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In this letter, we review a candidate for dark matter, known as O$f$DM, and explain how it relates to spacetime nonlocality. This connection provides a physical interpretation for why O$f$DM exists. Given the state of direct and indirect searches for dark matter, O$f$DM model would be an important candidate to consider, since it predicts all direct searches would fail to detect DM. The model has only one free parameter and in this regard, it is highly predictive. We review a few avenues to test this model.

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.

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.

In theories with derivative (self-)interactions, the propagation of perturbations on nontrivial field configurations is determined by effective metrics. Generalized scalar-tensor theories belong in this class and this implies that the matter fields and gravitational perturbations do not necessarily experience the same causal structure. Motivated by this, we explore the causal structure of black holes as perceived by scalar fields in the Horndeski class. We consider linearized perturbations on a fixed background metric that describes a generic black hole. The effective metric that determines the propagation of these perturbations does not generally coincide with the background metric (to which matter fields couple minimally). Assuming that the metric and the scalar respect stationarity and that the surface gravity of the horizon is constant, we prove that Killing horizons of the background metric are always Killing horizons of the effective metric as well. Hence, scalar perturbations cannot escape the region that matter fields perceive as the interior of the black hole. This result does not depend on asymptotics but only on local considerations and does not make any reference to no-hair theorems. We then demonstrate that, when one relaxes the stationarity assumption for the scalar, solutions where the horizons of the effective and the background metrics do not match can be found in the decoupling limit., Comment: v3: 10 pages, published version

A class of nonlocal Lorentzian quantum field theories is introduced in arXiv:1502.01655 and arXiv:1411.6513, where the d'Alembertian operator $\Box$ is replaced by a non-analytic function of the d'Alembertian, $f(\Box)$. This is inspired by the Causal Set program where such an evolution arises as the continuum limit of a wave equation on causal sets. The spectrum of these theories contains a continuum of massive excitations. This is perhaps the most important feature which leads to distinct/interesting phenomenology. In this paper, we study properties of the continuum massive modes in depth. We derive the path integral formulation of these theories. Meanwhile, this derivation introduces a dual picture in terms of local fields which clearly shows how continuum massive modes of the nonlocal field interact. The dual picture, in principle, provides a path to extension beyond scalar fields and addressing the issue of renormalization.

The recent detection of gravitational wave GW170817 has placed a severe bound on the deviation of the speed of gravitational waves from the speed of light. We explore the consequences of this detection for Horava gravity.

Lorentz-violating gravity theories with a preferred foliation can have instantaneous propagation. Nonetheless, it has been shown that black holes can still exist in such theories and the relevant notion of an event horizon has been dubbed `universal horizon'. In stationary spacetimes the universal horizon has to reside in a region of spacetime where the Killing vector associated with stationarity is spacelike. This raises the question of what happens to the universal horizon in the extremal limit, where no such region exists anymore. We use a decoupling limit approximation to study this problem. Our results suggest that at the extremal limit, the extremal Killing horizon appears to play the role of a degenerate universal horizon, despite being a null and not a spacelike surface, and hence not a leaf of the preferred foliation.

The response of inertial particle detectors coupled to a scalar field satisfying nonlocal dynamics described by nonanalytic functions of the d'Alembertian operator $\Box$ is studied. We show that spontaneous emission processes of a low energy particle detector are very sensitive to high-energy nonlocality scales. This allows us to suggest a nuclear physics experiment ($\sim$ MeV energy scales) that outperforms the sensitivity of LHC experiments by many orders of magnitude. This may have implications for the falsifiability of theoretical proposals of quantum gravity., Comment: 5 pages, 1 figure. RevTeX 4.1. This version matches the published one in PRD Rapid Communications

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.

Is Cosmic Censorship special to General Relativity, or can it survive a violation of equivalence principle? Recent studies have shown that singularities in Lorentz violating Einstein-Aether (or Horava-Lifhsitz) theories can lie behind a universal horizon in simple black hole spacetimes. Even infinitely fast signals cannot escape these universal horizons. We extend this result, for an incompressible aether, to 3+1d dynamical or spinning spacetimes which possess inner killing horizons, and show that a universal horizon always forms in between the outer and (would-be) inner horizons. This finding suggests a notion of Cosmic Censorship, given that geometry in these theories never evolves beyond the universal horizon (avoiding potentially singular inner killing horizons). A surprising result is that there are 3 distinct possible stationary universal horizons for a spinning black hole, only one of which matches the dynamical spherical solution. This motivates dynamical studies of collapse in Einstein-Aether theories beyond spherical symmetry, which may reveal instabilities around the spherical solution.

We show how quantum fields can be used to measure the curvature of spacetime. In particular, we find that knowledge of the imprint that spacetime curvature leaves in the correlators of quantum fields suffices, in principle, to reconstruct the metric. We then consider the possibility that the quantum fields obey a natural ultraviolet cutoff, for example, at the Planck scale. We investigate how such a cutoff limits the spatial resolution with which curvature can be deduced from the properties of quantum fields. We find that the metric deduced from the quantum correlator exhibits a peculiar scaling behavior as the scale of the natural UV cutoff is approached.

Curvature squared terms, when added to the Einstein-Hilbert action and treated non-perturbatively, generically result in the propagation of an extra massive scalar state and an extra massive spin-2 ghost state. Using the Stueckelberg trick, we study the high-energy limit in which the mass of the spin-2 state is taken to zero, with strong- coupling scales held fixed. The Stueckelberg approach makes transparent the interplay between the ghost graviton and the healthy graviton which allows the theory to evade the usual lambda-3 strong coupling scale of massive gravity and become renormalizable, at the expense of stability., Comment: 17 pages. v2 minus sign fixed, other small changes

We propose that dark matter is not yet another new particle in nature, but that it is a remnant of quantum gravitational effects on known fields. We arrive at this possibility in an indirect and surprising manner: by considering retarded, nonlocal, and Lorentzian evolution for quantum fields. This is inspired by recent developments in causal set theory, where such an evolution shows up as the continuum limit of scalar field propagation on a background causal set. Concretely, we study the quantum theory of a massless scalar field whose evolution is given not by the the d'Alembertian $\Box$, but by an operator $\tilde \Box$ which is Lorentz invariant, reduces to $\Box$ at low energies, and defines an explicitly retarded evolution: $(\tilde \Box \phi)(x)$ only depends on $\phi(y)$, with $y$ is in the causal past of $x$. This modification results in the existence of a continuum of massive particles, in addition to the usual massless ones, in the free theory. When interactions are introduced, these massive or off-shell quanta can be produced by the scattering of massless particles, but once produced, they no longer interact, which makes them a natural candidate for dark matter.

We present two results which concern certain aspects of the question: when is a causal set well approximated by a Lorentzian manifold? The first result is a theorem which shows that the number-volume correspondence, if required to hold even for arbitrarily small regions, is best realized via Poisson sprinkling. The second result concerns a family of lattices in $1+1$ dimensional Minkowski space, known as Lorentzian lattices, which we show provide a much better number-volume correspondence than Poisson sprinkling for large volumes. We argue, however, that this feature should not persist in higher dimensions. We conclude by conjecturing a form of the aforementioned theorem that holds under weaker assumptions, namely that Poisson sprinkling provides the best number-volume correspondence in $3+1$ dimensions for spacetime regions with macroscopically large volumes.

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 $\rho$. 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 $\{a,b_n\}$, 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 figures

arXiv:1205.2953 defines an entropy for a gaussian scalar field $\phi$ in an arbitrary region of either a causal set or a continuous spacetime, given only the correlator $\langle\phi(x)\phi(y)\rangle$ within the region. As a first application, we compute numerically the entanglement entropy in two cases where the asymptotic form is known or suspected from conformal field theory, finding excellent agreement when the required ultraviolet cutoff is implemented as a truncation on spacetime mode-sums. We also show how the symmetry of entanglement entropy reflects the fact that $RS$ and $SR$ share the same eigenvalues, $R$ and $S$ being arbitrary matrices., Comment: 20 pages, 5 figures

Motivations for the existence of a fundamental preferred frame range from pure phenomenology to attempts to solve the non-renormalizability of quantum gravity, the problem of time (and scale), and the cosmological constant problem(s). In many explicit constructions, such as Einstein-Aether or Gravitational Aether theories, K-essence, Cuscuton theory, Shape Dynamics, or (non-projectable) Horava-Lifshitz gravity, the low energy theory contains a fluid (which defines a preferred frame) with superluminal or incompressible excitations. We study here the formation of black holes in the presence of such a fluid. In particular, we focus on the incompressible limit of the fluid (or Constant Mean Curvature foliation) in the space-time of a spherically collapsing shell within an asymptotically cosmological space-time. In this case, ignoring the fluid back reaction, we can analytically show that an observer inside 3/4 of the Schwarzschild radius cannot send a signal outside, after a stage in collapse, even using signals that propagate infinitely fast in the preferred frame. This confirms the dynamical emergence of universal horizons that have been previously found in static solutions. We argue that this universal horizon should be considered as the future boundary of the classical space-time., Comment: 20 pages

We propose a novel solution for the endpoint of gravitational collapse, in which spacetime ends (and is orbifolded) at a microscopic distance from black hole event horizons. This model is motivated by the emergence of singular event horizons in the gravitational aether theory, a semi-classical solution to the cosmological constant problem(s), and thus suggests a catastrophic breakdown of general relativity close to black hole event horizons. A similar picture emerges in fuzzball models of black holes in string theory, as well as the recent firewall proposal to resolve the information paradox. We then demonstrate that positing a surface fluid in thermal equilibrium with Hawking radiation, with vanishing energy density (but non-vanishing pressure) at the new boundary of spacetime, which is required by Israel junction conditions, yields a thermodynamic entropy that is identical to the Bekenstein-Hawking area law, $S_{BH}$, for charged rotating black holes. To our knowledge, this is the first derivation of black hole entropy which only employs local thermodynamics. Furthermore, a model for the microscopic degrees of freedom of the surface fluid (which constitute the micro-states of the black hole) is suggested, which has a finite, but Lorentz-violating, quantum field theory. Finally, we comment on the effects of physical boundary on Hawking radiation, and show that relaxing the assumption of equilibrium with Hawking radiation sets $S_{BH}$ as an upper limit for Black Hole entropy., Comment: 12 pages