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Register a new userEntangled de Sitter from Stringy Axionic Bell pair I: An analysis using Bunch Davies vacuum
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In this work, we study the quantum entanglement and compute entanglement entropy in de Sitter space for a bipartite quantum field theory driven by axion originating from ${bf Type~ IIB}$ string compactification on a Calabi Yau three fold (${bf CY^3}$) and in presence of ${bf NS5}$ brane. For this compuation, we consider a spherical surface ${bf S}^2$, which divide the spatial slice of de Sitter (${bf dS_4}$) into exterior and interior sub regions. We also consider the initial choice of vaccum to be Bunch Davies state. First we derive the solution of the wave function of axion in a hyperbolic open chart by constructing a suitable basis for Bunch Davies vacuum state using Bogoliubov transformation. We then, derive the expression for density matrix by tracing over the exterior region. This allows us to compute entanglement entropy and R$acute{e}$nyi entropy in $3+1$ dimension. Further we quantify the UV finite contribution of entanglement entropy which contain the physics of long range quantum correlations of our expanding universe. Finally, our analysis compliments the necessary condition for the violation of Bells inequality in primordial cosmology due to the non vanishing entanglement entropy for axionic Bell pair.
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In this work, we study the phenomena of quantum entanglement by computing de Sitter entanglement entropy from von Neumann measure. For this purpose we consider a bipartite quantum field theoretic setup in presence of axion originating from ${bf Type~ II~B}$ string theory. We consider the initial vacuum to be CPT invariant non-adiabatic $alpha$ vacua state under ${bf SO(1,4)}$ ismometry, which is characterized by a real one-parameter family. To implement this technique we use a ${bf S^2}$ which divide the de Sitter into two exterior and interior sub-regions. First, we derive the wave function of axion in an open chart for $alpha$ vacua by applying Bogoliubov transformation on the solution for Bunch-Davies vacuum state. Further, we quantify the density matrix by tracing over the contribution from the exterior region. Using this result we derive entanglement entropy, R$acute{e}$nyi entropy and explain the long-range quantum effects in primordial cosmological correlations. We also provide a comparison between the results obtained from Bunch-Davies vacuum and the generalized $alpha$ vacua, which implies that the amount of quantum entanglement and the long-range effects are larger for non zero value of the parameter $alpha$. Most significantly, our derived results for $alpha$ vacua provides the necessary condition for generating non zero entanglement entropy in primordial cosmology.
We study the cosmological properties of a metastable de Sitter vacuum obtained recently in the framework of type IIB flux compactifications in the presence of three D7-brane stacks, based on perturbative quantum corrections at both world-sheet and string loop level that are dominant at large volume and weak coupling. In the simplest case, the model has one effective parameter controlling the shape of the potential of the inflaton which is identified with the volume modulus. The model provides a phenomenological successful small-field inflation for a value of the parameter that makes the minimum very shallow and near the maximum. The horizon exit is close to the inflection point while most of the required e-folds of the Universe expansion are generated near the minimum, with a prediction for the ratio of tensor-to-scalar primordial fluctuations $r sim 4 times 10^{-4}$. Despite its shallowness, the minimum turns out to be practically stable. We show that it can decay only through the Hawking-Moss instanton leading to an extremely long decay rate. Obviously, in order to end inflation and obtain a realistic model, new low-energy physics is needed around the minimum, at intermediate energy scales of order $10^{12}$ GeV. An attractive possibility is by introducing a waterfall field within the framework of hybrid inflation.
Many modern cosmological scenarios feature large volumes of spacetime in a de Sitter vacuum phase. Such models are said to be faced with a Boltzmann Brain problem - the overwhelming majority of observers with fixed local conditions are random fluctuations in the de Sitter vacuum, rather than arising via thermodynamically sensible evolution from a low-entropy past. We argue that this worry can be straightforwardly avoided in the Many-Worlds (Everett) approach to quantum mechanics, as long as the underlying Hilbert space is infinite-dimensional. In that case, de Sitter settles into a truly stationary quantum vacuum state. While there would be a nonzero probability for observing Boltzmann-Brain-like fluctuations in such a state, observation refers to a specific kind of dynamical process that does not occur in the vacuum (which is, after all, time-independent). Observers are necessarily out-of-equilibrium physical systems, which are absent in the vacuum. Hence, the fact that projection operators corresponding to states with observers in them do not annihilate the vacuum does not imply that such observers actually come into existence. The Boltzmann Brain problem is therefore much less generic than has been supposed.
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.
In de Sitter ambient space formalism, the linear gravity can be written in terms of a minimally coupled scalar field and a polarization tensor. In this formalism, the massless minimally coupled scalar field can be quantized on Bunch-Davies vacuum state, that preserves the de Sitter invariance, the analyticity and removes the infrared divergence. The de Sitter quantum linear gravity is then constructed on Bunch-Davies vacuum state, which is also covariant, analytic and free of any infrared divergences. We will conclude that the unique Bunch-Davies vacuum state can be used adequately to constructing the quantum field theory in de Sitter universe.
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