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Open AccessArticle

The Effect of a Positive Cosmological Constant on the Bounce of Loop Quantum Cosmology

Departamento de Física Teórica and IPARCOS, Universidad Complutense de Madrid, Parque de Ciencias 1, 28040 Madrid, Spain
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Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2020, 8(2), 186; https://doi.org/10.3390/math8020186
Received: 29 December 2019 / Revised: 20 January 2020 / Accepted: 29 January 2020 / Published: 4 February 2020
(This article belongs to the Special Issue Mathematical and Computational Cosmology)
We provide an analytical solution to the quantum dynamics of a flat Friedmann-Lemaître- Robertson-Walker model with a massless scalar field in the presence of a small and positive cosmological constant, in the context of Loop Quantum Cosmology. We use a perturbative treatment with respect to the model without a cosmological constant, which is exactly solvable. Our solution is approximate, but it is precisely valid at the high curvature regime where quantum gravity corrections are important. We compute explicitly the evolution of the expectation value of the volume. For semiclassical states characterized by a Gaussian spectral profile, the introduction of a positive cosmological constant displaces the bounce of the solvable model to lower volumes and to higher values of the scalar field. These displacements are state dependent, and in particular, they depend on the peak of the Gaussian profile, which measures the momentum of the scalar field. Moreover, for those semiclassical states, the bounce remains symmetric, as in the vanishing cosmological constant case. However, we show that the behavior of the volume is more intricate for generic states, leading in general to a non-symmetric bounce.
Keywords: loop quantum cosmology, quantum bounce, cosmological constant, early Universe physics loop quantum cosmology, quantum bounce, cosmological constant, early Universe physics
MDPI and ACS Style

Martín-Benito, M.; Neves, R.B. The Effect of a Positive Cosmological Constant on the Bounce of Loop Quantum Cosmology. Mathematics 2020, 8, 186.

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