Abstract
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 compacted 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 a massless axion field, in all three formalisms, 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 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.
Highlights
The concept of quantum entanglement is one of the most interesting features that one can study in the context of quantum mechanics
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
Apart from that, for massless and massive axion field, we find distinguishable features of the power spectrum for the field operator expansion (FOE), reduced density matrix (RDM), and non entangled state (NES) on the large scales, which is the result of quantum entanglement
Summary
The concept of quantum entanglement is one of the most interesting features that one can study in the context of quantum mechanics. Based on the physical set up used in our previous works [23,24], in this paper we studied the cosmological implications of quantum entanglement by focussing on the long range effects of the two point correlation function computed from the mean square vacuum fluctuation of stringy Axion field with Bunch Davies and α quantum states as initial choice of vacua. In Sections 3.2.1and 3.2.2 we discuss the quantum vacuum fluctuation using reduced density matrix (RDM) formalism using mixed state for Axion field and we derived the explicit form of the reduced density matrix in the de Sitter hyperbolic open chart This result is used to derive the power spectrum by computing the two point quantum correlation function from mean square vacuum fluctuation in large and small wave number limits for both massless and massve Axion fields. Small wavenumber (long wavelength) limit in super horizon time scale they are completely different
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