  In this work, we study the impact of quantum entanglement on the two-point
correlation function and the associated primordial power spectrum of mean
square vacuum fluctuation in a bipartite quantum field theoretic system. The
field theory that we consider is the effective theory of axion field arising
from Type IIB string theory compactified to four dimensions. We compute the
expression for the power spectrum of vacuum fluctuation in three different
approaches, namely (1) field operator expansion (FOE) technique with the
quantum entangled state, (2) reduced density matrix (RDM) formalism with mixed
quantum state and (3) the method of non-entangled state (NES). For massless
axion field, in all these three formalism, we reproduce, at the leading order,
the exact scale-invariant power spectrum which is well known in the literature.
We observe that due to quantum entanglement, the sub-leading terms for these
thee formalisms are different. Thus, such correction terms break the degeneracy
among the analysis of the FOE, RDM and NES formalisms in the super-horizon
limit. On the other hand, for massive axion field, we get a slight deviation
from scale invariance and exactly quantify the spectral tilt of the power
spectrum in small scales. Apart from that, for massless and massive axion
field, we find distinguishable features of the power spectrum for the FOE, RDM,
and NES on the large scales, which is the result of quantum entanglement. We
also find that such large-scale effects are comparable to or greater than the
curvature radius of the de Sitter space. Most importantly, in the near future,
if experiments probe for early universe phenomena, one can detect such small
quantum effects. In such a scenario, it is possible to test the implications of
quantum entanglement in primordial cosmology.

High Energy Physics - Theory;Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology;Quantum Physics