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 theorry 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 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
Based on the physical set up used in our previous works [24] and [25], in this paper we have 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
Further to know the exact wave number dependence of the amplitude of the normalised power spectrum from generalised α vacua we need to know the behaviour of the power spectrum at very short wavelengths ( p, pn >> 1)
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 [24] and [25], in this paper we have 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 our computation we have explicitly included the effect of Stringy Axion in the small field regime and as a result we get perturbatively corrected contributions in the expression for the power spectrum derived using FOE, RDM and NES formalisms Such correction terms can be interpreted as quantum effects which are appearing from the UV complete theory, such as a specific type of bipartite quantum field theory driven by axion. We have used three different approaches at super horizon time scale hoping that the quantum corrections, at small and large wave number limits when confronted with observations, can select the
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