Inflation with High Derivative Couplings

We study a class of generalized inflation models in which the inflaton is coupled to the Ricci scalar by a general $f(\phi, R)$ term. The scalar power spectrum, the spectral index, the running of the spectral index, the tensor mode spectrum and a new consistency relation of the model are calculated. We discuss in detail the issues of how to diagonize the coupled perturbation equations, how to deal with an entropy-like source, and how to determine the initial condition by quantization. By studying some explicit models, we find that rich phenomena such as a blue scalar power spectrum, a large running of the spectral index, and a blue tensor mode spectrum can be obtained.Comment: 26 pages, LaTeX; v2: refs. added; refs. correcte

Well-posedness in critical spaces for the compressible Navier-Stokes equations with density dependent viscosities

In this paper, we prove the local well-posedness in critical Besov spaces for the compressible Navier-Stokes equations with density dependent viscosities under the assumption that the initial density is bounded away from zero.Comment: 27page

Inflation with Holographic Dark Energy

We investigate the corrections of the holographic dark energy to inflation paradigm. We study the evolution of the holographic dark energy in the inflationary universe in detail, and carry out a model-independent analysis on the holographic dark energy correction to the primordial scalar power spectrum. It turns out that the corrections generically make the spectrum redder. To be consistent with the experimental data, there must be a upper bound on the reheating temperature. We also discuss the corrections due to different choices of the infrared cutoff.Comment: 15 pages, 3 figures, v2: references added, a fast-roll discussion added. v3: typos corrected. v4: final version to appear in NP

Universal quantum entanglement between an oscillator and continuous fields

Quantum entanglement has been actively sought in optomechanical and electromechanical systems. The simplest system is a mechanical oscillator interacting with a coherent optical field, while the oscillator also suffers from thermal decoherence. With a rigorous functional analysis, we develop a mathematical framework for treating quantum entanglement that involves infinite degrees of freedom. We show that the quantum entanglement is always present between the oscillator and continuous optical field—even when the environmental temperature is high and the oscillator is highly classical. Such a universal entanglement is also shown to be able to survive more than one mechanical oscillation period if the characteristic frequency of the optomechanical interaction is larger than that of the thermal noise. In addition, we introduce effective optical modes that are ordered by the entanglement strength to better understand the entanglement structure, analogously to the energy spectrum of an atomic system. In particular, we derive the optical mode that is maximally entangled with the mechanical oscillator, which will be useful for future quantum computing and encoding information into mechanical degrees of freedom

Non-adiabatic elimination of auxiliary modes in continuous quantum measurements

When measuring a complex quantum system, we are often interested in only a few degrees of freedom-the plant, while the rest of them are collected as auxiliary modes-the bath. The bath can have finite memory (non-Markovian), and simply ignoring its dynamics, i.e., adiabatically eliminating it, will prevent us from predicting the true quantum behavior of the plant. We generalize the technique introduced by Strunz et. al. [Phys. Rev. Lett 82, 1801 (1999)], and develop a formalism that allows us to eliminate the bath non-adiabatically in continuous quantum measurements, and obtain a non-Markovian stochastic master equation for the plant which we focus on. We apply this formalism to three interesting examples relevant to current experiments.Comment: a revised versio