Spatial curvature effects on molecular transport by diffusion

For a substance diffusing on a curved surface, we obtain an explicit relation valid for very small values of the time, between the local concentration, the diffusion coefficient, the intrinsic spatial curvature and the time. We recover the known solution of Fick's law of diffusion in the flat space limit. In the biological context, this result would be useful in understanding the variations in the diffusion rates of integral proteins and other molecules on membranes.Comment: 10 page

Semiclassical Effects and the Onset of Inflation

We present a class of exact solutions to the constraint equations of General Relativity coupled to a Klein - Gordon field, these solutions being isotropic but not homogeneous. We analyze the subsequent evolution of the consistent Cauchy data represented by those solutions, showing that only certain special initial conditions eventually lead to successfull Inflationary cosmologies. We argue, however, that these initial conditions are precisely the likely outcomes of quantum events occurred before the inflationary era.Comment: 22 pages, file written in RevTe

On the observational determination of squeezing in relic gravitational waves and primordial density perturbations

We develop a theory in which relic gravitational waves and primordial density perturbations are generated by strong variable gravitational field of the early Universe. The generating mechanism is the superadiabatic (parametric) amplification of the zero-point quantum oscillations. The generated fields have specific statistical properties of squeezed vacuum quantum states. Macroscopically, squeezing manifests itself in a non-stationary character of variances and correlation functions of the fields, the periodic structures of the metric power spectra, and, as a consequence, in oscillatory behavior of the higher order multipoles C_l of the cosmic microwave background anisotropy. We start with the gravitational wave background and then apply the theory to primordial density perturbations. We derive an analytical formula for the positions of peaks and dips in the angular power spectrum l(l+1)C_l as a function of l. This formula shows that the values of l at the peak positions are ordered in the proportion 1:3:5:..., whereas at the dips they are ordered as 1:2:3:.... We compare the derived positions with the actually observed features, and find them to be in reasonably good agreement. It appears that the observed structure is better described by our analytical formula based on the (squeezed) metric perturbations associated with the primordial density perturbations, rather than by the acoustic peaks reflecting the existence of plasma sound waves at the last scattering surface. We formulate a forecast for other features in the angular power spectrum, that may be detected by the advanced observational missions, such as MAP and PLANCK. We tentatively conclude that the observed structure is a macroscopic manifestation of squeezing in the primordial metric perturbations.Comment: 34 pages, 3 figures; to appear in Phys. Rev. D66, 0435XX (2002); includes Note Added in Proofs: "The latest CBI observations (T.J.Pearson et al., astro-ph/0205388) have detected four peaks, at l ~ 550, 800, 1150, 1500, and four dips, at l ~ 400, 700, 1050, 1400. These positions are in a very good agreement with the theoretical formula (6.35) of the present paper. We interpret this data as confirmation of our conclusion that it is gravity, and not acoustics, that is responsible for the observed structure.

The spherical collapse model in time varying vacuum cosmologies

We investigate the virialization of cosmic structures in the framework of flat FLRW cosmological models, in which the vacuum energy density evolves with time. In particular, our analysis focuses on the study of spherical matter perturbations, as they decouple from the background expansion, "turn around" and finally collapse. We generalize the spherical collapse model in the case when the vacuum energy is a running function of the Hubble rate, $\Lambda=\Lambda(H)$. A particularly well motivated model of this type is the so-called quantum field vacuum, in which $\Lambda(H)$ is a quadratic function, $\Lambda(H)=n_0+n_2\,H^2$, with $n_0\neq 0$. This model was previously studied by our team using the latest high quality cosmological data to constrain its free parameters, as well as the predicted cluster formation rate. It turns out that the corresponding Hubble expansion history resembles that of the traditional $\Lambda$CDM cosmology. We use this $\Lambda(t)$CDM framework to illustrate the fact that the properties of the spherical collapse model (virial density, collapse factor, etc.) depend on the choice of the considered vacuum energy (homogeneous or clustered). In particular, if the distribution of the vacuum energy is clustered, then, under specific conditions, we can produce more concentrated structures with respect to the homogeneous vacuum energy case.Comment: 14 pages, 4 figures, minor changes, accepted for publication in Phys. Rev.

Sky maps without anisotropies in the cosmic microwave background are a better fit to WMAP's uncalibrated time ordered data than the official sky maps

The purpose of this reanalysis of the WMAP uncalibrated time ordered data (TOD) was two fold. The first was to reassess the reliability of the detection of the anisotropies in the official WMAP sky maps of the cosmic microwave background (CMB). The second was to assess the performance of a proposed criterion in avoiding systematic error in detecting a signal of interest. The criterion was implemented by testing the null hypothesis that the uncalibrated TOD was consistent with no anisotropies when WMAP's hourly calibration parameters were allowed to vary. It was shown independently for all 20 WMAP channels that sky maps with no anisotropies were a better fit to the TOD than those from the official analysis. The recently launched Planck satellite should help sort out this perplexing result.Comment: 11 pages with 1 figure and 2 tables. Extensively rewritten to explain the research bette

Ellipsoidal Universe Can Solve The CMB Quadrupole Problem

The recent three-year WMAP data have confirmed the anomaly concerning the low quadrupole amplitude compared to the best-fit \Lambda CDM prediction. We show that, allowing the large-scale spatial geometry of our universe to be plane-symmetric with eccentricity at decoupling or order 10^{-2}, the quadrupole amplitude can be drastically reduced without affecting higher multipoles of the angular power spectrum of the temperature anisotropy.Comment: 4 pages, 2 figures, minor changes, reference added, to appear in Phys. Rev. Let

Particle production from nonlocal gravitational effective action

In this paper we show how the nonlocal effective action for gravity, obtained after integrating out the matter fields, can be used to compute particle production and spectra for different space-time metrics. Applying this technique to several examples, we find that the perturbative calculation of the effective action up to second order in curvatures yields exactly the same results for the total number of particles as the Bogolyubov transformations method, in the case of masless scalar fields propagating in a Robertson-Walker space-time. Using an adiabatic approximation we also obtain the corresponding spectra and compare the results with the traditional WKB approximation.Comment: 22 pages, LaTeX, no figures. Corrected version with new comments and results. To appear in Phys. Rev.

Scientific possibilities of a solar electric powered rendezvous with comet Encke

The minimum scientific spacecraft instrumentation is considered that is likely to result in as complete an understanding of the composition, structure, and activity of a cometary nucleus as is possible without landing on it. The payload will also give useful results on secondary goals of a better understanding of physical processes in the inner and outer coma. Studies of composition, by means of an actual landing on the surface, details of the internal structure of the nucleus, and sample return were considered beyond the scope of this mission

Those wonderful elastic waves

We consider in a simple and general way elastic waves in isotropic and anisotropic media, their polarization, speeds, reflection from interfaces with mode conversion, and surface waves. Reflection of quasi transverse waves in anisotropic media from a free surface is shown to be characterized by three critical angles.Comment: 11 Figures 26 page