Higher dimensional Loop Quantum Cosmology

Abstract

Loop quantum cosmology(LQC) is the symmetric model of loop quantum gravity. In this paper, we generalize the structure of loop quantum cosmology to the theories with arbitrary spacetime dimensions. The isotropic and homogenous cosmological model in n+1 dimensions is quantized by the loop quantization method. Interestingly, we find that the underlying quantum theories are divided into two qualitatively different sectors according to spacetime dimensions. The effective Hamiltonian and modified dynamical equations of n+1 dimensional LQC are obtained. Moreover, our results indicate that the classical big bang singularity is resolved in arbitrary spacetime dimensions by a quantum bounce. We also briefly discuss the similarities and differences between the n+1 dimensional model and the 3+1 dimensional one. Our model serves as a first example of higher dimensional loop quantum cosmology and offers possibility to investigate quantum gravity effects in higher dimensional cosmology.

14 pages. Minor revision and references added, presentation improved

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Cited by in corpus (13)

• Higher-dimensional quantum Oppenheimer-Snyder model
• Superposition type coherent states in all dimensional loop quantum gravity
• Twisted geometry coherent states in all dimensional loop quantum gravity: I. Construction and Peakedness properties
• The thermodynamics of isolated horizons in loop quantum gravity
• Spin foam amplitude of the black-to-white hole transition
• Twisted geometry coherent states in all dimensional loop quantum gravity: II. Ehrenfest Property
• Energy conditions in new model of loop quantum cosmology
• On the gauge reduction with respect to simplicity constraint in all dimensional loop quantum gravity
• Variety of $(d+1)$ dimensional Cosmological Evolutions with and without bounce in a class of LQC -- inspired Models
• A Class of LQC--inspired Models for Homogeneous, Anisotropic Cosmology in Higher Dimensional Early Universe
• Effective Dynamics of Loop Quantum Kaluza-Klein Cosmology
• Higher-dimensional quantum-corrected Oppenheimer-Snyder model with a cosmological constant
• Non singular M theory Universe in Loop Quantum Cosmology -- inspired Models