Pointer states for primordial fluctuations in inflationary cosmology

Primordial fluctuations in inflationary cosmology acquire classical properties through decoherence when their wavelengths become larger than the Hubble scale. Although decoherence is effective, it is not complete, so a significant part of primordial correlations remains up to the present moment. We address the issue of the pointer states which provide a classical basis for the fluctuations with respect to the influence by an environment (other fields). Applying methods from the quantum theory of open systems (the Lindblad equation), we show that this basis is given by narrow Gaussians that approximate eigenstates of field amplitudes. We calculate both the von Neumann and linear entropy of the fluctuations. Their ratio to the maximal entropy per field mode defines a degree of partial decoherence in the entropy sense. We also determine the time of partial decoherence making the Wigner function positive everywhere which, for super-Hubble modes during inflation, is virtually independent of coupling to the environment and is only slightly larger than the Hubble time. On the other hand, assuming a representative environment (a photon bath), the decoherence time for sub-Hubble modes is finite only if some real dissipation exists.