We investigate the squeezing of primordial gravitational waves (PGWs) in terms of quantum discord. We construct a classical state of PGWs without quantum discord and compare it with the Bunch-Davies vacuum. Then it is shown that the oscillatory behavior of the angular-power spectrum of the cosmic microwave background (CMB) fluctuations induced by PGWs can be the signature of the quantum discord of PGWs. In addition, we discuss the effect of quantum decoherence on the entanglement and the quantum discord of PGWs for super-horizon modes. For the state of PGWs with decoherence effect, we examine the decoherence condition and the correlation condition introduced by C. Kiefer et al. (Class. Quantum Grav. 24 (2007) 1699). We show that the decoherence condition is not sufficient for the separability of PGWs and the correlation condition implies that the PGWs in the matter-dominated era have quantum discord.
We investigate the quantumness of primordial cosmological fluctuations and its detectability. The quantum discord of inflationary perturbations is calculated for an arbitrary splitting of the system, and shown to be very large on super-Hubble scales. This entails the presence of large quantum correlations, due to the entangled production of particles with opposite momentums during inflation. To determine how this is reflected at the observational level, we study whether quantum correlators can be reproduced by a non-discordant state, i.e. a state with vanishing discord that contains classical …
In recent work we analyzed the evolution of primordial perturbations satisfying Planck-scale-modified dispersion relations and showed that there is no cosmological "squeezing" in the critical model that produces perturbations with a scale invariant spectrum. Nevertheless, the perturbations reenter the horizon as standing waves with the correct temporal phase because of the late-time decay of the momentum mode. Here we shed light on the absence of primordial squeezing by re-examining the problem in the dual rainbow frame, where $c$ is set to 1, shifting the varying $c$ effects elsewhere. In thi…
It has been shown that the primordial perturbations sourced by inflation are driven to classicality by unitary evolution alone. However, their coupling with the environment such as photons and subsequent decoherence renders the cosmological correlations quantum, losing primordial information in the process. We argue that the quantumness of the resulting cosmological correlations is given by quantum discord, which captures non-classical behavior beyond quantum entanglement. By considering the environment as a quantum channel in which primordial information contained in the perturbations is tran…
A direct quantization of the Newtonian interaction between two masses is known to establish entanglement, which if detected would witness the quantum nature of the gravitational field. Gravitational interaction is yet compatible also with gravitational decoherence models relying on classical channels, hence unable to create entanglement. Here, we show in paradigmatic cases that, despite the absence of entanglement, a classical-channel model of gravity can still establish quantum correlations in the form of quantum discord between two masses. This is demonstrated for the Kafri-Taylor-Milburn (K…
We develop a theory in which relic gravitational waves and primordial density perturbations are generated by strong variable gravitational field of the early Universe. The generating mechanism is the superadiabatic (parametric) amplification of the zero-point quantum oscillations. The generated fields have specific statistical properties of squeezed vacuum quantum states. Macroscopically, squeezing manifests itself in a non-stationary character of variances and correlation functions of the fields, the periodic structures of the metric power spectra, and, as a consequence, in oscillatory behavi…
The universe is believed to be originated from a quantum state. However, defining measurable quantities for the quantum properties in the present universe has gained interest recently. In this submission, we propose a quantum Poincare sphere as an observable quantity that can hint at the quantumness of primordial gravitational waves and large-scale magnetic fields. The Poincare sphere is defined in terms of quantum stokes operators associated with the polarization of those fields, which can be measured directly. We have further studied the effects of the initial non-BD vacuum on the power spec…
We show how consistency relations can be used to robustly extract the amplitude of local primordial non-Gaussianity ($f_{\rm NL}$) from the squeezed limit of the matter bispectrum, well into the non-linear regime. First, we derive a non-perturbative relation between primordial non-Gaussianity and the leading term in the squeezed bispectrum, revising some results present in the literature. This relation is then used to successfully measure $f_{\rm NL}$ from $N$-body simulations. We discuss the dependence of our results on different scale cuts and redshifts. Specifically, the analysis is strongl…
We show how the quantum-to-classical transition of the cosmological fluctuations produced during an inflationary stage can be described using the consistent histories approach. We identify the corresponding histories in the limit of infinite squeezing. To take the decaying mode into account, we propose an extension to coarse-grained histories.
We consider the possibility that the primordial fluctuations (scalar and tensor) might have been standing waves at their moment of creation, whether or not they had a quantum origin. We lay down the general conditions for spatial translational invariance, and isolate the pieces of the most general such theory that comply with, or break translational symmetry. We find that, in order to characterize statistically translationally invariant standing waves, it is essential to consider the correlator $\langle c_0({\mathbf k}) c_0({\mathbf k}')\rangle$ in addition to the better known $\langle c_0({\m…
We show how to determine the typical phase space volume $Γ$ for primordial gravitational waves produced during an inflationary stage, which is invariant under squeezing. An expression for $Γ$ is found in the long wavelength regime. The quasi-classical entropy of a pure vacuum initial state defined as the logarithm of $Γ$ modulo a constant remains zero in spite of the generation of fluctuations (creation of real gravitons).
The nonclassicality of primordial gravitational waves (PGWs) is characterized in terms of sub-Poissonian graviton statistics. The sub-Poissonian statistics are realized when quantum states are squeezed coherent states. In the presence of matter fields, the Universe experiences the squeezed coherent state during inflation. The condition to realize the sub-Poissonian graviton statistics is translated into the frequency range of gravitational waves. If the initial state is the Bunch-Davies vacuum, there is another necessary condition between phases of squeezing and coherent parameters. Here, we e…
In this article, we investigate various physical implications of quantum circuit complexity using squeezed state formalism of Primordial Gravitational Waves (PGW). Recently quantum information theoretic concepts, such as entanglement entropy, and complexity are playing a pivotal role to understand the dynamics of quantum system even in the diverse fields such as, high energy physics and cosmology. This paper is devoted in studying quantum circuit complexity of PGW for various cosmological models, such as de Sitter, inflation, radiation, reheating, matter, bouncing, cyclic and black hole gas mo…
In this paper we skim the true phenomenological requirements behind the concept of inflationary squeezing. We argue that all that is required is that at horizon re-entry the fluctuations form standing waves with the correct temporal phase (specifically, sine waves). We quantify this requirement and relate it to the initial conditions fed into the radiation dominated epoch by whatever phase of the Universe produced the fluctuations. The only relevant quantity turns out to be the degree of suppression of the momentum, $p$, of the fluctuations, $y$, which we measure by $σ\sim ω^2 |y|^2/|p|^2$. Ev…
Krylov complexity and oscillatory quantum dynamics in two-field inflation
Department of Physics, Guizhou Minzu University（贵州民族大学物理系）；Department of Physics, College of Physics, Mechanical and Electrical Engineering, Jishou University（吉首大学物理科学与机械电子工程学院物理系）
In the standard inflationary paradigm, cosmological density perturbations are generated as quantum fluctuations in the early Universe, but then undergo a quantum-to-classical transition. A key role in this transition is played by squeezing of the quantum state, which is a result of the strong suppression of the decaying mode component of the perturbations. Motivated by ever improving measurements of the cosmological perturbations, we ask whether there are scenarios where this decaying mode is nevertheless still observable in the late Universe, ideally leading to a ``smoking gun'' signature of …
Detailed measurements of the cosmic microwave background indicate the large-scale homogeneity of the universe. On very small scales, we observe however inhomogeneities such as galaxies, stars, planets and ourselves. In the context of hot Big-Bang cosmology, these inhomogeneities are often explained as the remains of quantum fluctuations at very early times, enlarged to observable scales through the process of inflation. In this dissertation, I examine two important questions surrounding this scenario: a) How do inherently quantal fluctuations transition to the observed inhomogeneities, which b…
The inflationary paradigm provides a mechanism to generate the primordial perturbations needed to explain the observed large scale structures in the universe. Inflation traces back all the inhomogeneities to quantum fluctuations although the structures look classical today. Squeezing of primordial quantum fluctuations along with the mechanism of decoherence accounts for many aspects of this quantum to classical transition, although it remains a matter of debate as to whether this is sufficient to explain the issue of realization of a single outcome (i.e. the issue of macro-objectification) fro…
The perturbations in the early universe are generated as a result of the interplay between quantum field theory and gravitation. Since these primordial perturbations lead to the anisotropies in the cosmic microwave background and eventually to the inhomogeneities in the Large Scale Structure (LSS), they provide a unique opportunity to probe issues which are fundamental to our understanding of quantum physics and gravitation. One such fundamental issue that remains to be satisfactorily addressed is the transition of the primordial perturbations from their quantum origins to the LSS which can be…
Primordial gravitational waves generated from early universe are placed in the squeezed vacuum state and the resulting stochastic background is studied for various models of the expanding universe. The quantum effect on the stochastic gravitational waves leads to overall enhancement of the amplitude and spectral energy density when compared to those in the absence of squeezing effect with continued increase in the amplitude in the accelerating stage and oscillatory behavior at higher frequency range of the spectrum in the accelerating universe. Through the quantum effect, it is also found that…
