Zero inertia limit of incompressible Qian–Sheng model

The Qian–Sheng model is a system describing the hydrodynamics of nematic liquid crystals in the Q-tensor framework. When the inertial effect is included, it is a hyperbolic-type system involving a second-order material derivative coupling with forced incompressible Navier–Stokes equations. If formally letting the inertial constant [Formula: see text] go to zero, the resulting system is the corresponding parabolic model. We provide the result on the rigorous justification of this limit in [Formula: see text] with small initial data, which validates mathematically the parabolic Qian–Sheng model. To achieve this, an initial layer is introduced to not only overcome the disparity of the initial conditions between the hyperbolic and parabolic models, but also make the convergence rate optimal. Moreover, a novel [Formula: see text]-dependent energy norm is carefully designed, which is non-negative only when [Formula: see text] is small enough, and handles the difficulty brought by the second-order material derivative.

Spontaneous leptogenesis in Higgs inflation

We propose a scenario of spontaneous leptogenesis in Higgs inflation with help from two additional operators: the Weinberg operator (Dim 5) and the derivative coupling of the Higgs field and the current of lepton number (Dim 6). The former is responsible for lepton number violation and the latter induces chemical potential for lepton number. The period of rapidly changing Higgs field, naturally realized in Higgs inflation during the reheating, allows large enhancement in the produced asymmetry in lepton number, which is eventually converted into baryon asymmetry of the universe. This scenario is compatible with high reheating temperature of Higgs inflation model.

Reheating constraints on an inflation model with nonminimal derivative coupling in the light of Planck 2018 data

Reheating is a process by which the inflaton’s energy density transfers to conventional matter after cosmic inflation. Currently, there is no cosmic observational evidence to directly detect the reheating era, but it may impose additional constraints on inflationary models. Depending upon the model, e-folding number during reheating [Formula: see text] and the final reheating temperature [Formula: see text], as well as its effective equation of state parameter [Formula: see text], may be directly linked to the inflation observables such as the scalar spectral index [Formula: see text] and the tensor-to-scalar ratio [Formula: see text]. By restricting the values of the effective equation of state parameter observationally, one can derive more stringent limits on inflationary models than those obtained from other routes. In this paper, we are interested to consider the reheating era in an inflation model with a nonminimal derivative coupling of the scalar field to impose some severe constraints on the parameter space of the model in the light of Planck 2018 data. We study the reheating final temperature and e-folds number in terms of the scalar spectral index and [Formula: see text] within a numerical analysis on the model’s parameter space. To realize a viable range of the reheating equation of state parameter in this nonminimal derivative inflation model, we obtain some observationally acceptable subspaces in the [Formula: see text] phase plane. To this end, we consider some sort of polynomial potentials to obtain some constraints on the model’s parameter space which corresponds to viable values of the scalar spectral index and tensor-to-scalar ratio released by Planck 2018 TT+TE+EE+LowE observational data. Finally, we compare the obtained constraints in this nonminimal set-up with those derived from a single, minimally coupled scalar field inflation model to reveal the physics of the reheating in the context of nonminimal derivative inflation model.

The Reconstruction of Non-Minimal Derivative Coupling Inflationary Potentials

We derive the reconstruction formulae for the inflation model with the non-minimal derivative coupling term. If reconstructing the potential from the tensor-to-scalar ratio r, we could obtain the potential without using the high friction limit. As an example, we reconstruct the potential from the parameterization r=8α/(N+β)γ, which is a general form of the α-attractor. The reconstructed potential has the same asymptotic behavior as the T- and E-model if we choose γ=2 and α≪1. We also discuss the constraints from the reheating phase by assuming the parameter wre of state equation during reheating is a constant. The scale of big-bang nucleosynthesis could put an upper limit on ns if wre=2/3 and a low limit on ns if wre=1/6.