Collective excitations analogous to phonons are derived in quantum gravity condensates within a group field theory model, yielding leading beyond-mean-field corrections to emergent Friedmann dynamics.
Robustness of key features of loop quantum cosmology
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abstract
Loop quantum cosmology of the k=0 FRW model (with a massless scalar field) is shown to be exactly soluble if the scalar field is used as the internal time already in the classical Hamiltonian theory. Analytical methods are then used i) to show that the quantum bounce is generic; ii) to establish that the matter density has an absolute upper bound which, furthermore, equals the critical density that first emerged in numerical simulations and effective equations; iii) to bring out the precise sense in which the Wheeler DeWitt theory approximates loop quantum cosmology and the sense in which this approximation fails; and iv) to show that discreteness underlying LQC is fundamental. Finally, the model is compared to analogous discussions in the literature and it is pointed out that some of their expectations do not survive a more careful examination. An effort has been made to make the underlying structure transparent also to those who are not familiar with details of loop quantum gravity.
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Polymer quantization on compact spaces yields finite graph Hilbert spaces whose exact ring and box spectra recover Schrödinger QM as lattice spacing vanishes.
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Collective excitations in quantum gravity condensates
Collective excitations analogous to phonons are derived in quantum gravity condensates within a group field theory model, yielding leading beyond-mean-field corrections to emergent Friedmann dynamics.
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Polymer quantum mechanics on compact configuration spaces
Polymer quantization on compact spaces yields finite graph Hilbert spaces whose exact ring and box spectra recover Schrödinger QM as lattice spacing vanishes.