The volume operator in loop quantum cosmology

Abstract

We show that for basically all states, the evolution of the expectation value of the volume operator in Wheeler-DeWitt and various homogenous isotropic loop quantum comology (LQC) models (k = 0, coupled to massless scalar field and without cosmological constant) is ill-defined. The expectation value of the volume operator become instantonously infinite during the evolution. The effect is produced by a very long tail in the volume spectrum, that is however semiclassically small and beyond reach of numerical simulations (that is why it went unnoticed so far). This is not necessarily problem of theory but rather it suggests that one should be extremely careful with unbounded observables.

Dressed metric predictions revisited

“…It would be of interest to check previous numerical calculations for signs of breaking from semiclassical regime, even so we expect smooth cutoff to be better. So far, in numerical studies no divergences were detected which suggests that they are extremely small in agreement with analytical predictions [1]. It is possible that just discovered infinities become visible way beyond first quantum corrections and thus one could still try to probe them.…”

“…The recent result [1] that motivated the current letter is that for the main LQC models, for every generic state of the quantum cosmological spacetime, that is a state Ψ such that Ĥo Ψ = 0 (4) the expectation value of the scale operator â(T ) suffers pathological property, namely…”

“…It was recently shown [1] that neither the scale factor operator's â nor its positive powers âǫ domains are preserved under the time evolution in the most important models of loop quantum cosmology (LQC) including the Ashtekar-Singh-Pawłowski (ASP) model, as well as the solvable LQC (sLQC). As a consequence, the expectation values like â(T ) are ill-defined for a generic semiclassical state at a generic instant of time.…”

Cosmic tango between the very small and the very large: Addressing CMB anomalies through Loop Quantum Cosmology

“…Initially, analysis of [69] suggested that the propagation of Q on the quantum geometry Ψ(a, φ) would be exactly the same as that on the corresponding dressed metric 3.1 and potential (3.3) for any Ψ(a, φ). However, Kaminski later found [70] that there is a subtle infrared problem (that can be missed in numerical simulations since they have to use an infrared cutoff). Kaminski, Kolanowski and Lewandowski [71] then showed that, as a result, the implications of [69] are not as general; the result would not hold without restrictions on the background quantum geometry Ψ(a, φ).…”

Challenges in recovering a consistent cosmology from the effective dynamics of loop quantum gravity

“…For certain models admitting massless scalar field (including the flat FLRW universe with non-negative cosmological constant or negative curvature), the semiclassicality property defined above may not be preserved by the dynamics (see for example [38,39], also the discussion in [29,40]). In these cases the Dirac observables corresponding to p(t) may be ill defined on the physical Hilbert space, thus alternative observables encoding the same information need to be used [29,40].…”