Abstract
We show that the entropy of cosmological perturbations originating as quantum vacuum fluctuations in the very early universe, including the contribution of the leading nonlinear interactions, can be viewed as momentum space entanglement entropy between sub- and super-Hubble modes. The interactions between these modes causes decoherence of the super-Hubble fluctuations which, in turn, leads to a non-vanishing entropy of the reduced density matrix corresponding to the super-Hubble inhomogeneities. In particular, applying this to inflationary cosmology reveals that the entanglement entropy produced by leading order nonlinearities dominates over that coming from the squeezing of the vacuum state unless inflation lasts for a very short period. Furthermore, demanding that this entanglement entropy be smaller than the thermal entropy at the beginning of the radiation phase of standard cosmology leads to an upper bound on the duration of inflation which is similar to what is obtained from the Trans-Planckian Censorship Conjecture.
Highlights
There has recently been a lot of interest in entanglement entropy in the context of quantum field theory and gravity
We show that the entropy of cosmological perturbations originating as quantum vacuum fluctuations in the very early universe, including the contribution of the leading nonlinear interactions, can be viewed as momentum space entanglement entropy between sub- and super-Hubble modes
The interactions between these modes cause decoherence of the super-Hubble fluctuations which, in turn, leads to a nonvanishing entropy of the reduced density matrix corresponding to the super-Hubble inhomogeneities. Applying this to inflationary cosmology reveals that the entanglement entropy produced by leading order nonlinearities dominates over that coming from the squeezing of the vacuum state unless inflation lasts for a very short period. Demanding that this entanglement entropy be smaller than the thermal entropy at the beginning of the radiation phase of standard cosmology leads to an upper bound on the duration of inflation which is similar to what is obtained from the trans-Planckian censorship conjecture
Summary
There has recently been a lot of interest in entanglement entropy in the context of quantum field theory and gravity (see, e.g., [1] for reviews). As discussed in [25,26,27,28], this leads to decoherence of the reduced density matrix of super-Hubble modes.2 This decoherence is crucial in order to explain why the cosmological perturbations become classical even though they have a quantum origin. III, we review the well-known argument that interaction between the perturbation modes, arising from minimal gravitational nonlinearities, leads to a suppression of the off-diagonal terms in the density matrix for the super-Hubble modes
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