Primordial black holes (PBHs) form when large primordial curvature perturbations re-enter the Hubble radius and exceed the classical collapse threshold. These perturbations originate as quantum fluctuations of the inflationary vacuum, motivating a quantum-information description of the PBH-producing scalar sector. We develop a conservative extension of the standard PBH and scalar-induced gravitational-wave (SIGW) framework in which Gaussian quantum discord is used as a diagnostic of residual quantum correlations, not as a new PBH-formation criterion. We describe each \((\bm k,-\bm k)\) pair as a two-mode Gaussian state and show that, in the pure squeezed limit, discord grows rapidly with the squeezing parameter, so low discord thresholds are automatically satisfied for strongly squeezed modes. The nontrivial regime is the mixed state produced by decoherence. Using a Lindblad open-system description, we motivate a Gaussian loss channel for the scalar covariance matrix and distinguish the discord from a covariance-survival factor \(Q_{\rm dec}(k)\). If the decoherence channel suppresses the scalar two-point covariance, PBH abundance can be affected through the classical collapse variance, while the SIGW spectrum is modified more directly by the factors \(Q_{\rm dec}(ku)Q_{\rm dec}(kv)\) inside the radiation-era convolution. For a narrow scalar peak and slowly varying \(Q_{\rm dec}\), this gives the benchmark scaling \(Ω_{\rm GW}^{\rm eff}\simeq Q_{\rm dec}^2Ω_{\rm GW}^{\rm class}\). Thus quantum discord and decoherence provide a controlled way to characterize the quantum-to-classical transition of PBH-producing perturbations, with the clearest imprint appearing in scalar-induced gravitational waves.
Scaler and tensor perturbations couple nonlinearly with each other in the Einstein-Hilbert action. We show that such interaction naturally leads to the quantum decoherence of the primordial perturbations during inflation at horizon crossing. The dominant interaction Hamiltonian contributing to decoherence is identified and the master equation responsible for the decohering process is derived.
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 …
We study the superposition of primordial massive particles and compute the associated decoherence time scale in the radiation dominated universe. We observe that for lighter primordial particles with masses up to $10^7\,\rm{kg}$, the corresponding decoherence time scale is significantly larger than the age of the observable universe, demonstrating that a primordial particle would persist in a pure quantum state, with its wavefunction spreading freely. For heavier particles, they can still be in a quantum state while their position uncertainties are limited by the wavelength of background photo…
Primordial fluctuations in inflationary cosmology acquire classical properties through decoherence when their wavelengths become larger than the Hubble scale. Although decoherence is effective, it is not complete, so a significant part of primordial correlations remains up to the present moment. We address the issue of the pointer states which provide a classical basis for the fluctuations with respect to the influence by an environment (other fields). Applying methods from the quantum theory of open systems (the Lindblad equation), we show that this basis is given by narrow Gaussians that app…
We study the evironment-induced decoherence of cosmological perturbations in an inflationary background. Splitting our spectrum of perturbations into two distinct sets characterized by their wavelengths (super and sub-Hubble), we identify the long wavelength modes with our system and the remainder with an environment. We examine the effects of the interactions between our system and the environment. This interaction causes the long-wavelength modes to decohere for realistic values of the coupling and we conclude that interactions due to backreaction are more than sufficient to decohere the sys…
Gravitationally Induced Quantum Decoherence of Macroscopic Objects
The Hakubi Center for Advanced Research, Kyoto University（京都大学白川中心）；Department of Physics, Kyoto University（京都大学物理系）；Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所引力物理与量子信息中心）
We show that, by treating the gravitational interaction between two mechanical resonators as a classical measurement channel, a gravitational decoherence model results that is equivalent to a model first proposed by Diosi. The resulting decoherence model implies that the classically mediated gravitational interaction between two gravitationally coupled resonators cannot create entanglement. The gravitational decoherence rate ( and the complementary heating rate) is of the order of the gravitationally induced normal mode splitting of the two resonators.
We present a series of arguments against the results of the paper "Universal decoherence due to gravitational time dilation" by Pikovski et al. (arXiv:1311.1095).
Models of gravitational decoherence are not commonly applied to ultra-relativistic systems, including photons. As a result, few quantum optical tests of gravitational decoherence have been developed. In this paper, we generalize the gravitational decoherence model of Anastopoulos and Hu (arXiv:1305.5231) to photons. In this model, decoherence originates from a bath of stochastic gravitational perturbations, possibly of fundamental origin. We derive a master equation for general states of the electromagnetic (EM) field; the only free parameter is a noise temperature $Θ$ of the gravitational flu…
In many theories of quantum gravity quantum fluctuations of spacetime may serve as an environment for decoherence. Here we study quantum-gravitational decoherence of high energy astrophysical neutrinos in the presence of fermionic dark sectors and for a realistic three neutrino scenario. We show how violation of global symmetries expected to arise in quantum gravitational interactions provides a possibility to pin down the number of dark matter fermions in the universe. Furthermore, we predict the expected total neutrino flux and flavor ratios at experiments depending on the flavor composition…
Among the many worthwhile quantum experiments taking advantage of long baselines in space, this white paper points to the far-reaching significance of gravitational decoherence experiments. These experiments can provide clues as to whether gravity is of a fundamental or an effective nature. They can also discriminate between the predictions of quantum field theory in curved spacetime, our default theory for quantum phenomena in background gravitational fields, and other popular alternative quantum theories.
The present work can be regarded as a corollary to the paper titled "Neutrino decoherence in presence of strong gravitational fields". Specifically, we investigate the gravitationally-induced decoherence on neutrino oscillation from the point of view of a locally inertial observer at rest with neutrino propagation. In so doing, we observe that in the aforementioned reference frame the effects of gravity can become manifest in a non-trivial manner with respect to an observer placed at infinity.
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…
We study the decoherence process associated with the scattering of stochastic backgrounds of gravitational waves. We show that it has a negligible influence on HYPER-like atomic interferometers although it may dominate decoherence of macroscopic motions, such as the planetary motion of the Moon around the Earth.
We consider the possibility to measure the quantum decoherence using gravitational wave interferometers. Gravitational wave interferometers create the superposition state of photons and measure the interference of the photon state. If the decoherence occurs, the interference of the photon state vanishes and it can be measured by the interferometers. As examples of decoherence mechanisms, we consider 1) decoherence by spontaneous localization, 2) gravitational decoherence and 3) decoherence by extra-dimensional gravity.
We discuss the interplay of wave packet decoherence and decoherence induced by quantum gravity via interactions with spacetime foam for high energy astrophysical neutrinos. In this context we point out a compelling consequence of the expectation that quantum gravity should break global symmetries, namely that quantum-gravity induced decoherence may not only be the most sensitive probe for quantum properties of spacetime, but also can provide both a powerful tool for the search for new particles, including totally decoupled backgrounds interacting only gravitationally, and at the same time a wi…
We study primordial gravitational waves produced during inflation in quantum gravity at a Lifshitz point proposed by Ho${\rm\check{r}}$ava. Assuming power-counting renormalizability, foliation preserving diffeomorphism invariance, and the condition of detailed balance, we show that primordial gravitational waves are circularly polarized due to parity violation. The chirality of primordial gravitational waves is a quite robust prediction of quantum gravity at a Lifshitz point which can be tested through observations of cosmic microwave background radiation and stochastic gravitational waves.
Schemes of gravitationally induced decoherence are being actively investigated as possible mechanisms for the quantum-to-classical transition. Here, we introduce a decoherence process due to quantum gravity effects. We assume a foamy quantum spacetime with a fluctuating minimal length coinciding on average with the Planck scale. Considering deformed canonical commutation relations with a fluctuating deformation parameter, we derive a Lindblad master equation that yields localization in energy space and decoherence times consistent with the currently available observational evidence. Compared t…
We study the effect of the scattering of gravitational waves on planetary motions, say the motion of the Moon around the Earth. Though this effect has a negligible influence on dissipation, it dominates fluctuations and the associated decoherence mechanism, due to the very high effective temperature of the background of gravitational waves in our galactic environment.
We study the decoherence process associated with the scattering of stochastic gravitational waves. We discuss the case of macroscopic systems, such as the planetary motion of the Moon around the Earth, for which gravitational scattering is found to dominate decoherence though it has a negligible influence on damping. This contrast is due to the very high effective temperature of the background of gravitational waves in our galactic environment.
A small quantum system is studied which is a superposition of states localized in different positions in a static gravitational field. The time evolution of the correlation between different positions is investigated, and it is seen that there are two time scales for such an evolution (decoherence). Both time scales are inversely proportional to the red shift difference between the two points. These time scales correspond to decoherences which are linear and quadratic, respectively, in time.
We discuss a mechanism of spin decoherence in gravitation within the framework of general relativity. The spin state of a particle moving in a gravitational field is shown to decohere due to the curvature of spacetime. As an example, we analyze a particle going around a static spherically-symmetric object.
We present a general master equation for the quantum dynamics of a scalar bosonic particle interacting with an external weak and stochastic gravitational field. The dynamics predicts decoherence in position as well as in momentum. We show how the master equation reproduces the results present in the literature by taking appropriate limits, thus explaining the apparent contradiction in their dynamical description. We apply our model to a matter wave experiment, providing a practical formula for determining of the magnitude of gravitational decoherence. We compare it with the standard experiment…
We consider possible detection of nonclassicality of primordial gravitational waves (PGWs) by applying Hanbury Brown - Twiss (HBT) interferometry to cosmology. We characterize the nonclassicality of PGWs in terms of sub-Poissonian statistics that can be measured by the HBT interferometry. We show that the presence of classical sources during inflation makes us possible to detect nonclassical PGWs with the HBT interferometry. We present two examples that realize the classical sources during inflation. It turns out that PGWs with frequencies higher than 10 kHz enable us to detect their nonclassi…
Both inflationary and ekpyrotic scenarios can account for the origin of the large scale structure of the universe. It is often said that detecting primordial gravitational waves is the key to distinguish both scenarios. We show that this is not true if the gauge kinetic function is present in the ekpyrotic scenario. In fact, primordial gravitational waves sourced by the gauge field can be produced in an ekpyrotic universe. We also study scalar fluctuations sourced by the gauge field and show that it is negligible compared to primordial gravitational waves. This comes from the fact that the fas…
We present a simple calculation leading to the quantum gravitationally-induced decoherence of a spatial superposition of a massive object in the linear coupling regime. The point of this calculation is to illustrate that the gravitationally-induced collapse could be of the same origin as any other collapse, i.e. due to the entanglement between the system (here a massive object) and its environment (in this case gravity, but it could well be the electromagnetic or any other field). We then point out that, in some cases, one has to be careful when concluding that matter-wave interference of larg…
We discuss decrease of coherence in a massive system due to the emission of gravitational waves. In particular we investigate environmental gravitational decoherence in the context of an interference experiment. The time-evolution of the reduced density matrix is solved analytically using the path-integral formalism. Furthermore, we study the impact of a tensor noise onto the coherence properties of massive systems. We discuss that a particular choice of tensor noise shows similarities to a mechanism proposed by Diosi and Penrose.
We derive a general quantum master equation for the dynamics of a scalar bosonic particle interacting with a weak, stochastic and classical external gravitational field. The dynamics predicts decoherence in position, momentum and energy. We show how our master equation reproduces the results present in the literature by taking appropriate limits, thus explaining the apparent contradiction in their dynamical description. Our result is relevant in light of the increasing interest in the low energy quantum-gravity regime.
We study the decoherence of atomic interferometers due to the scattering of stochastic gravitational waves. We evaluate the `direct' gravitational effect registered by the phase of the matter waves as well as the `indirect' effect registered by the light waves used as beam-splitters and mirrors for the matter waves. Considering as an example the space project HYPER, we show that both effects are negligible for the presently studied interferometers.
Adopting the viewpoint that the standard perturbative quantization of general relativity provides an effective description of quantum gravity that is valid at ordinary energies, we show that gravity as an environment induces the rapid decoherence of stationary matter superposition states when the energy differences in the superposition exceed the Planck energy scale.
We study the inflationary quantum-to-classical transition for the adiabatic curvature perturbation $ζ$ due to quantum decoherence, focusing on the role played by squeezed-limit mode couplings. We evolve the quantum state $Ψ$ in the Schrödinger picture, for a generic cubic coupling to additional environment degrees of freedom. Focusing on the case of minimal gravitational interactions, we find the evolution of the reduced density matrix for a given long-wavelength fluctuation by tracing out the other (mostly shorterwavelength) modes of $ζ$ as an environment. We show that inflation produces phas…
We study a theory of massive tensor gravitons which predicts blue-tilted and largely amplified primordial gravitational waves. After inflation, while their mass is significant until it diminishes to a small value, gravitons are diluted as non-relativistic matter and hence their amplitude can be substantially amplified compared to the massless gravitons which decay as radiation. We show that such gravitational waves can be detected by interferometer experiments, even if their signal is not observed on the CMB scales.
In this paper we constrain the tilt of the spectra of primordial gravitational waves from Background Imaging of Cosmic Extragalactic Polarization (BICEP2) data only. We find $r=0.21_{-0.10}^{+0.04}$ and $n_t=-0.06_{-0.23}^{+0.25}$ (at $68\%$ C.L.) which implies that a scale-invariant primordial gravitational waves spectra is consistent with BICEP2 nicely. Our results provide strong evidence for supporting inflation model, and the alternative models, for example the ekpyrotic model which predicts $n_t=2$, are ruled out at more than $5σ$ significance.
Real world quantum systems are open to perpetual influence from the wider environment. Quantum gravitational fluctuations provide a most fundamental source of the environmental influence through their universal interactions with all forms of energy and matter causing decoherence. This may have subtle implications on precision laboratory experiments and astronomical observations and could limit the ultimate capacities for quantum technologies prone to decoherence. To establish the essential physical mechanism of decoherence under weak spacetime fluctuations, we carry out a sequence of analytica…
We propose a new mechanism of generating the $μ$ distortion in cosmic microwave background (CMB) originated from primordial gravitational waves. Such $μ$ distortion is generated by the damping of the temperature anisotropies through the Thomson scattering, even on scales larger than that of Silk damping. This mechanism is in sharp contrast with that from the primordial curvature (scalar) perturbations, in which the temperature anisotropies mainly decay by Silk damping effects. We estimate the size of the $μ$ distortion from the new mechanism, which can be used to constrain the amplitude of pri…
We give a first principles derivation of a master equation for the evolution of a quantum matter field in a linearly perturbed Minkowski spacetime, based solely on quantum field theory and general relativity. We make no additional assumptions nor introduce extra ingredients, as is often done in alternative quantum theories. When the quantum matter field is projected to a one-particle state, the master equation for a non-relativistic quantum particle in a weak gravitational field predicts decoherence in the energy basis, in contrast to most existing theories of gravitational decoherence. We poi…
In this article we provide a new closed relationship between cosmic abundance of primordial gravitational waves and primordial blackholes originated from initial inflationary perturbations for inflection-point models of inflation where inflation occurs below the Planck scale. The current Planck constraint on tensor-to-scalar ratio, running of the spectral tilt, and from the abundance of dark matter content in the universe, we can deduce a strict bound on the current abundance of primordial blackholes to be within a range, $9.99712\times 10^{-3}<Ω_{PBH}h^{2}<9.99736\times 10^{-3}$.
There is a growing expectation that the gravitational wave detectors will start probing the stochastic gravitational wave backgrounds in the following years. We explore the spectral shapes of gravitational waves induced to second order by scalar perturbations and presumably have been produced in the early universe. We calculate the gravitational wave spectra generated during radiation and kination eras together with the associated primordial black hole counterpart. We employ power spectra for the primordial curvature perturbation generated by $α$-attractors and nonminimal derivative coupling i…
We investigate the dynamics of two quantum mechanical oscillator system-bath toy models obtained by truncating to zero spatial dimensions linearized gravity coupled to a massive scalar field and scalar QED. The scalar-gravity toy model maps onto the phase damped oscillator, while the scalar QED toy model approximately maps onto an oscillator system subject to two-photon damping. The toy models provide potentially useful insights into solving for open system quantum dynamics relevant to the full scalar QED and weak gravitational field systems, in particular operational probes of the decoherence…
The detection of primordial gravitational waves would not only have extraordinary implications for our understanding of early cosmology, but would also give non-trivial constraints on Standard Model parameters, under the assumption that no new physics enters below the Higgs instability scale. We study the resulting bounds on the top quark mass and the strong coupling constant, discussing their theoretical uncertainties and their robustness against changes in other parameters.
Whether or not the primordial gravitational wave (GW) produced during inflation is sufficiently strong to be observable, GWs are necessarily produced from the primordial curvature perturbations in the second order of perturbation. The induced GWs can be enhanced by curvature perturbations enhanced at small scales or by the presence of matter-dominated stages of the cosmological history. We analytically calculate the integral in the expression of the power spectrum of the induced GWs which is a universal part independent of the spectrum of the primordial curvature perturbations. This makes the …
We investigate the evolution of cosmological perturbations generated during de Sitter inflation in the conformal gravity. Primordial gravitational waves are composed of vector and tensor modes. We obtain the constant vector and tensor power spectra which seems to be correct because the conformal gravity is invariant under conformal transformation like the Maxwell kinetic term.
An observable stochastic background of gravitational waves is generated whenever primordial black holes are created in the early universe thanks to a small-scale enhancement of the curvature perturbation. We calculate the anisotropies and non-Gaussianity of such stochastic gravitational waves background which receive two contributions, the first at formation time and the second due to propagation effects. The former contribution can be generated if the distribution of the curvature perturbation is characterized by a local and scale-invariant shape of non-Gaussianity. Under such an assumption, …
We discuss effects of loss of coherence in low energy quantum systems caused by or related to gravitation, referred to as gravitational decoherence. These effects, resulting from random metric fluctuations, for instance, promise to be accessible by relatively inexpensive table-top experiments, way before the scales where true quantum gravity effects become important. Therefore, they can provide a first experimental view on gravity in the quantum regime. We will survey models of decoherence induced both by classical and quantum gravitational fluctuations; it will be manifest that a clear unders…
