Dark energy: a quantum fossil from the inflationary Universe?

The discovery of dark energy (DE) as the physical cause for the accelerated expansion of the Universe is the most remarkable experimental finding of modern cosmology. However, it leads to insurmountable theoretical difficulties from the point of view of fundamental physics. Inflation, on the other hand, constitutes another crucial ingredient, which seems necessary to solve other cosmological conundrums and provides the primeval quantum seeds for structure formation. One may wonder if there is any deep relationship between these two paradigms. In this work, we suggest that the existence of the DE in the present Universe could be linked to the quantum field theoretical mechanism that may have triggered primordial inflation in the early Universe. This mechanism, based on quantum conformal symmetry, induces a logarithmic, asymptotically-free, running of the gravitational coupling. If this evolution persists in the present Universe, and if matter is conserved, the general covariance of Einstein's equations demands the existence of dynamical DE in the form of a running cosmological term whose variation follows a power law of the redshift.Comment: LaTeX, 14 pages, extended discussion. References added. Accepted in J. Phys. A: Mathematical and Theoretica

Selling to Consumers with Endogenous Types

For many goods (such as experience goods or addictive goods), consumers' preferences may change over time.In this paper, we examine a monopolist's optimal pricing schedule when current consumption can affect a consumer's valuation in the future and valuations are unobservable.We assume that consumers are anonymous, i.e. the monopolist can't observe a consumer's past consumption history.For myopic consumers, the optimal consumption schedule is distorted upwards, involving substantial discounts for low valuation types.This pushes low types into higher valuations, from which rents can be extracted.For forward looking consumers, there may be a further upward distortion of consumption due to a reversal of the adverse selection effect; low valuation consumers now have a strong interest in consumption in order to increase their valuations.Firms will find it profitable to educate consumers and encourage forward looking behaviorendogenous types;experience goods;addictive goods;price discrimation

Design study of a fission-electric cell reactor

Fission electric cell reactor to generation of power in spac

Caustic formation in expanding condensates of cold atoms

We study the evolution of density in an expanding Bose-Einstein condensate that initially has a spatially varying phase, concentrating on behaviour when these phase variations are large. In this regime large density fluctuations develop during expansion. Maxima have a characteristic density that diverges with the amplitude of phase variations and their formation is analogous to that of caustics in geometrical optics. We analyse in detail caustic formation in a quasi-one dimensional condensate, which before expansion is subject to a periodic or random optical potential, and we discuss the equivalent problem for a quasi-two dimensional system. We also examine the influence of many-body correlations in the initial state on caustic formation for a Bose gas expanding from a strictly one-dimensional trap. In addition, we study a similar arrangement for non-interacting fermions, showing that Fermi surface discontinuities in the momentum distribution give rise in that case to sharp peaks in the spatial derivative of the density. We discuss recent experiments and argue that fringes reported in time of flight images by Chen and co-workers [Phys. Rev. A 77, 033632 (2008)] are an example of caustic formation.Comment: 10 pages, 5 figures. Published versio

An associative memory for the on-line recognition and prediction of temporal sequences

This paper presents the design of an associative memory with feedback that is capable of on-line temporal sequence learning. A framework for on-line sequence learning has been proposed, and different sequence learning models have been analysed according to this framework. The network model is an associative memory with a separate store for the sequence context of a symbol. A sparse distributed memory is used to gain scalability. The context store combines the functionality of a neural layer with a shift register. The sensitivity of the machine to the sequence context is controllable, resulting in different characteristic behaviours. The model can store and predict on-line sequences of various types and length. Numerical simulations on the model have been carried out to determine its properties.Comment: Published in IJCNN 2005, Montreal, Canad