Dependence of Temporal Properties on Energy in Long-Lag, Wide-Pulse Gamma-Ray Bursts

We employed a sample compiled by Norris et al. (2005, ApJ, 625, 324) to study the dependence of the pulse temporal properties on energy in long-lag, wide-pulse gamma-ray bursts. Our analysis shows that the pulse peak time, rise time scale and decay time scale are power law functions of energy, which is a preliminary report on the relationships between the three quantities and energy. The power law indexes associated with the pulse width, rise time scale and decay time scale are correlated and the correlation between the indexes associated with the pulse width and the decay time scale is more obvious. In addition, we have found that the pulse peak lag is strongly correlated with the CCF lag, but the centroid lag is less correlated with the peak lag and CCF lag. Based on these results and some previous investigations, we tend to believe that all energy-dependent pulse temporal properties may come from the joint contribution of both the hydrodynamic processes of the outflows and the curvature effect, where the energy-dependent spectral lag may be mainly dominated by the dynamic process and the energy-dependent pulse width may be mainly determined by the curvature effect.Comment: 20 pages, 7 figures, added references, matched to published version, accepted for publication in PAS

Inflation with Holographic Dark Energy

We investigate the corrections of the holographic dark energy to inflation paradigm. We study the evolution of the holographic dark energy in the inflationary universe in detail, and carry out a model-independent analysis on the holographic dark energy correction to the primordial scalar power spectrum. It turns out that the corrections generically make the spectrum redder. To be consistent with the experimental data, there must be a upper bound on the reheating temperature. We also discuss the corrections due to different choices of the infrared cutoff.Comment: 15 pages, 3 figures, v2: references added, a fast-roll discussion added. v3: typos corrected. v4: final version to appear in NP

Inflationary NonGaussianity from Thermal Fluctuations

We calculate the contribution of the fluctuations with the thermal origin to the inflationary nonGaussianity. We find that even a small component of radiation can lead to a large nonGaussianity. We show that this thermal nonGaussianity always has positive $f_{\rm NL}$. We illustrate our result in the chain inflation model and the very weakly dissipative warm inflation model. We show that $f_{NL}\sim {\cal O}(1)$ is general in such models. If we allow modified equation of state, or some decoupling effects, the large thermal nonGaussianity of order $f_{\rm NL}>5$ or even $f_{\rm NL}\sim 100$ can be produced. We also show that the power spectrum of chain inflation should have a thermal origin. In the Appendix A, we made a clarification on the different conventions used in the literature related to the calculation of $f_{\rm NL}$.Comment: 20 pages, 1 figure. v2, v3: references and acknowledgments update

Uniqueness theorems for meromorphic mappings sharing hyperplanes in general position

The purpose of this article is to study the uniqueness problem for meromorphic mappings from $\mathbb{C}^{n}$ into the complex projective space $\mathbb{P}^{N}(\mathbb{C}).$ By making using of the method of dealing with multiple values due to L. Yang and the technique of Dethloff-Quang-Tan respectively, we obtain two general uniqueness theorems which improve and extend some known results of meromorphic mappings sharing hyperplanes in general position.Comment: 10 page

Generalized Space-time Noncommutative Inflation

We study the noncommutative inflation with a time-dependent noncommutativity between space and time. From the numerical analysis of power law inflation, there are clues that the CMB spectrum indicates a nonconstant noncommutative inflation. Then we extend our treatment to the inflation models with more general noncommutativity and find that the scalar perturbation power spectrum depends sensitively on the time varying of the spacetime noncommutativity. This stringy effect may be probed in the future cosmological observations.Comment: 15 pages, 2 figure