Inflationary spacetimes are not past-complete

Many inflating spacetimes are likely to violate the weak energy condition, a key assumption of singularity theorems. Here we offer a simple kinematical argument, requiring no energy condition, that a cosmological model which is inflating -- or just expanding sufficiently fast -- must be incomplete in null and timelike past directions. Specifically, we obtain a bound on the integral of the Hubble parameter over a past-directed timelike or null geodesic. Thus inflationary models require physics other than inflation to describe the past boundary of the inflating region of spacetime.Comment: We improve the basic argument to apply to a wider class of spacetimes, use a better title and add a discussion of cyclic models. 4 pages, 1 figure, RevTe

Non-Singular Charged Black Hole Solution for Non-Linear Source

A non-singular exact black hole solution in General Relativity is presented. The source is a non-linear electromagnetic field, which reduces to the Maxwell theory for weak field. The solution corresponds to a charged black hole with |q| \leq 2s_c m \approx 0.6 m, having metric, curvature invariants, and electric field bounded everywhere.Comment: 3 pages, RevTe

Regular Black Hole in General Relativity Coupled to Nonlinear Electrodynamics

The first regular exact black hole solution in General Relativity is presented. The source is a nonlinear electrodynamic field satisfying the weak energy condition, which in the limit of weak field becomes the Maxwell field. The solution corresponds to a charged black hole with |q| \leq 2 s_c m \approx 0.6 m, having the metric, the curvature invariants, and the electric field regular everywhere.Comment: 5 pages, RevTex, 6 figure

Open and Closed Universes, Initial Singularities and Inflation

The existence of initial singularities in expanding universes is proved without assuming the timelike convergence condition. The assumptions made in the proof are ones likely to hold both in open universes and in many closed ones. (It is further argued that at least some of the expanding closed universes that do not obey a key assumption of the theorem will have initial singularities on other grounds.) The result is significant for two reasons: (a)~previous closed-universe singularity theorems have assumed the timelike convergence condition, and (b)~the timelike convergence condition is known to be violated in inflationary spacetimes. An immediate consequence of this theorem is that a recent result on initial singularities in open, future-eternal, inflating spacetimes may now be extended to include many closed universes. Also, as a fringe benefit, the time-reverse of the theorem may be applied to gravitational collapse.Comment: 27 pages, Plain TeX (figures are embedded in the file itself and they will emerge if it is processed according to the instructions at the top of the file

Eternal inflation and the initial singularity

It is shown that a physically reasonable spacetime that is eternally inflating to the future must possess an initial singularity.Comment: 11 pages, Tufts University cosmology preprin

Atom interferometer as a selective sensor of rotation or gravity

In the presence of Earth gravity and gravity-gradient forces, centrifugal and Coriolis forces caused by the Earth rotation, the phase of the time-domain atom interferometers is calculated with accuracy up to the terms proportional to the fourth degree of the time separation between pulses. We considered double-loop atom interferometers and found appropriate condition to eliminate their sensitivity to acceleration to get atomic gyroscope, or to eliminate the sensitivity to rotation to increase accuracy of the atomic gravimeter. Consequent use of these interferometers allows one to measure all components of the acceleration and rotation frequency projection on the plane perpendicular to gravity acceleration. Atom interference on the Raman transition driving by noncounterpropagating optical fields is proposed to exclude stimulated echo processes which can affect the accuracy of the atomic gyroscopes. Using noncounterpropagating optical fields allows one to get a new type of the Ramsey fringes arising in the unidirectional Raman pulses and therefore centered at the two-quantum line center. Density matrix in the Wigner representation is used to perform calculations. It is shown that in the time between pulses, in the noninertial frame, for atoms with fully quantized spatial degrees of freedom, this density matrix obeys classical Liouville equations.Comment: 21 pages, 4 figures, extended references, discussion, and motivatio

ℏ\hbar as parameter of Minkowski metric in effective theory

With the proper choice of the dimensionality of the metric components, the action for all fields becomes dimensionless. Such quantities as the vacuum speed of light c, the Planck constant \hbar, the electric charge e, the particle mass m, the Newton constant G never enter equations written in the covariant form, i.e., via the metric g^{\mu\nu}. The speed of light c and the Planck constant are parameters of a particular two-parametric family of solutions of general relativity equations describing the flat isotropic Minkowski vacuum in effective theory emerging at low energy: g^{\mu\nu}=diag(-\hbar^2, (\hbar c)^2, (\hbar c)^2, (\hbar c)^2). They parametrize the equilibrium quantum vacuum state. The physical quantities which enter the covariant equations are dimensionless quantities and dimensionful quantities of dimension of rest energy M or its power. Dimensionless quantities include the running coupling `constants' \alpha_i; topological and geometric quantum numbers (angular momentum quantum number j, weak charge, electric charge q, hypercharge, baryonic and leptonic charges, number of atoms N, etc). Dimensionful parameters include the rest energies of particles M_n (or/and mass matrices); the gravitational coupling K with dimension of M^2; cosmological constant with dimension M^4; etc. In effective theory, the interval s has the dimension of 1/M; it characterizes the dynamics of particles in the quantum vacuum rather than geometry of space-time. We discuss the effective action, and the measured physical quantities resulting from the action, including parameters which enter the Josepson effect, quantum Hall effect, etc.Comment: 18 pages, no figures, extended version of the paper accepted in JETP Letter

Methods of approaching decoherence in the flavour sector due to space-time foam

In the first part of this work we discuss possible effects of stochastic space-time foam configurations of quantum gravity on the propagation of ``flavoured'' (Klein-Gordon and Dirac) neutral particles, such as neutral mesons and neutrinos. The formalism is not the usually assumed Lindblad one, but it is based on random averages of quantum fluctuations of space time metrics over which the propagation of the matter particles is considered. We arrive at expressions for the respective oscillation probabilities between flavours which are quite distinct from the ones pertaining to Lindblad-type decoherence, including in addition to the (expected) Gaussian decay with time, a modification to oscillation behaviour, as well as a power-law cutoff of the time-profile of the respective probability. In the second part we consider space-time foam configurations of quantum-fluctuating charged black holes as a way of generating (parts of) neutrino mass differences, mimicking appropriately the celebrated MSW effects of neutrinos in stochastically fluctuating random media. We pay particular attention to disentangling genuine quantum-gravity effects from ordinary effects due to the propagation of a neutrino through ordinary matter. Our results are of interest to precision tests of quantum gravity models using neutrinos as probes.Comment: 35 pages revtex, no figures, typos corrected in section II

Recycling universe

If the effective cosmological constant is non-zero, our observable universe may enter a stage of exponential expansion. In such case, regions of it may tunnel back to the false vacuum of an inflaton scalar field, and inflation with a high expansion rate may resume in those regions. An ``ideal'' eternal observer would then witness an infinite succession of cycles from false vacuum to true, and back. Within each cycle, the entire history of a hot universe would be replayed. If there were several minima of the inflaton potential, our ideal observer would visit each one of these minima with a frequency which depends on the shape of the potential. We generalize the formalism of stochastic inflation to analyze the global structure of the universe when this `recycling' process is taken into account.Comment: 43 pages, 10 figure

Theorems on gravitational time delay and related issues

Two theorems related to gravitational time delay are proven. Both theorems apply to spacetimes satisfying the null energy condition and the null generic condition. The first theorem states that if the spacetime is null geodesically complete, then given any compact set $K$, there exists another compact set $K'$ such that for any $p,q \not\in K'$, if there exists a ``fastest null geodesic'', $\gamma$, between $p$ and $q$, then $\gamma$ cannot enter $K$. As an application of this theorem, we show that if, in addition, the spacetime is globally hyperbolic with a compact Cauchy surface, then any observer at sufficiently late times cannot have a particle horizon. The second theorem states that if a timelike conformal boundary can be attached to the spacetime such that the spacetime with boundary satisfies strong causality as well as a compactness condition, then any ``fastest null geodesic'' connecting two points on the boundary must lie entirely within the boundary. It follows from this theorem that generic perturbations of anti-de Sitter spacetime always produce a time delay relative to anti-de Sitter spacetime itself.Comment: 15 pages, 1 figure. Example of gauge perturbation changed/corrected. Two footnotes added and one footnote remove