On the theory of electric dc-conductivity : linear and non-linear microscopic evolution and macroscopic behaviour

We consider the Schrodinger time evolution of charged particles subject to a static substrate potential and to a homogeneous, macroscopic electric field (a magnetic field may also be present). We investigate the microscopic velocities and the resulting macroscopic current. We show that the microscopic velocities are in general non-linear with respect to the electric field. One kind of non-linearity arises from the highly non-linear adiabatic evolution and (or) from an admixture of parts of it in so-called intermediate states, and the other kind from non-quadratic transition rates between adiabatic states. The resulting macroscopic dc-current may or may not be linear in the field. Three cases can be distinguished : (a) The microscopic non-linearities can be neglected. This is assumed to be the case in linear response theory (Kubo formalism, ...). We give arguments which make it plausible that often such an assumption is indeed justified, in particular for the current parallel to the field. (b) The microscopic non-linearitites lead to macroscopic non-linearities. An example is the onset of dissipation by increasing the electric field in the breakdown of the quantum Hall effect. (c) The macroscopic current is linear although the microscopic non-linearities constitute an essential part of it and cannot be neglected. We show that the Hall current of a quantized Hall plateau belongs to this case. This illustrates that macroscopic linearity does not necessarily result from microscopic linearity. In the second and third cases linear response theory is inadequate. We elucidate also some other problems related to linear response theory.Comment: 24 pages, 6 figures, some typing errors have been corrected. Remark : in eq. (1) of the printed article an obvious typing error remain

The Deepest Supernova Search is Realized in the Hubble Ultra Deep Field Survey

The Hubble Ultra Deep Field Survey has not only provided the deepest optical and near infrared views of universe, but has enabled a search for the most distant supernovae to z~2.2. We have found four supernovae by searching spans of integrations of the Ultra Deep Field and the Ultra Deep Field Parallels taken with the Hubble Space Telescope paired with the Advanced Camera for Surveys and the Near Infrared Multi Object Spectrometer. Interestingly, none of these supernovae were at z>1.4, despite the substantially increased sensitivity per unit area to such objects over the Great Observatories Origins Deep Survey. We present the optical photometric data for the four supernovae. We also show that the low frequency of Type Ia supernovae observed at z>1.4 is statistically consistent with current estimates of the global star formation history combined with the non-trivial assembly time of SN Ia progenitors.Comment: 24 pages (6 figures), submitted to the Astronomical Journa

Why we need to see the dark matter to understand the dark energy

The cosmological concordance model contains two separate constituents which interact only gravitationally with themselves and everything else, the dark matter and the dark energy. In the standard dark energy models, the dark matter makes up some 20% of the total energy budget today, while the dark energy is responsible for about 75%. Here we show that these numbers are only robust for specific dark energy models and that in general we cannot measure the abundance of the dark constituents separately without making strong assumptions.Comment: 4 pages, to be published in the Journal of Physics: Conference Series as a contribution to the 2007 Europhysics Conference on High Energy Physic

Can the Universe escape eternal acceleration?

Recent astronomical observations of distant supernovae light-curves suggest that the expansion of the universe has recently begun to accelerate. Acceleration is created by an anti-gravitational repulsive stress, like that produced by a positive cosmological constant, or universal vacuum energy. It creates a rather bleak eschatological picture. An ever-expanding universe's future appears to be increasingly dominated by its constant vacuum energy. A universe doomed to accelerate forever will produce a state of growing uniformity and cosmic loneliness. Structures participating in the cosmological expansion will ultimately leave each others' horizons and information-processing must eventually die out. Here, we examine whether this picture is the only interpretation of the observations. We find that in many well-motivated scenarios the observed spell of vacuum domination is only a transient phenomenon. Soon after acceleration starts, the vacuum energy's anti-gravitational properties are reversed, and a matter-dominated decelerating cosmic expansion resumes. Thus, contrary to general expectations, once an accelerating universe does not mean always an accelerating universe.Comment: 6 pages, 2 figure

The Rate of Type Ia Supernovae at High Redshift

We derive the rates of Type Ia supernovae (SNIa) over a wide range of redshifts using a complete sample from the IfA Deep Survey. This sample of more than 100 SNIa is the largest set ever collected from a single survey, and therefore uniquely powerful for a detailed supernova rate (SNR) calculation. Measurements of the SNR as a function of cosmological time offer a glimpse into the relationship between the star formation rate (SFR) and Type Ia SNR, and may provide evidence for the progenitor pathway. We observe a progressively increasing Type Ia SNR between redshifts z~0.3-0.8. The Type Ia SNR measurements are consistent with a short time delay (t~1 Gyr) with respect to the SFR, indicating a fairly prompt evolution of SNIa progenitor systems. We derive a best-fit value of SFR/SNR 580 h_70^(-2) M_solar/SNIa for the conversion factor between star formation and SNIa rates, as determined for a delay time of t~1 Gyr between the SFR and the Type Ia SNR. More complete measurements of the Type Ia SNR at z>1 are necessary to conclusively determine the SFR--SNR relationship and constrain SNIa evolutionary pathways.Comment: 37 pages, 9 figures, accepted for publication in Astrophysical Journal. Figures 7-9 correcte

Natural extension of the Generalised Uncertainty Principle

We discuss a gedanken experiment for the simultaneous measurement of the position and momentum of a particle in de Sitter spacetime. We propose an extension of the so-called generalized uncertainty principle (GUP) which implies the existence of a minimum observable momentum. The new GUP is directly connected to the nonzero cosmological constant, which becomes a necessary ingredient for a more complete picture of the quantum spacetime.Comment: 4 pages, 1 figure, v2 with added references, revised and extended as published in CQ

Future state of the Universe

Following the observational evidence for cosmic acceleration which may exclude a possibility for the universe to recollapse to a second singularity, we review alternative scenarios of its future evolution. Although the de Sitter asymptotic state is still an option, some other asymptotic states which allow new types of singularities such as Big-Rip (due to a phantom matter) and sudden future singularities are also admissible and are reviewed in detail. The reality of these singularities which comes from the relation to observational characteristics of the universe expansion are also revealed and widely discussed.Comment: 12 pages, 1 figure, a contribution to Pomeranian Workshop in Fundamental Cosmology (COSMOFUN'05), Pobierowo, Poland, 1-6 September 200

Quintessential inflation from 5D warped product spaces on a dynamical foliation

Assuming the existence of a 5D purely kinetic scalar field on the class of warped product spaces we investigate the possibility of mimic both an inflationary and a quintessential scenarios on 4D hypersurfaces, by implementing a dynamical foliation on the fifth coordinate instead of a constant one. We obtain that an induced chaotic inflationary scenario with a geometrically induced scalar potential and an induced quasi-vacuum equation of state on 4D dynamical hypersurfaces is possible. While on a constant foliation the universe can be considered as matter dominated today, in a family of 4D dynamical hypersurfaces the universe can be passing for a period of accelerated expansion with a deceleration parameter nearly -1. This effect of the dynamical foliation results negligible at the inflationary epoch allowing for a chaotic scenario and becomes considerable at the present epoch allowing a quintessential scenario.Comment: 7 pages, 1 figure Accepted for publication in Modern Physics Letters

Constraints on CDM cosmology from galaxy power spectrum, CMB and SNIa evolution

We examine the constraints that can be obtained on standard cold dark matter models from the most currently used data set: CMB anisotropies, type Ia supernovae and the SDSS luminous red galaxies. We also examine how these constraints are widened when the equation of state parameter $w$ and the curvature parameter $\Omega_k$ are left as free parameters. For the $\Lambda$CDM model, our 'vanilla' model, cosmological parameters are tightly constrained and consistent with current estimates from various methods. When the dark energy parameter $w$ is free we find that the constraints remain mostly unchanged, i.e. changes are smaller than the 1 sigma uncertainties. Similarly, relaxing the assumption of a flat universe leads to nearly identical constraints on the dark energy density parameter of the universe $\Omega_\Lambda$, baryon density of the universe $\Omega_b$, the optical depth $\tau$, the index of the power spectrum of primordial fluctuations $n_S$, with most one sigma uncertainties better than 5%. More significant changes appear on other parameters: while preferred values are almost unchanged, uncertainties for the physical dark matter density $\Omega_ch^2$, Hubble constant $H_0$ and $\sigma_8$ are typically twice as large. We found that different methodological approaches on large scale structure estimates lead to appreciable differences in preferred values and uncertainty widths. We also found that possible evolution in SNIa intrinsic luminosity does not alter these constraints by much, except for $w$, for which the uncertainty is twice as large. At the same time, this possible evolution is severely constrained. We conclude that systematic uncertainties for some estimated quantities are similar or larger than statistical ones.Comment: Revised version, 9 pages, 8 figures, accepted for publication in A&

The conformal status of ω=−3/2\omega=-3/2 Brans-Dicke cosmology

Following recent fit of supernovae data to Brans-Dicke theory which favours the model with $\omega = - 3/2$ \cite{fabris} we discuss the status of this special case of Brans-Dicke cosmology in both isotropic and anisotropic framework. It emerges that the limit $\omega = -3/2$ is consistent only with the vacuum field equations and it makes such a Brans-Dicke theory conformally invariant. Then it is an example of the conformal relativity theory which allows the invariance with respect to conformal transformations of the metric. Besides, Brans-Dicke theory with $\omega = -3/2$ gives a border between a standard scalar field model and a ghost/phantom model. In this paper we show that in $\omega = -3/2$ Brans-Dicke theory, i.e., in the conformal relativity there are no isotropic Friedmann solutions of non-zero spatial curvature except for $k=-1$ case. Further we show that this $k=-1$ case, after the conformal transformation into the Einstein frame, is just the Milne universe and, as such, it is equivalent to Minkowski spacetime. It generally means that only flat models are fully consistent with the field equations. On the other hand, it is shown explicitly that the anisotropic non-zero spatial curvature models of Kantowski-Sachs type are admissible in $\omega = -3/2$ Brans-Dicke theory. It then seems that an additional scale factor which appears in anisotropic models gives an extra deegre of freedom and makes it less restrictive than in an isotropic Friedmann case.Comment: REVTEX4, 19 pages, 8 figures, references adde