Cosmology with Coupled Gravity and Dark Energy

Dark energy is a fundamental constituent of our universe, its status in the cosmological field equation should be equivalent to that of gravity. Here we construct a dark energy and matter gravity coupling (DEMC) model of cosmology in a way that dark energy and gravity are introduced into the cosmological field equation in parallel with each other from the beginning. The DEMC universe possesses a composite symmetry from global Galileo invariance and local Lorentz invariance. The observed evolution of the universe expansion rate at redshift z>1 is in tension with the standard LCDM model, but can be well predicted by the DEMC model from measurements of only nearby epochs. The so far most precise measured expansion rate at high z is quite a bit slower than the expectations from LCDM, but remarkably consistent with that from DEMC. It is hoped that the DEMC scenario can also help to solve other existing challenges to cosmology: large scale anomalies in CMB maps and large structures up to about 10^3 Mpc of a quasar group. The DEMC universe is a well defined mechanical system. From measurements we can quantitatively evaluate its total rest energy, present absolute radius and expanding speed.Comment: 9 pages, 4 figure

Heliospheric Origin of Gamma-Ray Bursts

Systematic variations of average observational characteristics and correlation properties between different parameters of gamma-ray bursts (GRBs) with time from 1991 April to 1994 September are revealed. It is hard to explain the observed long-term variability by variations of experimental conditions. The variability of GRB properties with the time scale of months to years, together with the similarity between GRBs, solar hard X-ray flares and terrestrial gamma-ray flashes, may indicate an origin of GRBs, at least partly, within the heliosphere. Large-voltage and high-temperature pinch plasma columns produced by disruptive electrical discharges in the outer heliosphere can generate hard X-ray and gamma-ray flashes with energy spectra and spectral evolution characters consistent with that observed in GRBs.Comment: LaTex, epsfig. 20 pages, 17 figures, replace to correct the definition of Epk and revise Figs 12-1

Constructing a Robust Universe with Attraction-Repulsion Coupling and Energy Conservation

The discovery of accelerated cosmic expansion implies that, in addition to the attractive gravity of matter, there exists in our universe some other form of energy (dark energy or cosmological constant) producing a repulsive force. The natural interpretation of dark energy is the vacuum energy. However, the density of vacuum energy expected by the quantum field theory is 120 orders of magnitude larger than what is allowed by cosmological observations, which is called the cosmological constant problem and remains one of the most significant unsolved problems in fundamental physics. Here we show that the huge discrepancy can be resolved by assuming that our universe is an attraction-repulsion coupled system with energy conservation, and that the pre-inflation vacuum is in equilibrium between attraction and repulsion (in flat Minkowski spacetime, not de Sitter or anti de Sitter). The attraction-repulsion coupling picture can also easily explain why both kinds of energy in our universe have similar magnitude today, and avoid singularity problems in general relativity and cosmology.Comment: 8 pages, 1 figur

Ramsey numbers of paths and graphs of the same order

For graphs $F_n$ and $G_n$ of order $n$, if $R(F_n, G_n)=(\chi(G_n)-1)(n-1)+\sigma(G_n)$, then $F_n$ is said to be $G_n$-good, where $\sigma(G_n)$ is the minimum size of a color class among all proper vertex-colorings of $G_n$ with $\chi(G_n)$ colors. Given $\Delta(G_n)\le \Delta$, it is shown that $P_n$ is asymptotically $G_n$-good if $\alpha(G_n)\le\frac{n}{4}$.Comment: 8 pages, 3 figure

Symmetry of Solutions for a Fractional System

We consider the following equations: \begin{equation*} \left\{\begin{array}{ll} (-\triangle)^{\alpha/2}u(x)=f(v(x)), \\ (-\triangle)^{\beta/2}v(x)=g(u(x)), &x \in R^{n},\\ u,v\geq 0, &x \in R^{n}, \end{array} \right. \end{equation*} for continuous $f, g$ and $\alpha, \beta \in (0,2)$. Under some natural assumptions on $f$ and $g$, by applying the \emph{method of moving planes} directly to the system, we obtain symmetry on non-negative solutions without any decay assumption on the solutions at infinity

On generalization of D'Aurizio-S\'andor trigonometric inequalities with a parameter

In this work, we generalize the D'Aurizio-S\'andor inequalities (\cite{D'Aurizio,Sandor}) using an elementary approach. In particular, our approach provides an alternative proof of the D'Aurizio-S\'andor inequalities. Moreover, as an immediate consequence of the generalized D'Aurizio-S\'andor inequalities, we establish the D'Aurizio-S\'andor-type inequalities for hyperbolic functions

Averaging algebras, Schr\"oder numbers, rooted trees and operads

In this paper, we study averaging operators from an algebraic and combinatorial point of view. We first construct free averaging algebras in terms of a class of bracketed words called averaging words. We next apply this construction to obtain one and two variable generating functions for subsets of averaging words when the averaging operator is taken to be idempotent. When the averaging algebra has an idempotent generator, the generating function in one variable is twice the generating function for large Schr\"oder numbers, leading us to give interpretations of large Schr\"oder numbers in terms of bracketed words and rooted trees, as well as a recursive formula for these numbers. We also give a representation of free averaging algebras by unreduced trees and apply it to give a combinatorial description of the operad of averaging algebras.Comment: 30 page

Representations of Polynomial Rota-Baxter Algebras

A Rota--Baxter operator is an algebraic abstraction of integration, which is the typical example of a weight zero Rota-Baxter operator. We show that studying the modules over the polynomial Rota--Baxter algebra $(k[x],P)$ is equivalent to studying the modules over the Jordan plane, and we generalize the direct decomposability results for the $(k[x],P)$-modules in [Iy] from algebraically closed fields of characteristic zero to fields of characteristic zero. Furthermore, we provide a classification of Rota--Baxter modules up to isomorphism based on indecomposable $k[x]$-modules

A Pohozaev Identity for the Fractional Heˊ\acute{e}non System

In this paper, we study the Pohozaev identity associated with a H$\acute{e}$non-Lane-Emden system involving the fractional Laplacian: \begin{equation} \left\{\begin{array}{ll} (-\triangle)^su=|x|^av^p,&x\in\Omega, (-\triangle)^sv=|x|^bu^q,&x\in\Omega, u=v=0,&x\in R^n\backslash\Omega, \end{array} \right. \end{equation} in a star-shaped and bounded domain $\Omega$ for $s\in(0,1)$. As an application of our identity, we deduce the nonexistence of positive solutions in the critical and supercritical cases

Improved CMB Map from WMAP Data

The cosmic microwave background (CMB) temperature maps published by the Wilkinson Microwave Anisotropy Probe (WMAP) team are found to be inconsistent with the differential time-ordered data (TOD), from which the maps are reconstructed. The inconsistency indicates that there is a serious problem in the map making routine of the WMAP team, and it is necessary to reprocess the WMAP data. We develop a self-consistent software package of map-making and power spectrum estimation independently of the WMAP team. Our software passes a variety of tests. New CMB maps are then reconstructed, which are significantly different from the official WMAP maps. In the new maps, the inconsistency disappeared, along with the hitherto unexplained high level alignment between the CMB quadrupole and octopole components detected in released WMAP maps. An improved CMB cross-power spectrum is then derived from the new maps which better agrees with that of BOOMRANG. Two important results are hence obtained: the CMB quadrupole drops to nearly zero, and the power in multiple moment range between 200 and 675 decreases on average by about 13%, causing the best-fit cosmological parameters to change considerably, e.g., the total matter density increases from 0.26 up to 0.32 and the dark energy density decreases from 0.74 down to 0.68. These new parameters match with improved accuracy those of other independent experiments. Our results indicate that there is still room for significant revision in the cosmological model parameters.Comment: Submitted to MNRAS. In the revised version (v3) we make foreground reduction with the same technique WMAP team used and add the results of reconstructing the sky maps with the WMAP default flagging and our softwar