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. 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.

Ever since the insightful analysis of the durations of gamma-ray bursts (GRBs) by Kouveliotou et al. (1993), GRBs have most often been classified into two populations: "short bursts" (shorter than 2.0 seconds) and "long bursts" (longer than 2.0 seconds). However, recent works have suggested the existence of an intermediate population in the bursts observed by the Swift satellite. Moreover, some researchers have questioned the universality of the 2.0-second dividing line between short and long bursts: some bursts may be short but actually result from collapsars, the physical mechanism behind normally long bursts, and some long ones may originate from mergers, the usual progenitors of short GRBs.In this work, we focus on GRBs detected by the Fermi satellite (which has a much higher detection rate than Swift and other burst-detecting satellites) and study the distribution of their durations measured in the observer's reference frame and, for those with known redshifts, in the bursts' reference frames. However, there are relatively few bursts with measured redshifts, and this makes an accurate study difficult. To overcome this problem, we follow Zhang and Wang (2018) and determine a "pseudo-redshift" from the correlation relation between the luminosity L p and the energy E p , both of which are calculated at the peak of the flux. Interestingly, we find that the uncertainties in the quantities observed and used in the determination of pseudo-redshifts, do affect the precision of the individual results significantly, but they keep the distribution of pseudo-redshifts very similar to that of the actual ones and thus allow us to use pseudo-redshifts for our statistical study. We briefly present the advantages and disadvantages of using pseudo-redshifts in this context.We use the reduced chi-square and the maximization of the log-likelihood to statistically analyze the distribution of Fermi GRB durations. Both methods show that the distribution of the observed (measured) and the intrinsic (source/rest frame) bursts durations are better represented by two groups/populations, rather than three.