Inflation in loop quantum cosmology: Dynamics and spectrum of gravitational waves

Abstract

Loop quantum cosmology provides an efficient framework to study the evolution of the Universe beyond the classical Big Bang paradigm. Because of holonomy corrections, the singularity is replaced by a "bounce." The dynamics of the background is investigated into the details, as a function of the parameters of the model. In particular, the conditions required for inflation to occur are carefully considered and are shown to be generically met. The propagation of gravitational waves is then investigated in this framework. By both numerical and analytical approaches, the primordial tensor power spectrum is computed for a wide range of parameters. Several interesting features could be observationally probed.

Note on the super-inflation in loop quantum cosmology

“…In the standard inflation theory, the scale factor a changes rapidly and the Hubble parameter H remains nearly constant. According to the truth that the e-folding number comes from the changing of the scale factor in standard inflation, someone concluded that the e-folding number created during super-inflation in LQC is not sufficient [14], but then it was found that the e-folding number during super-inflation depends on the initial conditions [19] or the parameter of the potential of the scalar field [16]. To show the change of the scale factor a during the super-inflation stage, we will discuss the Universe filled with the interacting field between massless scalar field and radiation at first, and, then give some numerical results in this section.…”

“…can be rewritten as (19) with t c , a c is the bouncing time and scale factor at the bouncing point. According to the above calculation, the same result of [18] could be obtained: when the Universe enters the expanding phase, all the points of the Universe are in causal contact and thus the Universe has had enough time to be homogeneous and isotropic when it bounces.…”

“…Some papers found that the scale factor changes too small to solve the flatness and horizon problem during super-inflation stage [14], whereas the Hubble parameter H is visibly growing during this stage, then some papers argued that the horizon problem can be solved at the super-inflation area [15,18]. Also, the duration of super-inflation, or the change of scale factor depends on the initial value of the scalar field [19], or the parameter of the potential of the scalar field [16]. All those researches discussed the Universe contains a selfinteract or massless scalar field.…”

Nonlinear (loop) quantum cosmology

“…(For details, see [5].) Potentially observable phenomena have been uncovered, showing physical consequences of discrete quantum geometry [4,6,7,8,9,10,11,12,13] and making the theory falsifiable [14,15]. At high density, the implications of quantum space-time can be dramatic: general properties of effective constrained systems show the presence of signature change, turning Lorentzian space-time into a quantum version of 4-dimensional Euclidean space [16,17,18,19].…”

Evidence for Bouncing Evolution Before Inflation After BICEP2

“…This scenario was also realized in the frame of loop quantum cosmology (namely see ref. [13] and references therein).…”