Reducing the Tension Between the BICEP2 and the Planck Measurements: A Complete Exploration of the Parameter Space

A large inflationary tensor-to-scalar ratio $r_\mathrm{0.002} = 0.20^{+0.07}_{-0.05}$ is reported by the BICEP2 team based on their B-mode polarization detection, which is outside of the $95\%$ confidence level of the Planck best fit model. We explore several possible ways to reduce the tension between the two by considering a model in which $\alpha_\mathrm{s}$, $n_\mathrm{t}$, $n_\mathrm{s}$ and the neutrino parameters $N_\mathrm{eff}$ and $\Sigma m_\mathrm{\nu}$ are set as free parameters. Using the Markov Chain Monte Carlo (MCMC) technique to survey the complete parameter space with and without the BICEP2 data, we find that the resulting constraints on $r_\mathrm{0.002}$ are consistent with each other and the apparent tension seems to be relaxed. Further detailed investigations on those fittings suggest that $N_\mathrm{eff}$ probably plays the most important role in reducing the tension. We also find that the results obtained from fitting without adopting the consistency relation do not deviate much from the consistency relation. With available Planck, WMAP, BICEP2 and BAO datasets all together, we obtain $r_{0.002} = 0.14_{-0.11}^{+0.05}$, $n_\mathrm{t} = 0.35_{-0.47}^{+0.28}$, $n_\mathrm{s}=0.98_{-0.02}^{+0.02}$, and $\alpha_\mathrm{s}=-0.0086_{-0.0189}^{+0.0148}$; if the consistency relation is adopted, we get $r_{0.002} = 0.22_{-0.06}^{+0.05}$.Comment: 8 pages, 4 figures, submitted to PL

Research on the Integrated Practical Teaching Model of Cross-border E-commerce Professional Knowledge and Innovation and Entrepreneurship Education

The development of cross-border e-commerce has stimulated a growing interest in related education. In response to this trend, a practical teaching approach that merges cross-border e-commerce expertise with innovation and entrepreneurship education has arisen and gained widespread traction. This innovative approach emphasizes the cultivation of students’ innovation skills and entrepreneurial ability through task-driven teaching that integrates professional knowledge and practical training. By participating in enterprise operations and completing assignments, students are able to master both theoretical knowledge and professional skills. This paper aims to explore the effectiveness of the task-driven teaching method in the integrated practical teaching of cross-border e-commerce and innovation and entrepreneurship. Practical suggestions for teaching reform in cross-border e-commerce are provided to meet the needs of application-oriented undergraduate colleges and to cultivate the application skills that enterprises require