Calogero-Vasiliev Oscillator in Dynamically Evolving Curved Spacetime

Abstract

In a recent work, the consequences of quantizing a real scalar field $Φ$ according to generalized ``quon'' statistics in a dynamically evolving curved spacetime (~which, prior to some initial time and subsequent to some later time, is flat~) were considered. Here a similar calculation is performed; this time we quantize $Φ$ via the Calogero-Vasiliev oscillator algebra, described by a real parameter $ν> -1/2$. It is found that both conservation ( $ν\rightarrow ν$ ) and anticonservation ( $ν\rightarrow - ν$ ) of statistics is allowed. We find that for mathematical consistency the Bogoliubov coefficients associated with the $i$'th field mode must satisfy $|α_i |^2 - | β_i |^2 = 1$ with $| β_i |^2$ taking an integer value.