  Since it is commonly believed that the observed large-scale structure of the
Universe is an imprint of quantum fluctuations existing at the very early stage
of its evolution, it is reasonable to pose the question: Do the effects of
quantum nonlocality, which are well established now by the laboratory studies,
manifest themselves also in the early Universe? We try to answer this question
by utilizing the results of a few experiments, namely, with the superconducting
multi-Josephson-junction loops and the ultracold gases in periodic potentials.
Employing a close analogy between the above-mentioned setups and the simplest
one-dimensional Friedmann-Robertson-Walker cosmological model, we show that the
specific nonlocal correlations revealed in the laboratory studies might be of
considerable importance also in treating the strongly-nonequilibrium phase
transitions of Higgs fields in the early Universe. Particularly, they should
substantially reduce the number of topological defects (e.g., domain walls)
expected due to independent establishment of the new phases in the remote
spatial regions. This gives us a hint for resolving a long-standing problem of
the excessive concentration of topological defects, inconsistent with
observational constraints. The same effect may be also relevant to the recent
problem of the anomalous behavior of cosmic microwave background fluctuations
at large angular scales.
