All-scale gauge-invariant extension of the Mukhanov–Sasaki variables

Determine whether a correction to the multifield Mukhanov–Sasaki variables exists that is gauge invariant at all scales and coincides with the scalar-field fluctuations in the spatially flat gauge.

Background

The paper constructs corrected multifield Mukhanov–Sasaki variables that are gauge invariant through second order on super-Hubble scales and that reduce to the covariant field perturbations in the spatially flat gauge. The resulting gauge-fixed Hamiltonian is shown to agree with the corresponding large-scale dynamics.

The construction is not established at finite or sub-Hubble wavelengths. Consequently, it remains unresolved whether an all-scale correction with both desired properties—gauge invariance and reduction to the spatially flat-gauge field fluctuations—exists. Resolving this issue would determine whether the variables and Hamiltonian can be used without qualification at small scales.