The classical action for a Bianchi VI_h model

TL;DR

This paper estimates the classical action for a Bianchi VI_h cosmology and uses it to explain the near-zero relative rotation of inertial frames, suggesting that only geometries with extremely small rotation contribute to the universe's wave function.

Contribution

It provides a semiclassical analysis of the Bianchi VI_h model's action and connects it to the observed inertial frame non-rotation, independent of quantum gravity details.

Findings

The saddlepoint occurs at zero rotation parameter b=0.

Classical geometries with relative rotation less than 10^(-130) radians/year dominate the wave function.

The result is consistent with experimental limits on frame rotation.

Abstract

An estimate for the classical action for a Bianchi VI_h homogeneous spatially closed cosmology is presented as a function of b, a parameter of the model that is proportional to the relative rotation of the average inertial frame and the bulk of matter in the universe. It is assumed (through the equation of state) that a relativistic early universe is followed by a matter-dominated late universe. The action is used in a saddlepoint approximation to a semiclassical estimate for the wave function in quantum cosmology to explain why our inertial frame seems not to rotate relative to the stars. The saddlepoint is at b=0, as would be expected. Application of the saddlepoint approximation leads to the result that only those classical geometries whose action differs from the saddlepoint value for the action by an amount less than Planck's constant contribute significantly to the integration to give the present value of the wave function. Using estimates for our universe implies that only those classical geometries for which the present relative rotation rate of inertial frames and matter are less than about 10^(-130) radians per year contribute significantly to the integration. This is well below the limit set by experiment. The result depends on the ratio of the Hubble distance to the Planck length, but does not depend on the details of the theory of quantum gravity.