Evolution of Small Scale Cosmological Baryon Perturbations and Matter Transfer Functions

The evolution of small scale cosmological perturbations is carefully re-examined. Through the interaction with photons via electrons, baryon perturbations show interesting behavior in some physical scales. Characteristic features of the evolution of baryon density fluctuations are discussed. In CDM models, it is found a power-law growing phase of the small-scale baryon density fluctuations, which is characterized by the terminal velocity, after the diffusion (Silk) damping and before the decoupling epoch. Then, a transfer function for total matter density fluctuations is studied by taking into account those physical processes. An analytic transfer function is presented, which is applicable for the entire range up to a solar mass scale in the high$-z$ universe, and it is suitable also to the high baryon fraction models.Comment: 29 pages, LaTex, Submitted to Astrophysical Journa

Kron Reduction and Effective Resistance of Directed Graphs

In network theory, the concept of effective resistance is a distance measure on a graph that relates the global network properties to individual connections between nodes. In addition, the Kron reduction method is a standard tool for reducing or eliminating the desired nodes, which preserves the interconnection structure and the effective resistance of the original graph. Although these two graph-theoretic concepts stem from the electric network on an undirected graph, they also have a number of applications throughout a wide variety of other fields. In this study, we propose a generalization of a Kron reduction for directed graphs. Furthermore, we prove that this reduction method preserves the structure of the original graphs, such as the strong connectivity or weight balance. In addition, we generalize the effective resistance to a directed graph using Markov chain theory, which is invariant under a Kron reduction. Although the effective resistance of our proposal is asymmetric, we prove that it induces two novel graph metrics in general strongly connected directed graphs. In particular, the effective resistance captures the commute and covering times for strongly connected weight balanced directed graphs. Finally, we compare our method with existing approaches and relate the hitting probability metrics and effective resistance in a stochastic case. In addition, we show that the effective resistance in a doubly stochastic case is the same as the resistance distance in an ergodic Markov chain

Consistency between causality and complementarity guaranteed by the Robertson inequality in quantum field theory

It has long been debated whether gravity should be quantized or not. Recently, the authors in [Sci. Rep. 6, 22777 (2016); Proc. Natl. Acad. Sci. U.S.A. 106, 3035 (2009)] discussed the inconsistency between causality and complementarity in a Gedankenexperiment involving the quantum superposition of massive/ charged bodies, and Belenchia et al. [Phys. Rev. D 98, 126009 (2018); Int. J. Mod. Phys. D 28, 1943001 (2019)] resolved the inconsistency by requiring the quantum radiation and vacuum fluctuations of gravitational/electromagnetic field. Stimulated by their works, we reanalyze the consistency between the two physical properties, causality and complementarity, according to the quantum field theory. In this analysis, we consider a Gedankenexperiment inspired by [Sci. Rep. 6, 22777 (2016); Proc. Natl. Acad. Sci. U.S.A. 106, 3035 (2009); Phys. Rev. D 98, 126009 (2018); Int. J. Mod. Phys. D 28, 1943001 (2019)], in which two charged particles coupled with a photon field are in a superposition of two trajectories. First, we observe that causality is satisfied by the retarded propagation of the photon field. Next, by introducing an inequality between visibility and which-path information, we show that the quantum radiation and vacuum fluctuations of the photon field ensure complementarity. We further find that the Robertson inequality associated with the photon field leads to the consistency between causality and complementarity in our Gedankenexperiment. Finally, we mention that a similar feature appears in the quantum field of gravity.Comment: 14 pages, 3 figure

Quantum uncertainty of gravitational field and entanglement in superposed massive particles

Investigating the quantum nature of gravity is an important issue in modern physics. Recently, studies pertaining to the quantum superposition of gravitational potential have garnered significant interest. Inspired by Mari \textit{et al.} [Sci. Rep. {\bf 6} 22777 (2016)] and Baym and Ozawa [Proc. Natl. Acad. Sci. U.S.A. {\bf 106}, 3035 (2009)], Belenchia \textit{et al.} [Phys. Rev. D {\bf 98}, 126009 (2018)] considered a gedanken experiment involving such a quantum superposition and mentioned that the superposition renders causality and complementarity inconsistent. They resolved this inconsistency by considering the quantized dynamical degrees of freedom of gravity. This suggests a strong relationship between the quantum superposition of the gravitational potential and the quantization of the gravitational field. In our previous study [Phys. Rev. D {\bf 106}, 125002 (2022)], we have shown that the quantum uncertainty of a field guarantees the consistency between causality and complementarity. In this study, we focus on the entanglement between two particles' states due to the electromagnetic/gravitational potential and investigate its relationship with quantum uncertainty, causality, and complementarity. Our numerical analyses show that the quantum uncertainty of the electromagnetic/gravitational field results in vacuum fluctuations and prohibits the entanglement between two particles' states when causality is satisfied. We further demonstrate that complementarity holds when the particles do not get entangled. The uncertainty relation does not cause the entanglement between two particles' states, which guarantees complementarity.Comment: 15pages, 5 figure

Nonlinear Evolution of Very Small Scale Cosmological Baryon Perturbations at Recombination

The evolution of baryon density perturbations on very small scales is investigated. In particular, the nonlinear growth induced by the radiation drag force from the shear velocity field on larger scales during the recombination epoch, which is originally proposed by Shaviv in 1998, is studied in detail. It is found that inclusion of the diffusion term which Shaviv neglected in his analysis results in rather mild growth whose growth rate is $\ll 100$ instead of enormous amplification $\sim 10^4$ of Shaviv's original claim since the diffusion suppresses the growth. The growth factor strongly depends on the amplitude of the large scale velocity field. The nonlinear growth mechanism is applied to density perturbations of general adiabatic cold dark matter (CDM) models. In these models, it has been found in the previous works that the baryon density perturbations are not completely erased by diffusion damping if there exists gravitational potential of CDM. With employing the perturbed rate equation which is derived in this paper, the nonlinear evolution of baryon density perturbations is investigated. It is found that: (1) The nonlinear growth is larger for smaller scales. This mechanism only affects the perturbations whose scales are smaller than $\sim 10^2M_\odot$, which are coincident with the stellar scales. (2) The maximum growth factors of baryon density fluctuations for various COBE normalized CDM models are typically less than factor 10 for $3-\sigma$ large scale velocity peaks. (3) The growth factor depends on $\Omega_{\rm b}$.Comment: 24 pages, 9 figures, submitted to Ap

Expanding Edges of Quantum Hall Systems in a Cosmology Language -- Hawking Radiation from de Sitter Horizon in Edge Modes

Expanding edge experiments are promising to open new physics windows of quantum Hall systems. In a static edge, the edge excitation, which is described by free fields decoupled with the bulk dynamics, is gapless, and the dynamics preserve conformal symmetry. When the edge expands, such properties need not be preserved. We formulate a quantum field theory in 1+1 dimensional curved spacetimes to analyze the edge dynamics. We propose methods to address the following questions using edge waveforms from the expanding region: Does the conformal symmetry survive? Is the nonlinear interaction of the edge excitations induced by edge expansion? Do the edge excitations interact with the bulk excitations? We additionally show that the expanding edges can be regarded as expanding universe simulators of two-dimensional dilaton-gravity models, including the Jackiw-Teitelboim gravity model. As an application, we point out that our theoretical setup might simulate emission of analog Hawking radiation with the Gibbons-Hawking temperature from the future de Sitter horizon formed in the expanding edge region.Comment: A subtitle and arguments about Hawking radiation in de Sitter space are adde