6 research outputs found
On the Decoherence of Primordial Fluctuations During Inflation
We study the process whereby quantum cosmological perturbations become
classical within inflationary cosmology. By setting up a master-equation
formulation we show how quantum coherence for super-Hubble modes can be
destroyed by their coupling to the environment provided by sub-Hubble modes. We
identify what features the sub-Hubble environment must have in order to
decohere the longer wavelengths, and identify how the onset of decoherence (and
how long it takes) depends on the properties of the sub-Hubble physics which
forms the environment. Our results show that the decoherence process is largely
insensitive to the details of the coupling between the sub- and super-Hubble
scales. They also show how locality implies, quite generally, that the
decohered density matrix at late times is diagonal in the field representation
(as is implicitly assumed by extant calculations of inflationary density
perturbations). Our calculations also imply that decoherence can arise even for
couplings which are as weak as gravitational in strength.Comment: 31 pages, 1 figur
Lectures on Cosmic Inflation and its Potential Stringy Realizations
These notes present a brief introduction to Hot Big Bang cosmology and Cosmic
Inflation, together with a selection of some recent attempts to embed inflation
into string theory. They provide a partial description of lectures presented in
courses at Dubrovnik in August 2006, at CERN in January 2007 and at Cargese in
August 2007. They are aimed at graduate students with a working knowledge of
quantum field theory, but who are unfamiliar with the details of cosmology or
of string theory.Comment: 68 pages, lectures given at Dubrovnik, Aug 2006; CERN, January 2007;
and Cargese, Aug 200
Classical approximation to quantum cosmological correlations
We investigate up to which order quantum effects can be neglected in
calculating cosmological correlation functions after horizon exit. As a toy
model, we study theory on a de Sitter background for a massless
minimally coupled scalar field . We find that for tree level and one loop
contributions in the quantum theory, a good classical approximation can be
constructed, but for higher loop corrections this is in general not expected to
be possible. The reason is that loop corrections get non-negligible
contributions from loop momenta with magnitude up to the Hubble scale H, at
which scale classical physics is not expected to be a good approximation to the
quantum theory. An explicit calculation of the one loop correction to the two
point function, supports the argument that contributions from loop momenta of
scale are not negligible. Generalization of the arguments for the toy model
to derivative interactions and the curvature perturbation leads to the
conclusion that the leading orders of non-Gaussian effects generated after
horizon exit, can be approximated quite well by classical methods. Furthermore
we compare with a theorem by Weinberg. We find that growing loop corrections
after horizon exit are not excluded, even in single field inflation.Comment: 44 pages, 1 figure; v2: corrected errors, added references,
conclusions unchanged; v3: added section in which we compare with stochastic
approach; this version matches published versio
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.Comment: 32 pages, 2 figures, matches published version: discussion expanded,
references added, conclusions unchange