Higher curvature counter terms cause the bounce in loop cosmology

Abstract

In the loop approach to the quantisation of gravity, one uses a Hilbert space which is too singular for some operators to be realised as derivatives. This is usually addressed by instead using finite difference operators at the Planck scale, a process known as ``polymerisation''. In the symmetry reduced example of loop cosmology, we study an ambiguity in the regularisation which we relate to the ambiguity of fixing the coefficients of infinitely many higher curvature counter terms augmenting the Einstein-Hilbert action. Thus the situation is comparable to he one in a naive perturbative treatment of quantum gravity with a cut-off where the necessary presence of infinitely many higher derivative terms compromises predictability. As a by-product, we demonstrate in an appendix that it is possible to have higher curvature actions for gravity which still lead to first order equations of motion like in the Friedmann case.

Added references

References in corpus (13)

• Quantum Nature of the Big Bang: Improved dynamics
• Quantum Nature of the Big Bang
• Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
• Loop quantum cosmology of k=1 FRW models
• Loop quantum gravity corrections to gravitational wave dispersion
• Quantum Gravity and Higher Curvature Actions
• Turning Big Bang into Big Bounce: I. Classical Dynamics
• Effective equations for isotropic quantum cosmology including matter
• Polymer quantization, singularity resolution and the 1/r^2 potential
• Covariant Effective Action for Loop Quantum Cosmology from Order Reduction
• String quantization: Fock vs. LQG Representations
• Foamy structure of spacetime
• Lessons from the LQG String

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• On the canonical structure of general relativity with a limiting curvature and its relation to loop quantum gravity
• Bouncing cosmologies via modified gravity in the ADM formalism: Application to Loop Quantum Cosmology
• Factor ordering and large-volume dynamics in quantum cosmology
• Variety of $(d+1)$ dimensional Cosmological Evolutions with and without bounce in a class of LQC -- inspired Models
• Quantum gravity effects on space-time