arXiv subjects

Bao-Fei Li

Publications and source records attributed to Bao-Fei Li.

33 records · Page 2Linked to original sources

arXiv2020

Towards a reduced phase space quantization in loop quantum cosmology with an inflationary potential

We explore a reduced phase space quantization of loop quantum cosmology (LQC) for a spatially flat FLRW universe filled with reference fields and an inflaton field in a Starobinsky inflationary potential. We consider three separate cases in which the reference fields are taken to be the Gaussian dust, the Brown-Kuchař dust, and massless Klein-Gordon scalar reference fields respectively. This is a "two-fluid" model in which reference fields act as global clocks providing a physical time in an inflationary spacetime, and allow bypassing various technical hurdles in conventional quantum cosmological models. The reduced phase space is obtained in terms of the Dirac observables of the gravitational as well as the inflaton degrees of freedom. The physical Hamiltonians of the two dust models take the same form but turn out to be quite different from that of the Klein-Gordon reference field which reflects an aspect of the multiple choice problem of time. Loop quantization is implemented using the so-called $\bar μ$ scheme and the Schrödinger equations involving the physical Hamiltonian operators generating the evolution in the physical time in the dust and massless Klein-Gordon models are obtained. These turn out to be quantum difference equations with same non-singular structure as for other models in LQC. We study some phenomenological implications of the quantization using the effective dynamics resulting from the reduced phase space quantization including the resolution of the big bang singularity via a quantum bounce, and effects of the different reference fields on e-foldings in both the pre-inflationary and the slow-roll inflationary phases. We find that different clocks, even when starting with a small but same energy density, can leave tiny but different imprints on the inflationary dynamics. (abridged)

gr-qc↗

arXiv2020

Quantum gravitational onset of Starobinsky inflation in a closed universe

Recent cosmic microwave background observations favor low energy scale inflationary models in a closed universe. However, onset of inflation in such models for a closed universe is known to be severely problematic. In particular, such a universe recollapses within a few Planck seconds and encounters a big crunch singularity when initial conditions are given in the Planck regime. We show that this problem of onset of inflation in low energy scale inflationary models can be successfully overcome in a quantum gravitational framework where the big bang/big crunch singularities are resolved and a non-singular cyclic evolution exists prior to inflation. As an example we consider a model in loop quantum cosmology and demonstrate that the successful onset of low energy scale inflation in a closed universe is possible for the Starobinsky inflationary model starting from a variety of initial conditions where it is impossible in the classical theory. For comparison we also investigate the onset of inflation in the $ϕ^2$ inflationary model under similar unfavorable conditions. The pre-inflationary phase with quantum gravity effects is shown to be composed of non-identical cycles of bounces and recollapses resulting in a hysteresis-like phenomenon, which plays an important role in creating suitable conditions for inflation to occur after some number of non-singular cycles. Our analysis shows that the tension in the classical theory amounting to the unsuitability of closed FLRW universes with respect to the onset of low energy scale inflation can be successfully resolved in loop quantum cosmology.

gr-qc↗

arXiv2020

Mukhanov-Sasaki equation in manifestly gauge-invariant linearized cosmological perturbation theory with dust reference fields

The aim of this article is to understand the role of dust reference fields, often also called clocks, on cosmological perturbations around a flat FLRW universe. We derive the Mukhanov-Sasaki (MS) equation for the Brown-Kuchar (BK) and Gaussian dust models, which both consider four dust fields as reference fields. The reduced phase space of Dirac observables, that is the gauge-invariant part of the theory, is constructed by means of an observable map applied to all elementary phase space variables of the coupled system, consisting of gravity, a massive scalar field and the dust degrees of freedom. The evolution of these observables is governed by a so called physical Hamiltonian which can be derived once the set of reference fields are chosen and differs for each model. First, the reduced phase space as well as the corresponding equations of motion are derived for full general relativity. Then from this, the gauge-invariant version of the equations of motion for the background are derived which contain a fingerprint of the dust reference fields. Afterwards we study linear cosmological perturbations around a FLRW metric using the scalar-vector-tensor decomposition and derive the equation of motion for the MS variable in this formalism for a chosen set of variables on the reduced phase space and expressed in terms of Dirac observables. The MS equation involves additional contributions that can be understood as back reactions from the dust reference fields. These additional dust contributions to the MS equation were absent if the dust energy and momentum density as well as their perturbations are vanishing. The nature of the correction terms suggest that BK and Gaussian dust reference fields contribute differently. Using numerical simulations we study the behavior of the dust contributions to the MS equation during inflation.

gr-qc↗

arXiv2020

Langer Modification, Quantization condition and Barrier Penetration in Quantum Mechanics

The WKB approximation plays an essential role in the development of quantum mechanics and various important results have been obtained from it. In this paper, we introduce another method, {\it the so-called uniform asymptotic approximations}, which is an analytical approximation method to calculate the wave functions of the Schrödinger-like equations, and is applicable to various problems, including cases with poles (singularities) and multiple turning points. An distinguished feature of the method is that in each order of the approximations the upper bounds of the errors are given explicitly. By properly choosing the freedom introduced in the method, the errors can be minimized, which significantly improves the accuracy of the calculations. A byproduct of the method is to provide a very clear explanation of the Langer modification encountered in the studies of the hydrogen atom and harmonic oscillator. To further test our method, we calculate (analytically) the wave functions for several exactly solvable potentials of the Schrödinger equation, and then obtain the transmission coefficients of particles over potential barriers, as well as the quantization conditions for bound states. We find that such obtained results agree with the exact ones extremely well. Possible applications of the method to other fields are also discussed.

quant-ph↗

arXiv2020

Primordial power spectrum from the dressed metric approach in loop cosmologies

We investigate the consequences of different regularizations and ambiguities in loop cosmological models on the predictions in the scalar and tensor primordial spectrum of the cosmic microwave background using the dressed metric approach. Three models, standard loop quantum cosmology (LQC), and two modified loop quantum cosmologies (mLQC-I and mLQC-II) arising from different regularizations of the Lorentzian term in the classical Hamiltonian constraint are explored for chaotic inflation in spatially-flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe. In each model, two different treatments of the conjugate momentum of the scale factor are considered. The first one corresponds to the conventional treatment in dressed metric approach, and the second one is inspired from the hybrid approach which uses the effective Hamiltonian constraint. For these two choices, we find the power spectrum to be scale-invariant in the ultra-violet regime for all three models, but there is at least a $10\%$ relative difference in amplitude in the infra-red and intermediate regimes. All three models result in significant differences in the latter regimes. In mLQC-I, the magnitude of the power spectrum in the infra-red regime is of the order of Planck scale irrespective of the ambiguity in conjugate momentum of the scale factor. The relative difference in the amplitude of the power spectrum between LQC and mLQC-II can be as large as $50\%$ throughout the infra-red and intermediate regimes. Differences in amplitude due to regularizations and ambiguities turn out to be small in the ultra-violet regime.

gr-qc↗

arXiv2019

Genericness of pre-inflationary dynamics and probability of the desired slow-roll inflation in modified loop quantum cosmologies

We study the evolution of spatially flat Friedmann-Lemaître-Robertson-Walker universe for chaotic and Starobinsky potentials in the framework of modified loop quantum cosmologies. These models result in a non-singular bounce as in loop quantum cosmology, but with far more complex modified Friedmann dynamics with higher order than quadratic terms in energy density. For the kinetic energy dominated bounce, we obtain analytical solutions using different approximations and compare with numerical evolution for various physical variables. The relative error turns out to be less than $0.3\%$ in the bounce regime for both of the potentials. Generic features of dynamics, shared with loop quantum cosmology, are established using analytical and numerical solutions. Detailed properties of three distinct phases in dynamics separating bounce regime, transition stage and inflationary phase are studied. For the potential energy dominated bounce, we qualitatively describe its generic features and confirm by simulations that they all lead to the desired slow-roll phase in the chaotic inflation. However, in the Starobinsky potential, the potential energy dominated bounce cannot give rise to any inflationary phase. Finally, we compute the probability for the desired slow-roll inflation to occur in the chaotic inflation and as in loop quantum cosmology, find a very large probability for the universe to undergo inflation.

gr-qc↗

arXiv2019

Preinflationary perturbations from the closed algebra approach in loop quantum cosmology

In this paper, the scalar and tensor perturbations in the closed algebra approach of loop quantum cosmology are studied. Instead of the distant past in the contracting phase, we choose the moment at which the initial conditions are imposed to be the silent point, which circumvents the problem due to the signature change in the super-inflationary phase and results in a well-defined Cauchy problem. For the ultraviolet and infrared modes, different approaches are applied in order to obtain analytical solutions with high accuracy. While previous numerical simulations reveal an exponentially divergent power spectrum in the ultraviolet regime, when the initial conditions are imposed in the remote contracting phase, we find a special set of initial conditions at the silent point, which can reproduce results that are consistent with current observations.

gr-qc↗

arXiv2018

Qualitative dynamics and inflationary attractors in loop cosmology

Qualitative dynamics of three different loop quantizations of spatially flat isotropic and homogeneous models is studied using effective spacetime description of the underlying quantum geometry. These include the standard loop quantum cosmology (LQC), its recently revived modification (referred to as mLQC-I), and another related modification of LQC (mLQC-II) whose dynamics is studied in detail for the first time. Various features of LQC, including quantum bounce and pre-inflationary dynamics, are found to be shared with the mLQC-I and mLQC-II models. We study universal properties of dynamics for chaotic inflation, fractional monodromy inflation, Starobinsky potential, non-minimal Higgs inflation, and an exponential potential. We find various critical points and study their stability, which reveal various qualitative similarities in the post-bounce phase for all these models. The pre-bounce qualitative dynamics of LQC and mLQC-II turns out to be very similar, but is strikingly different from that of mLQC-I. In the dynamical analysis, some of the fixed points turn out to be degenerate for which center manifold theory is used. For all these potentials, non-perturbative quantum gravitational effects always result in a non-singular inflationary scenario with a phase of super-inflation succeeded by the conventional inflation. We show the existence of inflationary attractors, and obtain scaling solutions in the case of the exponential potential. Since all of the models agree with general relativity at late times, our results are also of use in classical theory where qualitative dynamics of some of the potentials has not been studied earlier.

gr-qc↗

arXiv2018

Towards Cosmological Dynamics from Loop Quantum Gravity

We present a systematic study of the cosmological dynamics resulting from an effective Hamiltonian, recently derived in loop quantum gravity using Thiemann's regularization and earlier obtained in loop quantum cosmology (LQC) by keeping the Lorentzian term explicit in the Hamiltonian constraint. We show that quantum geometric effects result in higher than quadratic corrections in energy density in comparison to LQC causing a non-singular bounce. Dynamics can be described by the Hamilton's or the Friedmann-Raychaudhuri equations, but the map between the two descriptions is not one-to-one. A careful analysis resolves the tension on symmetric versus asymmetric bounce in this model, showing that the bounce must be asymmetric and symmetric bounce is physically inconsistent, in contrast to the standard LQC. In addition, the current observations only allow a scenario where the pre-bounce branch is asymptotically de Sitter, similar to a quantization of the Schwarzschild interior in LQC, and the post-bounce branch yields the classical general relativity. For a quadratic potential, we find that a slow-roll inflation generically happens after the bounce, which is quite similar to what happens in LQC.

gr-qc↗

arXiv2018

Schwinger Pair Production by Electric Field Coupled to Inflaton

We analytically investigate the Schwinger pair production in the de Sitter background by using {\em the uniform asymptotic approximation method}, and show that the equation of motion in general has two turning points, and the nature of these points could be single, double, real or complex, depending on the choice of the free parameters involved in the theory. Different natures of these points lead to different electric currents. In particular, when $β\equiv m^2/H^2-9/4$ is positive, both turning points are complex, and the electric current due to the Schwinger process is highly suppressed, where $m$ and $H$ denote, respectively, the mass of the particle and the Hubble parameter. For the turning points to be real, it is necessary to have $β< 0$, and the more negative of $β$, the easier to produce particles. In addition, when $β< 0$, we also study the particle production when the electric field $E$ is very weak. We find that the electric current in this case is proportional to $E^{1/2 - \sqrt{|β|}}$, which is strongly enhanced in the weak electric field limit when $m < \sqrt{2} H$.

gr-qc↗

arXiv2017

Universal horizons and Hawking radiation in nonprojectable 2d Hořava gravity coupled with a non-relativistic scalar field

In this paper, we study the non-projectable 2d Hořava gravity coupled with a non-relativistic scalar field, where the coupling is in general non-minimal and of the form $f(ϕ)R$, where $f(ϕ)$ is an arbitrary function of the scalar field $ϕ$, and $R$ denotes the 2d Ricci scalar. In particular, we first investigate the Hamiltonian structure, and show that there are two-first and two-second class constraints, similar to the pure gravity case, but now the local degree of freedom is one, due to the presence of the scalar field. Then, we present various exact stationary solutions of this coupled system, and find that some of them represent black holes but now with universal horizons as their boundaries. At these horizons, the Hawking radiations are thermal with temperatures proportional to their surface gravities, which normally depend on the non-linear dispersion relations of the particles radiated, similar to the (3+1)-dimensional case.

gr-qc↗

arXiv2016

Quantization of 2D Hořava gravity: non-projectable case

The quantization of two-dimensional Hořava theory of gravity without the projectability condition is considered. Our study of the Hamiltonian structure of the theory shows that there are two first-class and two second-class constraints. Then, following Dirac we quantize the theory by first requiring that the two second-class constraints be strongly equal to zero. This is carried out by replacing the Poisson bracket by the Dirac bracket. The two first-class constraints give rise to the Wheeler-DeWitt equations, which yield uniquely a plane-wave solution for the wavefunction. We also study the classical solutions of the theory and find that the characteristics of classical spacetimes are encoded solely in the phase of the plane-wave solution in terms of the extrinsic curvature of the foliations $t =$Constant, where $t$ denotes the globally-defined time of the theory.

gr-qc↗

arXiv2014

Quantization of (1+1)-dimensional Hořava-Lifshitz theory of gravity

In this paper, we study the quantization of the (1+1)-dimensional projectable Hořava-Lifshitz (HL) gravity, and find that, when only gravity is present, the system can be quantized by following the canonical Dirac quantization, and the corresponding wavefunction is normalizable for some orderings of the operators. The corresponding Hamilton can also be written in terms of a simple harmonic oscillator, whereby the quantization can be carried out quantum mechanically in the standard way. When the HL gravity minimally couples to a scalar field, the momentum constraint is solved explicitly in the case where the fundamental variables are functions of time only. In this case, the coupled system can also be quantized by following the Dirac process, and the corresponding wavefunction is also normalizable for some particular orderings of the operators. The Hamilton can be also written in terms of two interacting harmonic oscillators. But, when the interaction is turned off, one of the harmonic oscillators has positive energy, while the other has negative energy. A remarkable feature is that orderings of the operators from a classical Hamilton to a quantum mechanical one play a fundamental role in order for the Wheeler-DeWitt equation to have nontrivial solutions. In addition, the space-time is well quantized, even when it is classically singular.

hep-th↗

arXiv2011

Study on the mechanism of open-flavor strong decays

The open-flavor strong decays are studied based on the interaction of potential quark model. The decay process is related to the s-channel contribution of the same scalar confinment and one-gluon-exchange(OGE) interaction in the quark model. After we adopt the prescription of massive gluons in time-like region from the lattice calculation, the approximation of four-fermion interaction is applied. The numerical calculation is performed to the meson decays in $u$, $d$, $s$ light flavor sector. The analysis of the $D/S$ ratios of $b_1\rightarrow ωπ$ and $a_1\rightarrow ρπ$ show that the scalar interaction should be dominant in the open-flavor decays.

hep-ph↗

arXiv2010

Fine Splitting in Charmonium Spectrum with Channel Coupling Effect

We study the fine splitting in charmonium spectrum in quark model with the channel coupling effect, including $DD$, $DD^*$, $D^*D^*$ and $D_sD_s$, $D_sD_s^*$, $D_s^*D_s^*$ channels. The interaction for channel coupling is constructed from the current-current Lagrangian related to the color confinement and the one-gluon exchange potentials. By adopting the massive gluon propagator from the lattice calculation in the nonperturbative region, the coupling interaction is further simplified to the four-fermion interaction. The numerical calculation still prefers the assignment $1^{++}$ of X(3872).

hep-ph↗