Light deflection by gravitational waves from localized sources

We study the deflection of light (and the redshift, or integrated time delay) caused by the time-dependent gravitational field generated by a localized material source lying close to the line of sight. Our calculation explicitly takes into account the full, near-zone, plus intermediate-zone, plus wave-zone, retarded gravitational field. Contrary to several recent claims in the literature, we find that the deflections due to both the wave-zone 1/r gravitational wave and the intermediate-zone 1/r^2 retarded fields vanish exactly. The leading total time-dependent deflection caused by a localized material source, such as a binary system, is proven to be given by the quasi-static, near-zone quadrupolar piece of the gravitational field, and therefore to fall off as the inverse cube of the impact parameter.Comment: 12 pages, REVTeX 3.0, no figur

Nonstationary Stochastic Resonance in a Single Neuron-Like System

Stochastic resonance holds much promise for the detection of weak signals in the presence of relatively loud noise. Following the discovery of nondynamical and of aperiodic stochastic resonance, it was recently shown that the phenomenon can manifest itself even in the presence of nonstationary signals. This was found in a composite system of differentiated trigger mechanisms mounted in parallel, which suggests that it could be realized in some elementary neural networks or nonlinear electronic circuits. Here, we find that even an individual trigger system may be able to detect weak nonstationary signals using stochastic resonance. The very simple modification to the trigger mechanism that makes this possible is reminiscent of some aspects of actual neuron physics. Stochastic resonance may thus become relevant to more types of biological or electronic systems injected with an ever broader class of realistic signals.Comment: Plain Latex, 7 figure

The stability of modified gravity models

Conditions for the existence and stability of de Sitter space in modified gravity are derived by considering inhomogeneous perturbations in a gauge-invariant formalism. The stability condition coincides with the corresponding condition for stability with respect to homogeneous perturbations, while this is not the case in scalar-tensor gravity. The stability criterion is applied to various modified gravity models of the early and the present universe.Comment: 22 pages, LaTeX, to appear in Phys. Rev.

Nonstationary Stochastic Resonance

It is by now established that, remarkably, the addition of noise to a nonlinear system may sometimes facilitate, rather than hamper the detection of weak signals. This phenomenon, usually referred to as stochastic resonance, was originally associated with strictly periodic signals, but it was eventually shown to occur for stationary aperiodic signals as well. However, in several situations of practical interest, the signal can be markedly nonstationary. We demonstrate that the phenomenon of stochastic resonance extends to nonstationary signals as well, and thus could be relevant to a wider class of biological and electronic applications. Building on both nondynamic and aperiodic stochastic resonance, our scheme is based on a multilevel trigger mechanism, which could be realized as a parallel network of differentiated threshold sensors. We find that optimal detection is reached for a number of thresholds of order ten, and that little is gained by going much beyond that number. We raise the question of whether this is related to the fact that evolution has favored some fixed numbers of precisely this order of magnitude in certain aspects of sensory perception.Comment: Plain Latex, 6 figure

Multiple imaging by gravitational waves

Gravitational waves act like lenses for the light propagating through them. This phenomenon is described using the vector formalism employed for ordinary gravitational lenses, which was proved to be applicable also to a non-stationary spacetime, with the appropriate modifications. In order to have multiple imaging, an approximate condition analogous to that for ordinary gravitational lenses must be satisfied. Certain astrophysical sources of gravitational waves satisfy this condition, while the gravitational wave background, on average, does not. Multiple imaging by gravitational waves is, in principle, possible, but the probability of observing such a phenomenon is extremely low.Comment: 23 pages, LaTeX, no figures, to appear in Int. J. Mod. Phys.

Non-chaotic dynamics in general-relativistic and scalar-tensor cosmology

In the context of scalar-tensor models of dark energy and inflation, the dynamics of vacuum scalar-tensor cosmology are analysed without specifying the coupling function or the scalar field potential. A conformal transformation to the Einstein frame is used and the dynamics of general relativity with a minimally coupled scalar field are derived for a generic potential. It is shown that the dynamics are non-chaotic, thus settling an existing debate.Comment: 20 pages, LaTeX, to appear in Class. Quantum Gra

Complete constraints on a nonminimally coupled chaotic inflationary scenario from the cosmic microwave background

We present complete constraints imposed from observations of the cosmic microwave background radiation (CMBR) on the chaotic inflationary scenario with a nonminimally coupled inflaton field proposed by Fakir and Unruh (FU). Our constraints are complete in the sense that we investigate both the scalar density perturbation and the tensor gravitational wave in the Jordan frame, as well as in the Einstein frame. This makes the constraints extremely strong without any ambiguities due to the choice of frames. We find that the FU scenario generates tiny tensor contributions to the CMBR relative to chaotic models in minimal coupling theory, in spite of its spectral index of scalar perturbation being slightly tilted. This means that the FU scenario will be excluded if any tensor contributions to CMBR are detected by the forthcoming satellite missions. Conversely, if no tensor nature is detected despite the tilted spectrum, a minimal chaotic scenario will be hard to explain and the FU scenario will be supported.Comment: 7 pages, no figure, RevTeX, to appear in Phys.Rev. D59 (Mar. 15, 1999

Bending of Light by Gravity Waves

We describe the statistical properties of light rays propagating though a random sea of gravity waves and compare with the case for scalar metric perturbations from density inhomogeneities. For scalar fluctuations the deflection angle grows as the square-root of the path length $D$ in the manner of a random walk, and the rms displacement of a ray from the unperturbed trajectory grows as $D^{3/2}$. For gravity waves the situation is very different. The mean square deflection angle remains finite and is dominated by the effect of the metric fluctuations at the ends of the ray, and the mean square displacement grows only as the logarithm of the path length. In terms of power spectra, the displacement for scalar perturbations has $P(k) \propto 1/ k^4$ while for gravity waves the trajectories of photons have $P(k) \propto 1/k$ which is a scale-invariant or `flicker-noise' process, and departures from rectilinear motion are suppressed, relative to the scalar case, by a factor $\sim (\lambda / D)^{3/2}$ where $\lambda$ is the characteristic scale of the metric fluctuations and $D$ is the path length. This result casts doubt on the viability of some recent proposals for detecting or constraining the gravity wave background by astronomical measurements.Comment: 14 pages, aastex, submitted to Astrophysical Journa

Inflation and quintessence with nonminimal coupling

The nonminimal coupling (NMC) of the scalar field to the Ricci curvature is unavoidable in many cosmological scenarios. Inflation and quintessence models based on nonminimally coupled scalar fields are studied, with particular attention to the balance between the scalar potential and the NMC term in the action. NMC makes acceleration of the universe harder to achieve for the usual potentials, but it is beneficial in obtaining cosmic acceleration with unusual potentials. The slow-roll approximation with NMC, conformal transformation techniques, and other aspects of the physics of NMC are clarified.Comment: 36 pages, LaTeX. Typos in Eq. (2.5) correcte

Phase Transition in Conformally Induced Gravity with Torsion

We have considered the quantum behavior of a conformally induced gravity in the minimal Riemann-Cartan space. The regularized one-loop effective potential considering the quantum fluctuations of the dilaton and the torsion fields in the Coleman-Weinberg sector gives a sensible phase transition for an inflationary phase in De Sitter space. For this effective potential, we have analyzed the semi-classical equation of motion of the dilaton field in the slow-rolling regime.Comment: 7pages, no figur