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#### Cosmological spectrum of two-point correlation function from vacuum fluctuation of Stringy Axion field in De Sitter space: A study of the role of Quantum Entanglement

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##### Citation

Choudhury, S., & Panda, S. (2020). Cosmological spectrum of two-point correlation
function from vacuum fluctuation of Stringy Axion field in De Sitter space: A study of the role of Quantum Entanglement.* Universe,* *6*(6): 79. doi:10.3390/universe6060079.

Cite as: https://hdl.handle.net/21.11116/0000-0006-CE09-9

##### 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 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.

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.