Measuring the spectral running from cosmic microwave background and primordial black holes

We constrain the spectral running by combining cosmic microwave background (CMB) data, baryon acoustic oscillation (BAO) data and the constraint from primordial black holes (PBHs). We find that the constraint from PBHs has a significant impact on the running of running of scalar spectral index, and a power-law scalar power spectrum without running is consistent with observational data once the constraint from PBHs is taken into account. In addition, from the constraints on the slow-roll parameters, the derived tensor spectral index in the single-field slow-roll inflation model is quite small, namely $|n_t|\lesssim 9.3\times 10^{-3}$ which will be very difficult to be measured by CMB data only in the future, and the absolute value of derived running of tensor spectral index is not larger than $2.1\times 10^{-4}$ at 95% confidence level.Comment: 5 pages, 3 figure

Surface excitations, shape deformation and the long-time behavior in a stirred Bose-Einstein condensate

The surface excitations, shape deformation and the formation of persistent current for a Gaussian obstacle potential rotating in an highly oblate Bose-Einstein condensate(BEC)are investigated. Vortex dipole can be produced and trapped in the center of the stirrer even for slow motion of the stirring beam. When the barrier angular velocity is above some critical value, the condensate shape can be deformed remarkably according to the rotation frequency due to the existence of plenty of surface wave excitations. After a long enough time, a few vortices are found to be left either trapped in the condensate or pinned by the obstacle, a vortex dipole or several vortices can be trapped at the beam center, which enables the possibility of vortex manipulation.Comment: 5 pages, 4 figure