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**Pre-inflationary universe in loop quantum cosmology**

Tao Zhu, Anzhong Wang, Gerald Cleaver, Klaus Kirsten, Qin Sheng

(Submitted on 22 May 2017 (v1), last revised 4 Jun 2017 (this version, v2))

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 evolution of the background is studied and matched to that given in other two phases, whereby the e-folds of the expansion in each of these three phases are obtained. In this phase the perturbation modes are all oscillating and can be easily matched to the ones given in other phases. Then, 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.

Comments: revtex4, 24 figures, and 5 tables. Some typos were corrected

Subjects: General Relativity and Quantum Cosmology (gr-qc); Cosmology and Nongalactic Astrophysics (astro-ph.CO); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th)

Cite as: arXiv:1705.07544 [gr-qc]

and

**Measuring the effects of Loop Quantum Cosmology in the CMB data**

Spyros Basilakos, Vahid Kamali, Ahmad Mehrabi

(Submitted on 16 May 2017)

In this Essay we investigate the observational signatures of Loop Quantum Cosmology (LQC) in the CMB data. First, we concentrate on the dynamics of LQC and we provide the basic cosmological functions. We then obtain the power spectrum of scalar and tensor perturbations in order to study the performance of LQC against the latest CMB data. We find that LQC provides a robust prediction for the main slow-roll parameters, like the scalar spectral index and the tensor-to-scalar fluctuation ratio, which are in excellent agreement within 1σ with the values recently measured by the Planck collaboration. This result indicates that LQC can be seen as an alternative scenario with respect to that of standard inflation.

Comments: 7 pages, 1 figure. To appear in IJMPD. This essay received an honorable mention in the 2017 Essay Competition of the Gravity Research Foundation. For a comprehensive presentation of these results, see arXiv:1703.01409

Subjects: General Relativity and Quantum Cosmology (gr-qc); Cosmology and Nongalactic Astrophysics (astro-ph.CO); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th)

Cite as: arXiv:1705.05585 [gr-qc]

(or arXiv:1705.05585v1 [gr-qc] for this version)

and

**Hybrid loop quantum cosmology and predictions for the cosmic microwave background**

Laura Castelló Gomar, Daniel Martín de Blas, Guillermo A. Mena Marugán, Javier Olmedo

(Submitted on 20 Feb 2017 (v1), last revised 30 May 2017 (this version, v2))

We investigate the consequences of the hybrid quantization approach for primordial perturbations in loop quantum cosmology, obtaining predictions for the cosmic microwave background and comparing them with data collected by the Planck mission. In this work, we complete previous studies about the scalar perturbations and incorporate tensor modes. We compute their power spectrum for a variety of vacuum states. We then analyze the tensor-to-scalar ratio and the consistency relation between this quantity and the spectral index of the tensor power spectrum. We also compute the temperature-temperature, electric-electric, temperature-electric, and magnetic-magnetic correlation functions. Finally, we discuss the effects of the quantum geometry in these correlation functions and confront them with observations.

Comments: 34 pages, 23 figures, 1 table; v2: revised and minor improvements included

Subjects: General Relativity and Quantum Cosmology (gr-qc)

Report number: IGC-17|2-1

Cite as: arXiv:1702.06036 [gr-qc]

(or arXiv:1702.06036v2 [gr-qc] for this version)

**Some Clarifications on the Duration of Inflation in Loop Quantum Cosmology**

Boris Bolliet, Aurélien Barrau, Killian Martineau, Flora Moulin

(Submitted on 9 Jan 2017)

The prediction of a phase of inflation whose number of e-folds is constrained is an important feature of loop quantum cosmology. This work aims at giving some elementary clarifications on the role of the different hypotheses leading to this conclusion. We show that the duration of inflation does not depend significantly on the modified background dynamics in the quantum regime.

Subjects: General Relativity and Quantum Cosmology (gr-qc); Cosmology and Nongalactic Astrophysics (astro-ph.CO); High Energy Physics - Phenomenology (hep-ph)

DOI: 10.1088/1361-6382/aa7779

Cite as: arXiv:1701.02282 [gr-qc]

these predictions were

1- validated by observation and experiment, survives peer review, and nobel prizes are awarded and these results become standard textbooks in the field and

2- only loop quantum cosmology makes these predictions, other frameworks, such as string theory are unable to reproduce these unique predictions from loop quantum cosmology - no other candidate theory of QG such as string theory can make the same predictions as LQC which are then validated by observation to 5-sigma levels significance.

what would be the implications to fundamental physics, quantum gravity, string theory, and cosmology if loop quantum cosmology predictions provided in the above papers and in other similar papers are validated by experiment and observation.