Preinflationary dynamics of an α− attractor in loop quantum cosmology

Abstract

We systematically study the preinflationary dynamics of the spatially flat Friedmann-Lemaitre-Robertson-Walker universe filled with a single scalar field that has the generalized α−attractor potentials, in the framework of loop quantum cosmology, in which the big bang singularity is replaced generically by a non-singular quantum bounce due to purely quantum geometric effects. The evolution can be divided into two different classes, one is dominated initially (at the quantum bounce) by the kinetic energy of the scalar field, and one is not. In both cases, we identify numerically the physically viable initial conditions that lead to not only a slow-roll inflationary phase, but also enough e-folds to be consistent with observations, and find that the output of such a viable slow-roll inflationary phase is generic. In addition, we also show that in the case when the evolution of the universe is dominated initially by the kinetic energy of the scalar field (except for a very small set in the phase space), the evolution before reheating is aways divided into three different phases: bouncing, transition and slow-roll inflation. This universal feature does not depend on the initial conditions of the system nor on the specific potentials of the scalar field, as long as it is dominated initially by the kinetic energy of the scalar field at the bounce. Moreover, we carry out phase space analyses for the models under consideration and compare our results with the power-law and Starobinsky potentials.

Preinflationary Dynamics of Power-Law Potential in Loop Quantum Cosmology †

“…The potential under consideration generates the desired slow-roll inflation in the case of both KED and PED initial conditions, and produces enough e-folds that are compatible with observations, whereas Starobinsky and α−attractor (dependence on the range of α) models provide the slow-roll inflation only for KED initial conditions and not for PED ones [24][25][26]28].…”

“…The background evolution with the bouncing regime has been studied extensively. One of the main results is that beginning from the bounce, a desired slow-roll inflation is achieved [7,22,23,[25][26][27][28]. Keeping this in mind, we shall discuss "bounce and the slow-roll inflation" with the following potential:…”

“…In Reference [13], the post-bounce regime of the slow-roll inflation for the primordial power spectrum of tensor and scalar perturbations are discussed, whereas the effective equations of evolution for the scalar and tensor perturbations are distinct as the discrepancy seems to be in the mass term, which arises due to the different quantization procedures [19]. It is fascinating to see that the Universe which starts at the quantum bounce generically enters the slow-roll inflation [20][21][22][23][24][25][26][27][28]. In this article, I am mainly concerned with the background evolution of the Universe in LQC.…”

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

“…Finally, when the magnitude of the driving force becomes almost equal to that of the conservative force (−m 2 φ), the acceleration of the inflaton becomes negligible as compared to its velocity, and, hence the slow-roll inflation takes place. In addition to the initial conditions shown in Tables I and II, we have also studied various other initial conditions, and found that, for KE well-dominated cases at the bounce, the evolution of mLQC-I/II universe before reheating can be generically divided into three distinctive phases, bouncing, transition, slow-roll inflation, similar to that in the LQC case [28][29][30][31][32][33]35], although some differences may appear when considering them in details.…”

“…Our goal in this manuscript is to answer this question by investigating these two issues: genericness of the preinflationary dynamics and the probability of the desired slow-roll inflation in above two modified cosmological models. In LQC, the former was studied in [28][29][30][31][32][33][34][35][36], while the latter in [37][38][39][40][41][42][43][44]. For mLQC-I and mLQC-II, some aspects of pre-inflationary dynamics were noted by authors in [21] and [22].…”