In expanding universes, the entanglement entropy must be time-dependent because the background geometry changes with time. For understanding time evolution of quantum correlations, we take into account two distinct holographic models, the dS boundary model and the braneworld model. In this work, we focus on two-dimensional expanding universes for analytic calculation and comparison. Although two holographic models realize expanding universes in totally different ways, we show that they result in the qualitatively same time-dependence for eternal inflation. We further investigate the time-dependent correlations in the radiation-dominated era of the braneworld model. Intriguingly, the holographic result reveals that a thermal system in the expanding universe is {\it dethermalized} after a critical time characterized by the subsystem size.
We evaluate self-interaction effects on the quantum correlations of field modes of opposite momenta for scalar $λϕ^4$ theory in a two-dimensional asymptotically flat Robertson-Walker spacetime. Such correlations are encoded both in the von-Neumann entropy defined through the reduced density matrix in one of the modes and in the covariance expressed in terms of the expectation value of the number operators for each mode in the evolved state. The entanglement between field modes carries information about the underlying spacetime evolution.
We study the one-photon scalar pair production QED process on the expanding de Sitter spacetime. Using perturbation theory, we obtain the transition probability and study its properties as a function of the expansion parameter $ω$. On flat space the process is forbidden by energy-momentum conservation. It is expected that for a dynamical background there is an energy exchange correlate to the strength of the gravitational field. We use momentum space plots and compute the mean production angle to illustrate this. We show that the mean angle grows with $ω$, but also find that in the flat limit …
We study the evolution of the two scalar fields entangled via a mutual interaction in an expanding spacetime. We compute the logarithmic negativity to leading order in perturbation theory and show that for lowest order in the coupling constants, the mutual interaction will give rise to the survival of the quantum correlations in the limit of the smooth expansion. The results suggest that interacting fields can codify more information about the underlying expansion spacetime and lead to interesting observable effects.
We evaluate the effect of quantum electrodynamics on the correlations between Dirac field modes corresponding electron-positron pairs of opposite momenta generated by expansion of an asymptotically flat Friedmann-Robertson-Walker (FRW) universe. The mutual information of out-going electron-positron pairs is evaluated to leading order in the coupling strength and compared with the free case. It is shown a decrease in the mutual information between the electron and positron. In addition, it is found that the change in the electron-positron mutual information depends on how the momentum is distri…
The exact general evolution of circular strings in $2+1$ dimensional de Sitter spacetime is described closely and completely in terms of elliptic functions. The evolution depends on a constant parameter $b$, related to the string energy, and falls into three classes depending on whether $b<1/4$ (oscillatory motion), $b=1/4$ (degenerated, hyperbolic motion) or $b>1/4$ (unbounded motion). The novel feature here is that one single world-sheet generically describes {\it infinitely many} (different and independent) strings. The world-sheet time $τ$ is an infinite-valued function of the string physi…
The lowest order contribution of the amplitude of the Dirac-Coulomb scattering in de Sitter spacetime is calculated assuming that the initial and final states of the Dirac field are described by exact solutions of the free Dirac equation on de Sitter spacetime with a given momentum and helicity. One studies the difficulties that arises when one passes from the amplitude to cross section.
The lowest order contribution of the amplitude of Dirac-Coulomb scattering in de Sitter spacetime is calculated assuming that the initial and final states of the Dirac field are described by exact solutions of the free Dirac equation on de Sitter spacetime with a given energy and helicity. We find that the total energy is conserved in the scattering process.
The geometric properties of spacetimes representing expanding impulsive gravitational waves, propagating on a flat background and generated by snapped cosmic strings, are studied. The construction of the line element is reviewed, and suitable forms of the string-generating complex mapping are derived for various configurations such as previously studied examples of a pair of snapping cosmic strings. Moreover, these mappings are related to the topology of the flat half-space in front of the wave. Their understanding seems to be crucial for further analysis of the global geometry, the relation b…
We present the complete family of higher dimensional spacetimes that admit a geodesic, shearfree, twistfree and expanding null congruence, thus extending the well-known D=4 class of Robinson-Trautman solutions. Einstein's equations are solved for empty space with an arbitrary cosmological constant and for aligned pure radiation. Main differences with respect to the D=4 case (such as the absence of type III/N solutions, related to ``violations'' of the Goldberg-Sachs theorem in D>4) are pointed out, also in connection with other recent works. A formal analogy with electromagnetic fields is brie…
We show that a dynamical spacetime generates entanglement between modes of a quantum field. Conversely, the entanglement encodes information concerning the underlying spacetime structure, which hints at the prospect of applications of this observation to cosmology. Here we illustrate this point by way of an analytically exactly soluble example, that of a scalar quantum field on a two-dimensional asymptotically flat Robertson-Walker expanding spacetime. We explicitly calculate the entanglement in the far future, for a quantum field residing in the vacuum state in the distant past. In this toy u…
We investigate a quantum teleportation process between two comoving observers Alice and Bob in an anisotropic expanding spacetime. In this model, we calculate the fidelity of teleportation and we noted an oscillation of its spectrum as a function of the azimuthal angle. We found that for the polar angle $ϕ= \fracπ{2}$ and the azimuthal angle $θ\neq \frac{3π}{4} + nπ$ with $n = 0, 1, 2, ...$ the efficiency of the process decreases, i.e., the fidelity is less than one. In addition, it is shown that the anisotropic effects on the fidelity becomes more significative in the regime of smooth expansi…
Phonons have the characteristic linear dispersion relation of massless relativistic particles. They arise as low energy excitations of Bose-Einstein condensates and, in nonhomogeneous situations, are governed by a space- and time-dependent acoustic metric. We discuss how this metric can be experimentally designed to realize curved spacetime geometries, in particular, expanding Friedmann-Lemaître-Robertson-Walker cosmologies, with negative, vanishing, or positive spatial curvature. A nonvanishing Hubble rate can be obtained through a time-dependent scattering length of the background condensate…
The interest of part of the quantum-gravity community in the possibility of Planck-scale-deformed Lorentz symmetry is also fueled by the opportunities for testing the relevant scenarios with analyses, from a signal-propagation perspective, of observations of bursts of particles from cosmological distances. In this respect the fact that so far the implications of deformed Lorentz symmetry have been investigated only for flat (Minkowskian) spacetimes represents a very significant limitation, since for propagation over cosmological distances the curvature/expansion of spacetime is evidently tangi…
General properties of Kerr-Schild spacetimes with (A)dS background in arbitrary dimension are studied. It is shown that the geodetic Kerr-Schild vector k is a multiple WAND of the spacetime. Einstein Kerr-Schild spacetimes with non-expanding k are shown to be of Weyl type N, while the expanding spacetimes are of type II or D. It is shown that this class of spacetimes obeys the optical constraint. This allows us to solve Sachs equation, determine r-dependence of boost weight zero components of the Weyl tensor and discuss curvature singularities.
We obtain a non-relativistic diffeomorphism invariant string action as a special limit of the Nambu-Goto action in an FLRW background. We use this action to study non-relativistic string dynamics in an expanding universe and construct an analytic model describing the macroscopic properties of non-relativistic string networks. The non-relativistic constraint equations allow arbitrarily small string velocities and thus a `frustrated' equation of state for non-interacting strings can be obtained without the need of a velocity damping mechanism. Assuming that colliding string segments reconnect by…
In this work, we investigate how the anisotropy affects the cosmological parameters estimation. Here the anisotropy is incorporated as a small gravitational disturbance. We calculate the Fisher information for both cosmological parameters $ε$ (expansion volume) and $ρ$ (expansion rate), and we show that the anisotropy introduces oscillations in the Fisher information spectrum. This implies that the estimation of the cosmological parameters is sensible to the direction of the momentum $k$ of particles. In addition, we observe that for small values of the momentum $k$ there is a substantial diff…
It was recently shown that velocity-dependent forces between parallel fundamental strings moving apart in a $D-$dimensional spacetime implied an accelerating expanding universe in $D-1$-dimensional space-time. Exact solutions were obtained for the early time expansion in $D=5,6$. Here we show that this result also holds for fundamental strings in the background of a fivebrane, and argue that the feature of an accelerating universe would hold for more general $p$-brane-seeded models.
We examine a quantised massive scalar field in $(1+1)$-dimensional spatially compact cosmological spacetimes in which the early time and late time expansion laws provide distinguished definitions of Fock "in" and "out" vacua, with the possible exception of the spatially constant sector, which may become effectively massless at early or late times. We show, generalising the work of Ford and Pathinayake, that when such a massive zero mode occurs, the freedom in the respective "in" and "out" states is a family with two real parameters. As an application, we consider massive untwisted and twisted …
The emergence of (3+1)-dimensional expanding spacetime from complex Langevin simulations of the Lorentzian type IIB matrix model with deformations
National Technical University of Athens（雅典国立技术大学）；Setsunan University（摂南大学）；Università degli Studi di Milano-Bicocca（米兰比可卡大学）；Istituto Nazionale di Fisica Nucleare (INFN)（意大利国家核物理研究所）；High Energy Accelerator Research Organization（高能加速器研究机构）；SOKENDAI（日本综合研究大学院大学）；Shizuoka University（静冈大学）
We investigate general properties of Kerr-Schild (KS) metrics in n>4 spacetime dimensions. First, we show that the Weyl tensor is of type II or more special if the null KS vector k is geodetic (or, equivalently, if T_{ab}k^ak^b=0). We subsequently specialize to vacuum KS solutions, which naturally split into two families of non-expanding and expanding metrics. After demonstrating that non-expanding solutions are equivalent to the known class of vacuum Kundt solutions of type N, we analyze expanding solutions in detail. We show that they can only be of the type II or D, and we characterize opti…
We study the time evolution of entanglement entropy in expanding universes with various matters. To describe expanding universes holographically, we take into account a braneworld moving in an asymptotic AdS space involving a uniform $p$-brane gas. In the braneworld model, an observer living in the braneworld detects the bulk motion of the braneworld as an expanding universe. We show that the entanglement entropy of expanding universes increases by the volume law in the early time and by the area law in the late time. We further consider the cosmological horizon, which is the border of the vis…
Five dimensional gravity coupled, both in the bulk and on a brane, to a scalar Liouville field yields a geometry confined to a strip around the brane and with time dependent scale factors for the four geometry. In various limits known models can be recovered as well as a temporally expanding four geometry with a warp factor falling exponentially away from the brane. The effective theory on the brane has a time dependent Planck mass and ``cosmological constant''. Although the scale factor expands, the expansion is not an acceleration.
We compute the boundary stress-energies of time-dependent asymptotically AdS spacetimes in 5 and 7 dimensions, and find that their traces are equal to the respective 4 and 6 dimensional field-theoretic trace anomalies. This provides good supporting evidence in favour of the AdS/CFT correspondence in time-dependent backgrounds.
This paper has been withdrawn by the authors in order to replace it with a more correct treatment. The basic results remain the same but the treatment is more rigorously correct.
Besides tunneling in static potential landscapes, for example, the Wentzel-Kramers-Brillouin (WKB) approach is a powerful nonperturbative approximation tool to study particle creation due to time-dependent background fields, such as cosmological particle production or the Sauter-Schwinger effect, i.e., electron-positron pair creation in a strong electric field. However, our understanding of particle creation processes in background fields depending on both space and time is rather incomplete. In order to venture into this direction, we propose a generalization of the WKB method to truly spacet…
We consider a D5-brane solution in AdS black hole spacetime. This is a defect solution moving in subspace of AdS5 x S5. This non-local object is realized by the probe D5-brane moving in black hole spacetime. We found this probe brane does not penetrate the black hole horizon. We also found the solution does not depend on the motion on S5 subspace.
We consider an eight-dimensional Einstein-Yang-Mills theory to explore whether Yang-Mills instantons formed in extra dimensions can induce the dynamical instability of our four-dimensional spacetime. We show that the Yang-Mills instantons in extra dimensions can trigger the expansion of our universe in four-dimensional spacetime as well as the dynamical compactification of extra dimensions. We also discuss a possibility to realize a reheating mechanism via the quantum back-reaction from the contracting tiny internal space with a smeared instanton.
We investigate the quantum estimation on the Hubble parameter of an expanding de Sitter space by quantum metrological techniques. By exploring the dynamics of a freely falling Unruh-DeWitt detector, which interacts with a scalar field coupling to curvature, we calculate the Fisher information (FI) and quantum Fisher information (QFI) for the detector, which bound the highest precision of the estimation on Hubble parameter. In standard Bunch-Davies vacuum, we show that the maxima of FI/QFI are located for particular initial state of probe. Beside its dependence on the evolving time of detector …
We study quantum effects in the presence of a spherical semi-transparent mirror or a system of two concentric mirrors which expand with a constant acceleration in a flat D-dimensional spacetime. Using the Euclidean approach, we obtain expressions for fluctuations and the renormalized value of stress-energy tensor for a scalar non-minimally coupled massless field. Explicit expressions are obtained for the energy fluxes at the null infinity generated by such mirrors in the physical spacetime and their properties are discussed.
We discuss several aspects of particle production in: (a) time dependent electric field and (b) expanding Friedmann background. In the first part of the paper, we provide an algebraic mapping between the differential equations describing these two phenomena. This mapping allows a direct comparison between (a) and (b) and we highlight several interesting features of both cases using this approach. We determine the form of the (equivalent) electric field corresponding to different Friedmann spacetimes and discover, for example, a time-dependent electric field which, in a specific limit, leads to…
We study the phenomenon of mass loss by a scalar charge -- a point particle that acts a source for a noninteracting scalar field -- in an expanding universe. The charge is placed on comoving world lines of two cosmological spacetimes: a de Sitter universe, and a spatially-flat, matter-dominated universe. In both cases, we find that the particle's rest mass is not a constant, but that it changes in response to the emission of monopole scalar radiation by the particle. In de Sitter spacetime, the particle radiates all of its mass within a finite proper time. In the matter-dominated cosmology, th…
We address the optimal estimation of quantum parameters, in the framework of local quantum estimation theory, for a massive scalar quantum field in the expanding Robertson-Walker universe exhibiting Lorentz invariance violation (LIV). The information about the history of the expanding spacetime in the presence of LIV can be extracted by taking measurements on the entangled state of particle modes. We find that, in the estimation of cosmological parameters, the ultimate bounds to the precision of the Lorentz-invariant massive scalar field can be improved due to the effects of LIV under some app…
We propose an executable scheme to mimic the expanding cosmos in 1+2 dimensions in laboratory. Furthermore, we develop a general procedure to use nonlinear metamaterials to mimic D-brane and noncommutativity in string theory.
An analysis is first given of the situation where a scalar field is contained between two fixed, spatially flat, branes. The usual fine-tuning (RS) condition is relaxed, and the branes are allowed to possess a positive effective cosmological constant λ. We first analyze the eigenvalue problem for the Kaluza-Klein masses when the metric is time dependent, and consider in detail the case when λis small. Thereafter we consider, in the case of one single brane, the opposite limit in which λis large, acting in a brief period of time T, and present a "sudden approximation" calculation of the energy …
In this paper we study the quantum brownian motion of a scalar point particle in the analog Friedman-Robertson-Walker spacetime in the presence of a disclination, in a condensed matter system. The analog spacetime is obtained as an effective description of a Bose-Einstein condensate in terms of quantum excitations of sound waves, named phonons. The dynamics of the phonons is described by a massless real scalar field whose modes are also subjected to a quasi-periodic condition. In this sense, we find exact solutions for the real scalar field in this scenario and calculate the two-point function…
We present evidence that recent numerical results from the reduced classical equations of the Lorentzian IIB matrix model can be interpreted as corresponding to the emergence of an expanding universe. In addition, we propose an effective metric to describe the emerging (3+1)-dimensional spacetime. This metric gives, at all times, finite values for the Ricci and Kretschmann curvature scalars. With these results, we are able to give a heuristic discussion of the origin of the Universe in the context of the IIB matrix model.
We present a time-dependent and spatially inhomogeneous solution that interpolates the extremal Reissner-Nordström (RN) black hole and the Friedmann-Lemaître-Robertson-Walker (FLRW) universe with arbitrary power-law expansion. It is an exact solution of the $D$-dimensional Einstein-"Maxwell"-dilaton system, where two Abelian gauge fields couple to the dilaton with different coupling constants, and the dilaton field has a Liouville-type exponential potential. It is shown that the system satisfies the weak energy condition. The solution involves two harmonic functions on a $(D-1)$-dimensional Ri…
We examine several different types of five dimensional stationary spacetimes with bulk scalar fields and parallel 3-branes. We study different methods for avoiding the appearance of spacetime singularities in the bulk for models with and without cosmological expansion. For non-expanding models, we demonstrate that in general the Randall-Sundrum warp factor is recovered in the asymptotic bulk region, although elsewhere the warping may be steeper than exponential. We show that nonsingular expanding models can be constructed as long as the gradient of the bulk scalar field vanishes at zeros of th…
We show that the velocity-dependent forces between parallel fundamental strings moving apart in a D-dimensional spacetime imply an expanding universe in (D-1)-dimensional spacetime.
We present a new approach to the problem of the thermodynamical equilibrium of a quantum relativistic fluid in a curved spacetime in the limit of small curvature. We calculate the mean value of local operators by expanding the four-temperature Killing vector field in Riemann normal coordinates about the same spacetime point and we derive corrections with respect to the flat spacetime expressions. Thereby, we clarify the origin of the terms proportional to Riemann and Ricci tensors introduced in general hydrodynamic expansion of the stress-energy tensor.
A direct relation between the time dependent Milne geometry and the Rindler spacetime is shown. Milne's metric corresponds to that one beyond Rindler's event horizon (in the region $t \succ |x|)$). It was found that the shear tensor from the dissipative term of the RHIC expanding fireball has the same structure as that corresponding to the anisotropic fluid from the black hole interior, even though the latter geometry is curved.
The time evolution of self-interacting spherically symmetric scalar fields in Minkowski spacetime is investigated based on the use of Green's theorem. It is shown that a massive Klein-Gordon field can be characterized by the formation of certain expanding shell structures where all the shells are built up by very high frequency oscillations. This oscillation is found to be modulated by the product of a simple time decaying factor of the form $t^{-{3}/{2}}$ and of an essentially self-similar expansion. Apart from this self-similar expansion the developed shell structure is preserved by the evol…
For a 4-dimensional spatially-flat Friedmann-Robertson-Walker universe with a scalar field $ϕ(x)$, potential $V(ϕ)$ and constant equation of state $w=p/ρ$, we show that an expanding solution characterized by $ε=3(1+w)/2$ produces the same scalar perturbations as a contracting solution with $\hatε=1/ε$. The same symmetry applies to both the dominant and subdominant scalar perturbation modes. This result admits a simple physical interpretation and generalizes to $d$ spacetime dimensions if we define $ε\equiv [(2d-5)+(d-1)w]/(d-2)$.
The lack of energy conservation introduces new particle processes in curved spacetime that are forbidden in flat space. Therefore one has to be very cautious about using the results calculated in Minkowskian space in early universe applications. This is true for particle decay rates in particular, which need to be calculated using quantum field theory in curved spacetime. Previous studies are usually restricted to using minimal or conformal coupling for the decaying particle, while using a more general coupling would give deeper insight into particle decay. This paper presents the results we o…
The primordial Universe might be highly inhomogeneous. We perform the 3+1D Numerical Relativity simulation for the evolution of scalar field in an initial inhomogeneous expanding Universe, and investigate how it populates the landscape with both de Sitter (dS) and AdS vacua. The simulation results show that eventually either the field in different region separates into different vacua, so that the expanding dS or AdS bubbles (the bubble wall is expanding but the spacetime inside AdS bubbles is contracting) come into being with clear bounderies, or overall region is dS expanding with a few smal…
In this work, we have obtained the solutions of the (1 + 1) dimensional Dirac equation on a gravitational background within the generalized uncertainty principle. We have shown that how minimal length parameters effect the Dirac particle in a spacetime described by conformally flat metric. Also, supersymmetric quantum mechanics is used both to factorize the Dirac Hamiltonians and obtain new metric functions. Finally, it is observed that the energy dependent potentials may be extended to the energy dependent metric functions.
