High-order quantum back-reaction and quantum cosmology with a positive cosmological constant

Abstract

When quantum back-reaction by fluctuations, correlations and higher moments of a state becomes strong, semiclassical quantum mechanics resembles a dynamical system with a high-dimensional phase space. Here, systematic computational methods to derive the dynamical equations including all quantum corrections to high order in the moments are introduced, together with a (deparameterized) quantum cosmological example to illustrate some implications. The results show, for instance, that the Gaussian form of an initial state is maintained only briefly, but that the evolving state settles down to a new characteristic shape afterwards. Remarkably, even in the regime of large high-order moments, we observe a strong convergence within all considered orders that supports the use of this effective approach.

Nonlinear (loop) quantum cosmology

“…Hamiltonian equations of motion usually couple infinitely many moments to the expectation values, but a semiclassical expansion to some finite order in results in finitely coupled equations which can be solved at least numerically. Computer-algebra codes exist to automate the generation of equations to rather high orders [55] (so far restricted to canonical commutators).…”

Loop Quantum Cosmology, Modified Gravity and Extra Dimensions

“…The effective description of LQC is a delicate and topical issue since it may relate the quantum gravity effects to low-energy physics. The effective equations of LQC are being studied from both the canonical perspective [43][44][45][46] and the path integral perspective [47][48][49][50][51][52][53]. Since the key element in the polymer-like quantization of the previous subsection is to take holonomies rather than connections as basic variables, a heuristic and simple way to get the effective equations is to do the replacementc → sin(μc) µ [30].…”

Loop quantum modified gravity and its cosmological application

“…The effective description of LQC is a delicate and topical issue since it may relate the quantum gravity effects to low-energy physics. The effective equations of LQC are being studied from both canonical perspective [44][45][46][47] and path integral perspective [48][49][50][51][52]. Since the key element in the polymer-like quantization of previous subsection is to take holonomies rather than connections as basic variables, a heuristic and simple way to get the effective equations is to do the replacementc → sin(μc) …”