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

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.

Quantum aspects of chaos and complexity from bouncing cosmology: A study with two-mode single field squeezed state formalism

“…An interesting study would be to see how this complexity can be used to study the non equilibrium phenomenon and chaoticity in various entangled systems [222][223][224][225][226][227][228]. This measure might be used to see if the long-range correlation between systems induces chaoticity and quantum randomness or not.…”

The Generalized OTOC from Supersymmetric Quantum Mechanics—Study of Random Fluctuations from Eigenstate Representation of Correlation Functions

“…Very recently, in Reference [110][111][112][113][114], the authors have studied various relevant measures for an entangled open quantum system. The study of OTOCs for such type of entangled systems [115][116][117][118] will be quite relevant for understanding the rtime disorder averaging phenomena and chaos for such an entangled OQS. • Last but not least, very recently, we proposed a detailed mechanism and framework, using which one is able to compute the OTOC within the framework of primordial cosmological perturbation theory by making use of the gauge invariant scalar perturbations and its associated canonically conjugate momenta [89], and, finally, found out the chaotic-like behavior in the representative cosmological version of OTOC.…”

Quantum aspects of chaos and complexity from bouncing cosmology: A study with two-mode single field squeezed state formalism

“…• Prospect III: An interesting study would be to see how this complexity can be used to study the non equilibrium phenomenon and chaoticity in various entangled systems [226][227][228][229][230][231][232]. This measure might be used to see if the long-range correlation between systems induces chaoticity and quantum randomness or not.…”