Loop quantum cosmology with higher order holonomy corrections

Abstract

With a well-motivated extension of higher order holonomy corrections, the quantum theory of loop quantum cosmology (LQC) for the $k=0$ Friedmann-Robertson-Walker model (with a free massless scalar) is rigorously formulated. The analytical investigation reveals that, regardless of the order of holonomy corrections and for any arbitrary states, the matter density remains finite, bounded from above by an upper bound, which equals the critical density obtained at the level of heuristic effective dynamics. Particularly, with all orders of corrections included, the dynamical evolution is shown to follow the bouncing scenario in which two Wheeler-DeWitt (WDW) solutions (expanding and contracting) are bridged together through the quantum bounce. These observations provide further evidence that the quantum bounce is essentially a consequence of the intrinsic discreteness of LQC and LQC is fundamentally different from the WDW theory. Meanwhile, the possibility is also explored that the higher order holonomy corrections can be interpreted as a result of admitting generic SU(2) representations for the Hamiltonian constraint operators.

32 pages, 2 figures; typos corrected; version to appear in PRD

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• Loop Quantum Gravity
• Protected $SL(2,\mathbb{R})$ Symmetry in Quantum Cosmology
• New Hamiltonians for loop quantum cosmology with arbitrary spin representations
• Numerical Techniques in Loop Quantum Cosmology
• On the UV dimensions of Loop Quantum Gravity
• Unimodular Loop Quantum Cosmology
• Constraining the loop quantum gravity parameter space from phenomenology
• Loop quantization of spherically symmetric midisuperspaces and loop quantum geometry of the maximally extended Schwarzschild spacetime
• Non-Gaussian features from the inverse volume corrections in loop quantum cosmology
• Cosmological implications of generalized holonomy corrections
• Cosmological inflation driven by holonomy corrections of loop quantum cosmology
• New Approach to Evolving Gravitational Waves in Loop Quantum Cosmology
• Time Asymmetry of Cosmic Background Evolution in Loop Quantum Cosmology
• Loop Quantum Cosmology of Bianchi I Model in $\bar{\mu }$ and ${\bar{\mu }}^{\prime }$ Schemes with Higher Order Holonomy Corrections