w = 1/3 to w = −1 evolution in a Robertson–Walker space-time with constant scalar curvature

The Ricci tensor of a Robertson\u2013Walker (RW) space-time is here specified by requiring constancy of the scalar curvature and a vanishing spatial curvature. By entering this Ricci tensor in Einstein\u2019s equations (without cosmological constant), the cosmological fluid shows a transition from a pure radiation to a Lambda equation of state. In other words, the RW geometry with constant scalar curvature and flat space fixes the limit values w = 1/3 and w = 121, without any hypothesis on the cosmological fluid. The value of the scalar curvature fixes the time-scale for the transition. For this reason, we investigate the \u2018toy-universe\u2019 with Hubble parameter h = 0.673 and temperature TCMB = 2.72 K. The model predicts an age of the universe in the range 7.3\u201313.7 Gyr

On the weyl and ricci tensors of generalized robertson-walker space-times

We prove theorems about the Ricci and the Weyl tensors on Generalized Robertson- Walker space-times of dimension n 65 3. In particular, we show that the concircular vector introduced by Chen decomposes the Ricci tensor as a perfect fluid term plus a term linear in the contracted Weyl tensor. The Weyl tensor is harmonic if and only if it is annihilated by Chen's vector, and any of the two conditions is necessary and sufficient for the Generalized Robertson-Walker (GRW) space-time to be a quasi-Einstein (perfect fluid) manifold. Finally, the general structure of the Riemann tensor for Robertson-Walker space-times is given, in terms of Chen's vector. In n = 4, a GRW space-time with harmonic Weyl tensor is a Robertson-Walker space-time

Random antagonistic matrices

The ensemble of antagonistic matrices is introduced and studied. In antagonistic matrices the entries A(ij) and A(ji) i are real and have opposite signs, or are both zero, and the diagonal is zero. This generalization of antisymmetric matrices is suggested by the linearized dynamics of competitive species in ecology

A note on concircular structure space-times

In this note we show that Lorentzian Concircular Structure manifolds (LCS)_n coincide with Generalized Robertson-Walker space-times

Identities and exponential inequalities for transfer matrices

Rigorous results are presented for the decay of eigenvalues of transfer matrices, based on the theorem by Demko Moss and Smit on the decay of matrix elements for the inverse of a band matrix

An introduction to functional methods for many-body Green functions

This is an introduction to the coherent-state representation of the generating functional of correlators for fermions. Ward's identities, Dyson's equations, and the effective potential are discussed for systems of electrons with Coulomb interaction

Cosmological Perfect Fluids in Gauss-Bonnet Gravity

In a n-dimensional Friedmann-Robertson-Walker metric, it is rigorously shown that any analytical theory of gravity f(R,G), where R is the curvature scalar and G is the Gauss- Bonnet topological invariant, can be associated to a perfect-fluid stress-energy tensor. In this perspective, dark components of the cosmological Hubble flow can be geometrically interpreted

An exactly solvable self-convolutive recurrence

We consider a self-convolutive recurrence whose solution is the sequence of coefficients in the asymptotic expansion of the logarithmic derivative of the confluent hypergeometic function $U(a,b,z)$. By application of the Hilbert transform we convert this expression into an explicit, non-recursive solution in which the $n$th coefficient is expressed as the $(n-1)$th moment of a measure, and also as the trace of the $(n-1)$th iterate of a linear operator. Applications of these sequences, and hence of the explicit solution provided, are found in quantum field theory as the number of Feynman diagrams of a certain type and order, in Brownian motion theory, and in combinatorics

Protons in near earth orbit

The proton spectrum in the kinetic energy range 0.1 to 200 GeV was measured by the Alpha Magnetic Spectrometer (AMS) during space shuttle flight STS-91 at an altitude of 380 km. Above the geomagnetic cutoff the observed spectrum is parameterized by a power law. Below the geomagnetic cutoff a substantial second spectrum was observed concentrated at equatorial latitudes with a flux ~ 70 m^-2 sec^-1 sr^-1. Most of these second spectrum protons follow a complicated trajectory and originate from a restricted geographic region.Comment: 19 pages, Latex, 7 .eps figure