arXiv subjects

Bichu Li

Publications and source records attributed to Bichu Li.

9 recordsLinked to original sources

arXiv2026

A Bogoliubov-ratio framework for quantum-information diagnostics of time-dependent two-mode Boson Hamiltonian

We present a compact and unified framework for quantum-information diagnostics of time-dependent two-mode bosonic systems based on the Bogoliubov ratio $\lambda_k(\eta) \equiv \beta_k(\eta)/\alpha_k(\eta)$. For a general time-dependent quadratic two-mode Hamiltonian, the state dynamics is exactly reduced to a single complex Riccati equation for $\lambda_k$. Upon tracing out one partner mode, the spectrum of the one-mode reduced density matrix is determined entirely by the squared magnitude $q_k(\eta) = \vert{}\lambda_k(\eta)\vert{}^2$. Consequently, we could construct the explicit, model-independent formula for the reduced-state purity, linear entropy, R\'enyi-2 entropy, and von Neumann entropy without reconstructing and diagonalizing the reduced density matrix on a model-by-model basis using coupled squeezing parameters ($r_k, \phi_k$). We demonstrate the utility of this framework in two distinct non-stationary setups: primordial cosmological perturbations and a chirped-pulse nondegenerate optical parametric amplifier. In the cosmological context, our formulation clarifies how background-induced phase rotation and frequency softening regulate squeezing growth and state mixedness; in the optical domain, it captures the delayed onset, suppression of squeezing accumulation, and late-time entropy saturation induced by finite pump duration and frequency chirp. By cleanly factorizing model-dependent driving protocols from universal information-theoretic metrics, this framework offers an efficient, standardized diagnostic tool for a broad class of parametrically driven quadratic bosonic systems.

quant-ph↗

arXiv2026

Quantum-information diagnostics of cosmological perturbations with nontrivial sound speed in inflation

In this work, we systematically investigate the quantum-information diagnostics of cosmological perturbations with a nontrivial sound speed, utilizing a normalized open two-mode squeezed-state framework. Rather than introducing new observables, our analysis focuses on how a modified sound speed dynamically reshapes the Schr\"odinger evolution of the squeezing parameters ($r_k$ and $\phi_k$). We demonstrate how these dynamical changes are inherited by the reduced density matrix of the observable sector. By employing a sound-speed-resonance parametrization, we derive and evaluate the purity, von Neumann entropy, R\'enyi entropies, and logarithmic negativity. To overcome the intrinsic multiscale stiffness of the post-inflationary equations, we introduce a bounded variable $x = \tanh r_k$ as a partial regularization, which enables reliable numerical simulations exclusively within the inflationary regime. Our numerical results reveal that a nontrivial sound speed significantly suppresses the purity of the reduced state, indicating enhanced effective mixedness. Simultaneously, it strongly amplifies and modulates both the entropic and entanglement diagnostics. More precisely, a nontrivial sound speed postpones the onset of classicality by modulating the decoherence process. Ultimately, we show that a nontrivial sound speed leaves distinct and identifiable quantum-information signatures within the entanglement structure of the early universe.

gr-qc↗

arXiv2026

Non-minimally Coupled Running Curvaton for DESI-preferred Dynamical Dark Energy and Hubble Tension

Recent DESI 2025 results have renewed interest in dynamical dark energy models with phantom crossing. In this work, we extend the running curvaton scenario by introducing a non-minimal gravitational coupling, $\xi \chi^2 R$. We show that this coupling can drive the late-time equation of state into the DESI-preferred region in the $(w_0,w_a)$ plane. We further find that, at leading order, the early-universe predictions of the original running curvaton model can be preserved through a parameter redefinition, while the scalar sector remains free of gradient instability in the regime considered. A parameter scan identifies viable regions and a benchmark solution that also shifts the background-inferred value of $H_0$ upward. These results suggest that the non-minimally coupled running curvaton provides a viable framework for DESI-motivated dark energy evolution, with possible implications for the Hubble tension.

astro-ph.CO↗

arXiv2025

A quantum information method for early universe with non-trivial sound speed

Many quantum gravitational frameworks, such as DBI inflation, k-essence, and effective field theories obtained by integrating out heavy modes, can lead to a non-trivial sound speed. Meanwhile, our universe can be described as an open system. Under the non-trivial sound speed, we employ the method of open quantum systems combined with Arnoldi iterations to study the Krylov complexity throughout the early universe, including the inflationary, radiation-dominated, and matter-dominated epochs. A key ingredient in our analysis is the open two-mode squeezed state formalism and the generalized Lanczos algorithm. To numerically compute the Krylov complexity, we are the first time to derive the evolution equations for the parameters $r_k$ and $\phi_k$ within an open two-mode squeezed state. Our results indicate that the Krylov complexity exhibits a similar trend in both the standard case and the case with non-trivial sound speed. To distinguish between these two scenarios, we also investigate the Krylov entropy for completeness. The evolution of the Krylov entropy shows a clear difference between the standard case and the non-trivial sound speed case. Furthermore, based on the behavior of the Lanczos coefficients, we find that the case of non-trivial sound speed behaves as a maximally chaotic system. However, our numerical results suggest that the Krylov complexity does not saturate to a constant value due to the huge expansion of spacetime background. This study offers a new perspective for exploring the early universe through the quantum information.

gr-qc↗

arXiv2025

Microlensing of dark matter models in the Milky Way

We investigate constraints on the abundance of primordial black holes (PBHs) as dark matter (DM) candidates using five years of microlensing data from the OGLE survey. While the majority of OGLE's $\sim\!2000$ microlensing events are well-explained by stellar populations such as brown dwarfs, main-sequence stars, and compact remnants, a subset of six ultrashort-timescale events ($t_E \sim 0.1\text{--}0.3~\mathrm{days}$) may signal the presence of PBHs. Building upon prior work that adopted the Navarro-Frenk-White (NFW) DM profile, we examine how alternative DM halo models -- specifically the Einasto and Burkert profiles, affect microlensing predictions and the constraints on PBH abundance. In light of kinematic data of Milky Way, we could obtain the range of ($r_s, \rho_s$) for both profiles. We computed differential microlensing event rates for both profiles, using the main-sequence star rate as an observational benchmark. Our results show that neither the Einasto nor Burkert profiles reproduce the distribution of main-sequence star events, yet both allow for viable explanations of the ultrashort-timescale events with PBH masses $M_{\mathrm{PBH}} \sim 10^{-5} M_\odot$. Using a Poisson likelihood analysis under the null hypothesis that no PBH is observed in OGLE dataset, we derive $95\%~\text{C.L.}$ upper and lower bounds on $f_{\mathrm{PBH}}$ for both profiles, finding that the constraints are significantly relaxed under Burkert profiles compared to the NFW case. These results show the sensitivity of PBH constraints to the assumed DM halo structure and highlight the importance of accurately modeling the inner Galactic density profile to robustly assess PBH dark matter scenarios.

astro-ph.GA↗

arXiv2024

The evolution of two-point correlation function of galaxies with a twin-peak initial power spectrum

The evolution equation of two-point correlation function $\xi$ of galaxies can analytically describe the large scale structure of the galaxy distribution, and the solution depends also upon the initial condition. The primeval spectrum of the baryon acoustic oscillations (BAO) contains multi peaks that survived the Silk damping, and, as a relevant portion, two peaks of the primeval BAO spectrum fall into the range of current galaxy surveys. Incorporating this portion, we use a twin-peak initial power spectrum of the galaxies, and obtain the evolution solution from a redshift $z=8$ to $z=0$ in the Gaussian approximation. The outcome $\xi(r)$ at $z=0.6$ still exhibits the 100 Mpc periodic bumps as observed by the WiggleZ survey, a feature largely determined by the Jeans length $\lambda_J$ in the equation. In particular, due to the superposition of the twin peaks in the initial condition, $\xi(r)$ shows a shallow trough at $\sim 70 h^{-1}$Mpc and a deep trough at $\sim 140 h^{-1}$Mpc, agreeing with the observational data, much better than our previous work that used a simple one-peak initial spectrum.

astro-ph.GA↗

arXiv2024

Space-based optical lattice clocks as gravitational wave detectors in search for new physics

We investigate the sensitivity and performance of space-based Optical Lattice Clocks (OLCs) in detecting gravitational waves, in particular the Stochastic Gravitational Wave Background (SGWB) at low frequencies $(10^{-4}, 1) \rm Hz$, which are inaccessible to ground-based detectors. We first analyze the response characteristics of a single OLC detector for SGWB detection and compare its sensitivity with that of Laser Interferometer Space Antenna (LISA). Due to longer arm lengths, space-based OLC detectors can exhibit unique frequency responses and enhance the capability to detect SGWB in the low-frequency range, but the sensitivity of a single OLC detector remains insufficient overall compared to LISA. Then, as a preliminary plan, we adopt a method of cross-correlation on two OLC detectors to improve the signal-to-noise ratio (SNR). This method leverages the uncorrelated origins but statistically similar properties of noise in two detectors while the SGWB signal is correlated between them, thus achieving effective noise suppression and sensitivity enhancement. Future advancements in OLC stability are expected to further enhance their detection performance. This work highlights the potential of OLC detectors as a promising platform for SGWB detection, offering complementary capabilities to LISA, and opening an observational window into more astrophysical sources and the early universe.

gr-qc↗

arXiv2023

The backreaction effect of the sound speed resonance in DBI inflation

We examine the backreaction effect of the enhanced small-scale scalar perturbations from the sound speed resonance (SSR) mechanism for primordial black hole formation in Dirac-Born-Infeld (DBI) inflation on background as well as curvature perturbation, which can generate a considerable amount of primordial black holes (PBH) in the radiation-dominated epoch. Within the perturbative regime, the backreaction effect of perturbations on the background dynamics can be described by an effective action after integrating out the perturbation sector. Starting with the effective field theory of a specific DBI inflation model that incorporates SSR, we obtain the one-loop effective action by integrating out the scalar perturbations at the quadratic level. Using the effective Friedmann equations derived from this one-loop effective action, we solve the Hubble parameter with backreaction and the effective perturbation dynamics on this background as well. Our numerical findings reveal that, for a viable parameter space, the backreaction effect results in a relative correction to the Hubble parameter of approximately $10^{-7}$, whereas the relative correction to the slow-roll parameter can vary between $-0.3$ and $0.1$, before gradually converging to $10^{-7}$. Furthermore, our results show that the backreaction effect on SSR sound speed causes a slight reduction in the resonant peak of the curvature power spectrum, and the subsequent PBH formation predicted by the SSR mechanism remains almost unchanged.

astro-ph.CO↗

arXiv2021

The nonlinear equation of correlation function of galaxies in the expanding universe and the solution in linear approximation

We present an analytic study of the density fluctuation of a Newtonian self-gravity fluid in the expanding universe with $Ω_Λ+Ω_m=1$, which extends our previous work in the static case. By use of field theory techniques, we obtain the nonlinear, hyperbolic equation of 2-pt correlation function $ξ$ of perturbation. Under the Zel'dolvich approximation the equation becomes an integro-differential equation and contains also the 3-pt and 4-pt correlation functions. By adopting the Groth-Peebles and Fry-Peebles ansatz, the equation becomes closed, contains a pressure term and a delta source term which were neglected in Davis and Peebles' milestone work. The equation has three parameters of fluid: the particle mass $m$ in the source, the overdensity $γ$, and the sound speed $c_s$. We solve only the linear equation and apply to the system of galaxies. We assume two models of $c_s$ and, take an initial power spectrum at a redshift $z=7$, which inherits the relevant imprint from the spectrum of baryon acoustic oscillations at the decoupling. The solution $ξ({\bf r}, z)$ is growing during expansion, and contains $100$Mpc periodic bumps at large scales, and a main mountain (a global maximum with $ξ\propto r^{-1}$) at small scales $r\lesssim 50$Mpc. The profile of $ξ$ agrees with the observed ones from galaxy and quasar surveys. The bump separation is given by the Jeans length $λ_J$ as the correlation scale, also modified by $γ$ and $c_s$. The main mountain is largely generated by the source $\propto m$ as the clustering scale. Since the outcome is affected by the initial condition and the parameters as well, it is hard to infer the imprint of baryon acoustic oscillations accurately. The difficulties with the sound horizon as a distance ruler are pointed out.

astro-ph.CO↗