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In this paper, we systematically study the evolution of the Universe within the framework of a modified loop quantum cosmological model (mLQC-I) using various inflationary potentials, including chaotic, Starobinsky, generalized Starobinsky, polynomials of the first and second kinds, generalized T-models and natural inflation. In all these models, the big bang singularity is replaced by a quantum bounce, and the evolution of the Universe, both before and after the bounce, is universal and weakly dependent on the inflationary potentials, as long as the evolution is dominated by the kinetic energy of the inflaton at the bounce. In particular, the pre-bounce evolution can be universally divided into three different phases: pre-bouncing, pre-transition, and pre-de Sitter. The pre-bouncing phase occurs immediately before the quantum bounce, during which the evolution of the Universe is dominated by the kinetic energy of the inflaton. Thus, the equation of state of the inflaton is about one, w(ϕ)≃1. Soon, the inflation potential takes over, so w(ϕ) rapidly falls from one to negative one. This pre-transition phase is very short and quickly turns into the pre-de Sitter phase, whereby the effective cosmological constant of Planck size takes over and dominates the rest of the contracting phase. Throughout the entire pre-bounce regime, the evolution of both the expansion factor and the inflaton can be approximated by universal analytical solutions, independent of the specific inflation potentials.
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Recalculating Total Number of e-folds in Loop Quantum Cosmology in View of Generalized Reheating
In loop quantum cosmology, the slow-roll inflation is generic, and when the kinetic energy of the scalar field dominates at the bounce, the evolution of the Friedmann-Lemaître-Robertson-Walker universe will go through three distinguishable epochs, bouncing, transition, and finally slow-roll inflation, before the reheating commences. The bouncing dynamics are insensitive of the potential and initial conditions, so that the expansion factor and the scalar field can be described uniquely by a universal solution during this epoch. After about 105 Planck time, the epoch of transition starts and the universe rapidly turns over from the kinetic energy dominated state to the potential energy dominated one, whereby the slow-roll inflationary phase begins. In this paper, we consider the power law plateau potential and study the pre-inflationary cosmology for different sets of initial conditions, so that during the slow-roll inflation epoch enough e-folds will be produced. Considering the generalized reheating and comparing with the recent Planck 2018 data, we are able to constrain the total number of e-folds (NT) from the bounce till today to be consistent with the current observable universe. Depending on the matter driving the reheating (subject to the different dominant equations of states), we report the observationally allowed NT and reheating temperature and find in particular NT≃127, which is significantly different from the one NT≳141 obtained previously without considering the reheating phase.
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- Award ID(s):
- 2308845
- PAR ID:
- 10569136
- Publisher / Repository:
- Cornell University
- Date Published:
- Journal Name:
- arXivorg
- ISSN:
- 2331-8422
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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