A New Redshift Interpretation

A nonhomogeneous universe with vacuum energy, but without spacetime expansion, is utilized together with gravitational and Doppler redshifts as the basis for proposing a new interpretation of the Hubble relation and the 2.7K Cosmic Blackbody Radiation.Comment: 9 pages LaTeX, no figure

Post-Newtonian expansion for Gauss-Bonnet Gravity

The Parametrized Post-Newtonian expansion of gravitational theories with a scalar field coupled to the Gauss-Bonnet invariant is performed and confrontation of such theories with Solar system experiments is discussed.Comment: 4 pages; typos corrected, published versio

Inflation without Slow Roll

We draw attention to the possibility that inflation (i.e. accelerated expansion) might continue after the end of slow roll, during a period of fast oscillations of the inflaton field \phi . This phenomenon takes place when a mild non-convexity inequality is satisfied by the potential V(\phi). The presence of such a period of \phi-oscillation-driven inflation can substantially modify reheating scenarios. In some models the effect of these fast oscillations might be imprinted on the primordial perturbation spectrum at cosmological scales.Comment: 9 pages, Revtex, psfig, 1 figure, minor modifications, references adde

Coleman - de Luccia instanton of the second order in a brane world

The second order Coleman - de Luccia instanton and its action in the Randall - Sundrum type II model are investigated and the comparison with the results in Einstein's general relativity is done in the present paper.Comment: 4 pages, accepted in IJT

Displacement energy of unit disk cotangent bundles

We give an upper bound of a Hamiltonian displacement energy of a unit disk cotangent bundle $D^*M$ in a cotangent bundle $T^*M$, when the base manifold $M$ is an open Riemannian manifold. Our main result is that the displacement energy is not greater than $C r(M)$, where $r(M)$ is the inner radius of $M$, and $C$ is a dimensional constant. As an immediate application, we study symplectic embedding problems of unit disk cotangent bundles. Moreover, combined with results in symplectic geometry, our main result shows the existence of short periodic billiard trajectories and short geodesic loops.Comment: Title slightly changed. Close to the version published online in Math Zei

Making predictions in the multiverse

I describe reasons to think we are living in an eternally inflating multiverse where the observable "constants" of nature vary from place to place. The major obstacle to making predictions in this context is that we must regulate the infinities of eternal inflation. I review a number of proposed regulators, or measures. Recent work has ruled out a number of measures by showing that they conflict with observation, and focused attention on a few proposals. Further, several different measures have been shown to be equivalent. I describe some of the many nontrivial tests these measures will face as we learn more from theory, experiment, and observation.Comment: 20 pages, 3 figures; invited review for Classical and Quantum Gravity; v2: references improve

Classification of Inflationary Einstein--Scalar--Field--Models via Catastrophe Theory

Various scenarios of the initial inflation of the universe are distinguished by the choice of a scalar field {\em potential} $U(\phi)$ which simulates a {\it temporarily} non--vanishing {\em cosmological term}. Our new method, which involves a reparametrization in terms of the Hubble expansion parameter $H$, provides a classification of allowed inflationary potentials and of the stability of the critical points. It is broad enough to embody all known {\it exact} solutions involving one scalar field as special cases. Inflation corresponds to the evolution of critical points of some catastrophe manifold. The coalescence of its nondegenerate critical points with the creation of a degenerate critical point corresponds the reheating phase of the universe. This is illustrated by several examples.Comment: 12 pages, REVTeX, no figure

A time varying speed of light as a solution to cosmological puzzles

We consider the cosmological implications of light travelling faster in the early Universe. We propose a prescription for deriving corrections to the cosmological evolution equations while the speed of light $c$ is changing. We then show how the horizon, flatness, and cosmological constant problems may be solved. We also study cosmological perturbations in this scenario and show how one may solve the homogeneity and isotropy problems. As it stands, our scenario appears to most easily produce extreme homogeneity, requiring structure to be produced in the Standard Big Bang epoch. Producing significant perturbations during the earlier epoch would require a rather careful design of the function $c(t)$. The large entropy inside the horizon nowadays can also be accounted for in this scenario.Comment: To be published in Physical Review D. Note added referring to John Moffat's early work on VSL theorie

Boltzmann brains and the scale-factor cutoff measure of the multiverse

To make predictions for an eternally inflating "multiverse", one must adopt a procedure for regulating its divergent spacetime volume. Recently, a new test of such spacetime measures has emerged: normal observers - who evolve in pocket universes cooling from hot big bang conditions - must not be vastly outnumbered by "Boltzmann brains" - freak observers that pop in and out of existence as a result of rare quantum fluctuations. If the Boltzmann brains prevail, then a randomly chosen observer would be overwhelmingly likely to be surrounded by an empty world, where all but vacuum energy has redshifted away, rather than the rich structure that we observe. Using the scale-factor cutoff measure, we calculate the ratio of Boltzmann brains to normal observers. We find the ratio to be finite, and give an expression for it in terms of Boltzmann brain nucleation rates and vacuum decay rates. We discuss the conditions that these rates must obey for the ratio to be acceptable, and we discuss estimates of the rates under a variety of assumptions.Comment: 32 pp, 2 figs. Modified to conform to the version accepted by Phys. Rev. D. The last paragraph of Sec. V-A, about Boltzmann brains in Minkowski space, has been significantly enlarged. Two sentences were added to the introduction concerning the classical approximation and the hope of finding a motivating principle for the measure. Several references were adde

Some Remarks on Oscillating Inflation

In a recent paper Damour and Mukhanov describe a scenario where inflation may continue during the oscillatory phase. This effect is possible because the scalar field spends a significant fraction of each period of oscillation on the upper part of the potential. Such additional period of inflation could push perturbations after the slow roll regime to observable scales. Although in this work we show that the small region of the Damour-Mukhanov parameter q gives the main contribution to oscillating inflation, it was not satisfactory understood until now. Furthermore, it gives an expression for the energy density spectrum of perturbations, which is well behaved in the whole physical range of q .Comment: 4 pages including figures caption, 3 ps-figures. To appear in Phys. Rev.