Inflation and Alternatives with Blue Tensor Spectra

We study the tilt of the primordial gravitational waves spectrum. A hint of blue tilt is shown from analyzing the BICEP2 and POLARBEAR data. Motivated by this, we explore the possibilities of blue tensor spectra from the very early universe cosmology models, including null energy condition violating inflation, inflation with general initial conditions, and string gas cosmology, etc. For the simplest G-inflation, blue tensor spectrum also implies blue scalar spectrum. In general, the inflation models with blue tensor spectra indicate large non-Gaussianities. On the other hand, string gas cosmology predicts blue tensor spectrum with highly Gaussian fluctuations. If further experiments do confirm the blue tensor spectrum, non-Gaussianity becomes a distinguishing test between inflation and alternatives.Comment: 13 pages, 10 figures. v2: references and minor improvements added. v3: version to appear on JCA

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

Topological phase transition in the quench dynamics of a one-dimensional Fermi gas

We study the quench dynamics of a one-dimensional ultracold Fermi gas in an optical lattice potential with synthetic spin-orbit coupling. At equilibrium, the ground state of the system can undergo a topological phase transition and become a topological superfluid with Majorana edge states. As the interaction is quenched near the topological phase boundary, we identify an interesting dynamical phase transition of the quenched state in the long-time limit, characterized by an abrupt change of the pairing gap at a critical quenched interaction strength. We further demonstrate the topological nature of this dynamical phase transition from edge-state analysis of the quenched states. Our findings provide interesting clues for the understanding of topological phase transitions in dynamical processes, and can be useful for the dynamical detection of Majorana edge states in corresponding systems.Comment: 7 pages, 5 figure

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

Signatures of Bose-Einstein condensation in an optical lattice

We discuss typical experimental signatures for the Bose-Einstein condensation (BEC) of an ultracold Bose gas in an inhomogeneous optical lattice at finite temperature. Applying the Hartree-Fock-Bogoliubov-Popov formalism, we calculate quantities such as the momentum-space density distribution, visibility and peak width as the system is tuned through the superfluid to normal phase transition. Different from previous studies, we consider systems with fixed total particle number, which is of direct experimental relevance. We show that the onset of BEC is accompanied by sharp features in all these signatures, which can be probed via typical time-of-flight imaging techniques. In particular, we find a two-platform structure in the peak width across the phase transition. We show that the onset of condensation is related to the emergence of the higher platform, which can be used as an effective experimental signature.Comment: 5 pages, 3 figure