parameter
. The prototypes of these operators arose in earlier work as averages of
matrix operators meant to describe the propagation of a scalar field in a
causal set. We generalize the original definitions to produce an infinite
family of ''Generalized Causet Box (GCB) operators'' parametrized by certain
coefficients , and we derive the conditions on the latter needed for
the usual d'Alembertian to be recovered in the infrared limit. The continuum
average of a GCB operator is an integral operator, and it is these continuum
operators that we mainly study. To that end, we compute their action on plane
waves, or equivalently their Fourier transforms g(p) [p being the
momentum-vector]. For timelike p, g(p) has an imaginary part whose sign depends
on whether p is past or future-directed. For small p, g(p) is necessarily
proportional to p.p, but for large p it becomes constant, raising the
possibility of a genuinely Lorentzian perturbative regulator for quantum field
theory. We also address the question of whether or not the evolution defined by
the GCB operators is stable, finding evidence that the original 4D causal set
d'Alembertian is unstable, while its 2D counterpart is stable.Comment: 26 pages, 4 figure
Off-shell dark matter: a cosmological relic of quantum gravity
We study a novel proposal for the origin of cosmological cold dark matter (CDM) which is rooted in the quantum nature of spacetime. In this model, off-shell modes of quantum fields can exist in asymptotic states as a result of spacetime nonlocality (expected in generic theories of quantum gravity), and play the role of CDM, which we dub off-shell dark matter (OfDM). However, their rate of production is suppressed by the scale of non-locality (e.g. Planck length). As a result, we show that OfDM is only produced in the first moments of big bang, and then effectively decouples (except through its gravitational interactions). We examine the observational predictions of this model: In the context of cosmic inflation, we show that this proposal relates the reheating temperature to the inflaton mass, which narrows down the uncertainty in the number of e-foldings of specific inflationary scenarios. We also demonstrate that OfDM is indeed cold, and discuss potentially observable signatures on small scale matter power spectrum
Classification of shift-symmetric Horndeski theories and hairy black holes
No-hair theorems for scalar-tensor theories imply that the trivial scalar field configuration is the unique configuration around stationary black hole spacetimes. The most basic assumption in these theorems is that a constant scalar configuration is actually admissible. In this paper, we classify shift-symmetric Horndeski theories according to whether or not they admit the trivial scalar configuration as a solution and under which conditions. Local Lorentz symmetry and the presence of a linear coupling between the scalar field and Gauss-Bonnet invariant plays feature prominently in this classification. We then use the classification to show that any theory without linear Gauss-Bonnet coupling that respects Local Lorentz symmetry admits all GR solutions. We also study the scalar hair configuration around black hole spacetimes in theories where the linear Gauss-Bonnet coupling is present. We show that the scalar hair of the configuration is secondary, fixed by the regularity of the horizon, and is determined by the black hole horizon properties