K-Inflation in Noncommutative Space-Time

The power spectra of the scalar and tensor perturbations in the noncommutative k-inflation model are calculated in this paper. In this model, all the modes created when the stringy space-time uncertainty relation is satisfied are generated inside the sound/Hubble horizon during inflation for the scalar/tensor perturbations. It turns out that a linear term describing the noncommutative space-time effect contributes to the power spectra of the scalar and tensor perturbations. Confronting the general noncommutative k-inflation model with latest results from \textit{Planck} and BICEP2, and taking $c_S$ and $\lambda$ as free parameters, we find that it is well consistent with observations. However, for the two specific models, i.e. the tachyon and DBI inflation models, it is found that the DBI model is not favored, while the tachyon model lies inside the $1\sigma$ contour, if the e-folds number is assumed to be around $50\sim60$.Comment: 9 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1404.016

Is Cosmological Constant Needed in Higgs Inflation?

The detection of B-mode shows a very powerful constraint to theoretical inflation models through the measurement of the tensor-to-scalar ratio $r$. Higgs boson is the most likely candidate of the inflaton field. But usually, Higgs inflation models predict a small value of $r$, which is not quite consistent with the recent results from BICEP2. In this paper, we explored whether a cosmological constant energy component is needed to improve the situation. And we found the answer is yes. For the so-called Higgs chaotic inflation model with a quadratic potential, it predicts $r\approx 0.2$, $n_s\approx0.96$ with e-folds number $N\approx 56$, which is large enough to overcome the problems such as the horizon problem in the Big Bang cosmology. The required energy scale of the cosmological constant is roughly $\Lambda \sim (10^{14} \text{GeV})^2$, which means a mechanism is still needed to solve the fine-tuning problem in the later time evolution of the universe, e.g. by introducing some dark energy component.Comment: 4 pages, 2 figure

Quasi-two-body decays B→ηc(1S,2S) [ρ(770),ρ(1450),ρ(1700)→] ππB \to \eta_c {(1S ,2S)}\;[\rho(770),\rho(1450),\rho(1700) \to ]\; \pi\pi in the perturbative QCD approach

In this paper, we calculated the branching ratios of the quasi-two-body decays $B \to \eta_c (1S ,2S)$ $[\rho(770), \rho(1450),\rho(1700)\to ] \pi\pi$ by employing the perturbative QCD (PQCD) approach. The contributions from the $P$-wave resonances $\rho(770)$, $\rho(1450)$ and $\rho(1700)$ were taken into account. The two-pion distribution amplitude $\Phi_{\pi\pi}^{\rm P}$ is parameterized by the vector current time-like form factor $F_{\pi}$ to study the considered decay modes. We found that (a) the PQCD predictions for the branching ratios of the considered quasi-two-body decays are in the order of $10^{-7} \sim 10^{-6}$, while the two-body decay rates ${\cal B}(B \to \eta_c{(1S,2S)} (\rho(1450),\rho(1700)))$ are extracted from those for the corresponding quasi-two-body decays; (b) the whole pattern of the pion form factor-squared $|F_\pi|^2$ measured by the BABAR Collaboration could be understood based on our theoretical results; (c) the general expectation based on the similarity between $B \to \eta_c \pi\pi$ and $B \to J/\psi \pi\pi$ decays are confirmed: $R_2(\eta_c)\approx 0.45$ is consistent with the measured $R_2(J/\psi)\approx 0.56\pm 0.09$ within errors; and (d) new ratios $R_3(\eta_c(1S))$ and $R_4(\eta_c(2S))$ among the branching ratios of the considered decay modes are defined and could be tested by future experiments.Comment: 10 pages, 3 figure