Detailed investigation of the duration of inflation in loop quantum cosmology for a Bianchi I universe with different inflaton potentials and initial conditions

Martineau, Killian; Barrau, A.; Schander, Susanne

doi:10.1103/physrevd.95.083507

Cited by 44 publications

(48 citation statements)

References 51 publications

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“…For exemple, even within the narrow community of loop quantum cosmology, there is a lively debate on the "most probable" number of inflationary e-folds predicted by the model after the bounce. The approach advocated in [24,25] does not agree at all with the one pushed in [26][27][28][29]. Another known huge discrepancy is between the probability for inflation estimated in [30] and the one calculated in [31].…”

Section: Fine-tuning and Inflation Potentialmentioning

confidence: 80%

A pure general relativistic non-singular bouncing origin for the Universe

Barrau

2020

Eur. Phys. J. C

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In this article, we argue that the past of the Universe, extrapolated from standard physics and measured cosmological parameters, might be a non-singular bounce. We also show that, in this framework, quite stringent constraints can be put on the reheating temperature and number of inflationary e-folds, basically fixing T R H ∼ T GU T and N ∼ 70. We draw some conclusions about the shape of the inflaton potential and raise the "naturalness" issue in this context. Finally, we argue that this could open a very specific window on the "pre big bounce" universe.

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Section: Fine-tuning and Inflation Potentialmentioning

confidence: 80%

A pure general relativistic non-singular bouncing origin for the Universe

Barrau

2020

Eur. Phys. J. C

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“…As we explained in Sec. V, this is a subtle issue during the bouncing phase because in general there is not a preferred initial state for a quantum field in arbitrarily curved spacetime [62,66,67] (see also [68,69] for a recent discussion). The general solution of the Bogoliubov coefficients α k and β k given by Eqs.…”

Section: Discussionmentioning

confidence: 99%

“…In the framework of LQC, various sets of initial conditions have been investigated [38,55,[62][63][64][65][66][67][68][69]. However, this is a subtle issue, because in general there is not a preferred initial state for a quantum field in arbitrarily curved space-times.…”

Section: A Initial Conditions Of Primordial Perturbationsmentioning

confidence: 99%

Pre-inflationary universe in loop quantum cosmology

et al. 2017

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The evolutions of the flat FLRW universe and its linear perturbations are studied systematically in the dressed metric approach of LQC. When it is dominated by the kinetic energy of the inflaton at the quantum bounce, the evolution of the background can be divided into three different phases prior to the preheating, {\em bouncing, transition and slow-roll inflation}. During the bouncing phase, the evolution is independent of not only the initial conditions, but also the inflationary potentials. In particular, the expansion factor can be well described by the same exact solution in all the cases considered. In contrast, in the potential dominated case such a universality is lost. It is because of this universality that the linear perturbations are also independent of the inflationary models and obtained exactly. During the transition phase, the evolutions of the background and its linear perturbations are found explicitly, and then matched to the ones given in the other two phases. Hence, once the initial conditions are imposed, the linear scalar and tensor perturbations will be uniquely determined. Considering two different sets of initial conditions, one imposed during the contracting phase and the other at the bounce, we calculate the Bogoliubov coefficients and find that the two sets yield the same results and all lead to particle creations at the onset of the inflation. Due to the pre-inflationary dynamics, the scalar and tensor power spectra become scale-dependent. Comparing with the Planck 2015 data, we find constraints on the total e-folds that the universe must have expanded since the bounce, in order to be consistent with current observations.Comment: revtex4, 23 figures, and 5 tables. Some typos were corrected. Phys. Rev. D 96, 083520 (2017

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“…Theμ scheme made it possible to perform thermodynamical analyses where the Loopquantized FLRW model is considered a thermodynamical system, and the energy density and pressure are given a precise thermodynamical meaning [97,98]; the computations for the duration of the inflationary de Sitter phase give results consistent with the minimum amount of e-folds necessary to solve the paradoxes (although slightly higher, depending on some parameters, such as the shear at the Bounce in anisotropic models), predict a phase of deflation in the contracting branch and also allow the extension of the standard inflationary paradigm from the Planck scale up to the onset of slow roll inflation, yielding novel effects, such as non-Gaussianities [99][100][101][102][103][104]. Most importantly, the improved scheme allows for a computation of the primordial power spectrum through two main methods: in the first, the implementation of holonomy corrections as a deformed algebra yields a slightly blue-tilted scale invariant spectrum followed by oscillations and an exponential behavior in the ultraviolet [105,106]; in the other, a test field approximation is used such that the evolution of tensor modes on any background quantum geometry is completely equivalent to that of the same modes propagating on a smooth but quantum-corrected metric called "dressed metric", and it is able to recover the red-titled ultraviolet power spectrum of classical cosmology [99,107].…”

Section: Improved Loop Quantum Cosmologymentioning

confidence: 63%

An Overview on the Nature of the Bounce in LQC and PQM

2021

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We present a review on some of the basic aspects concerning quantum cosmology in the presence of cut-off physics as it has emerged in the literature during the last fifteen years. We first analyze how the Wheeler–DeWitt equation describes the quantum Universe dynamics, when a pure metric approach is concerned, showing how, in general, the primordial singularity is not removed by the quantum effects. We then analyze the main implications of applying the loop quantum gravity prescriptions to the minisuperspace model, i.e., we discuss the basic features of the so-called loop quantum cosmology. For the isotropic Universe dynamics, we compare the original approach, dubbed the μ0 scheme, and the most commonly accepted formulation for which the area gap is taken as physically scaled, i.e., the so-called μ¯ scheme. Furthermore, some fundamental results concerning the Bianchi Universes are discussed, especially with respect to the morphology of the Bianchi IX model. Finally, we consider some relevant criticisms developed over the last ten years about the real link existing between the full theory of loop quantum gravity and its minisuperspace implementation, especially with respect to the preservation of the internal SU(2) symmetry. In the second part of the review, we consider the dynamics of the isotropic Universe and of the Bianchi models in the framework of polymer quantum mechanics. Throughout the paper, we focus on the effective semiclassical dynamics and study the full quantum theory only in some cases, such as the FLRW model and the Bianchi I model in the Ashtekar variables. We first address the polymerization in terms of the Ashtekar–Barbero–Immirzi connection and show how the resulting dynamics is isomorphic to the μ0 scheme of loop quantum cosmology with a critical energy density of the Universe that depends on the initial conditions of the dynamics. The following step is to analyze the polymerization of volume-like variables, both for the isotropic and Bianchi I models, and we see that if the Universe volume (the cubed scale factor) is one of the configurational variables, then the resulting dynamics is isomorphic to that one emerging in loop quantum cosmology for the μ¯ scheme, with the critical energy density value being fixed only by fundamental constants and the Immirzi parameter. Finally, we consider the polymer quantum dynamics of the homogeneous and inhomogeneous Mixmaster model by means of a metric approach. In particular, we compare the results obtained by using the volume variable, which leads to the emergence of a singularity- and chaos-free cosmology, to the use of the standard Misner variable. In the latter case, we deal with the surprising result of a cosmology that is still singular, and its chaotic properties depend on the ratio between the lattice steps for the isotropic and anisotropic variables. We conclude the review with some considerations of the problem of changing variables in the polymer representation of the minisuperspace dynamics. In particular, on a semiclassical level, we consider how the dynamics can be properly mapped in two different sets of variables (at the price of having to deal with a coordinate dependent lattice step), and we infer some possible implications on the equivalence of the μ0 and μ¯ scheme of loop quantum cosmology.

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Detailed investigation of the duration of inflation in loop quantum cosmology for a Bianchi I universe with different inflaton potentials and initial conditions

Cited by 44 publications

References 51 publications

A pure general relativistic non-singular bouncing origin for the Universe

A pure general relativistic non-singular bouncing origin for the Universe

Pre-inflationary universe in loop quantum cosmology

An Overview on the Nature of the Bounce in LQC and PQM

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