Lorentzian quintessential inflation

From the assumption that the slow-roll parameter [Formula: see text] has a Lorentzian form as a function of the e-folds number [Formula: see text], a successful model of a quintessential inflation is obtained. The form corresponds to the vacuum energy both in the inflationary and in the dark energy epochs. The form satisfies the condition to climb from small values of [Formula: see text] to [Formula: see text] at the end of the inflationary epoch. At the late universe, [Formula: see text] becomes small again and this leads to the dark energy epoch. The observables that the models predict fits with the latest Planck data: [Formula: see text]. Naturally, a large dimensionless factor that exponentially amplifies the inflationary scale and exponentially suppresses the dark energy scale appearance, producing a sort of cosmological seesaw mechanism. We find the corresponding scalar Quintessential Inflationary potential with two flat regions — one inflationary and one as a dark energy with slow-roll behavior.

Can Lorentz transformations be determined by the null Michelson-Morley result?

The so-called principle of relativity is able to fix a general coordinate transformation which differs from the standard Lorentzian form only by an unknown speed which cannot in principle be identified with the light speed. Based on a reanalysis of the Michelson-Morley experiment using this extended transformation we show that such unknown speed is analytically determined regardless of the Maxwell equations and conceptual issues related to synchronization procedures, time and causality definitions. Such a result demonstrates in a pedagogical manner that the constancy of the speed of light does not need to be assumed as a basic postulate of the special relativity theory since it can be directly deduced from an optical experiment in combination with the principle of relativity. The approach presented here provides a simple and insightful derivation of the Lorentz transformations appropriated for an introductory special relativity theory course.

The effects of modulation frequency and rf ENDOR power on 53Cr3+ ENDOR lines in CsAl sulfate alum

An investigation was made of the effects of modulation frequency and rf ENDOR power on the single and double quantum ENDOR spectral lines of 53Cr3+ ions in single crystals and powders of CsAl sulfate alum. Measurements were made of the linewidths and intensities in the single crystals and of the linewidths in the powders. It was found in the single crystals that a factor of 2/1 exists for the ratio of single/double quantum linewidths at the limit of zero ENDOR power and modulation frequency. Interpretation of the line intensity results with the results of lineshape theory indicates that the ENDOR lines are of Lorentzian form, at least for low values of ENDOR power.

Symétrisation de la longueur et du temps dans un espace de Lorentz C3 en algèbre lineaire, pouvant servir en théorie trichromatique des couleurs

It is proposed to express time as a composition of three auxiliary variables tx, ty, tz. which will be named components of vector t. Event P is expressed as a composition of six variables x, y, z, tx, ty, tz in R6 or of three coordinates ξ = x + itx, η = y + ity, and ζ = z + itz in C3. A quadratic function is defined, called 'carré simple', of P, which comes to the same as taking the square of the Lorentzian form of P in R4, equalling.s2. In this formalism, length r(x, y, z) and time t (tx, ty, tz) play roles exactly symmetrical and are exchangeable one for the other. This formalism will be applied to trichromatic theory.

Induced Anisotropy and Light Scattering in Liquids. II.

The spectra of light scattered by molecular liquids have been studied in order to obtain information about motions in the liquid on a time scale of 10−11 to 10−13 s. Integrated intensities and polarization ratios were measured. The spectra were decomposed by least squares curve fitting techniques into two components: a narrow component of Lorentzian form with line width approximately constant for all the liquids, and a broad component of the form [Formula: see text] with a line width parameter 1/ν0 equal to 2πγ−1(μ/kT)1/2. The proportionality constant γ−1 has the value of 0.62 Å for all the liquids studied. This interaction length appears to be common to all liquids.