Dynamical Dark Energy in Light of Cosmic Distance Measurements.Ⅰ.A Demonstration Using Simulated Datasets

We develop methods to extract key dark energy information from cosmic distance measurements including the BAO scales and supernova(SN) luminosity distances.Demonstrated using simulated data sets of the complete DESI,LSST and Roman surveys designed for BAO and SN distance measurements,we show that using our method,the dynamical behavior of the energy,pressure,equation of state(with its time derivative) of dark energy and the cosmic deceleration function can all be accurately recovered from high-quality data,which allows for robust diagnostic tests for dark energy models.

Classical Cosmology I. Anomalous Redshift for Galaxies in NED-D

Three mechanisms for an alternative to the Doppler effect as an explanation for the redshift are reviewed. A fourth mechanism is the attenuation of the light as given by the Beer-Lambert law. The average value of the Hubble constant is therefore derived by processing the galaxies of the NED-D catalog in which the distances are independent of the redshift. The observed anisotropy of the Hubble constant is reproduced by adopting a rim model, a chord model, and both 2D and 3D Voronoi diagrams.

Classical Cosmology III. Modified Tired Light and Distance Modulus for Supernovae

We analyze a simple model for tired light in a cosmological environment, a generalized model, and a spectroscopic model. The three models are tested on different compilations for the distance modulus of supernovae. The tests are negative for the simple tired light and the spectroscopic models, but positive for the generalized tired light model. The percentage error of the distance modulus for the generalized tired light model compared with the distance modulus of standard cosmology is less than one percent over the considered ranges in redshift.

Estimating the power spectrum of a discrete cosmic momentum field with fast Fourier transform

Fast Fourier transform based estimators are formulated for measuring momentum power spectra,including the auto power spectra of the momentum,the momentum divergence,and the cross spectrum of density fluctuation and momentum divergence.Algorithms using the third order Bettle-Lemariéscaling function to assign discrete objects to regular grids for fast Fourier transform are proposed to clean alias effects.Numerical experiments prove that the implementation can achieve sub-percent precision till close to the Nyquist frequency.The impact of removing bulk flow on the estimation of momentum power spectra is derived theoretically and verified numerically.Subtracting bulk flow has little effects at large scales but might induce meaningful differences in nonlinear regime,and probably it is not necessary to subtract bulk flow for samples which peculiar velocities are exact or sufficiently accurate.Momentum power spectra of dark matter samples from N-body simulation are measured and discussed.As expected,the prediction of the one loop Eulerian perturbation theory agrees with simulation only slightly better than the linear theory at z=0,but can be applied to higher redshift with improved accuracy.Measurements of simulation data and the one loop Eulerian theory both reveal that the momentum field contains strong rotational part,and there is a large stochastic component in the divergence of momentum which is not correlated with the density field.The three kinds of momentum power spectra have their own characteristics.

New Probability Distributions in Astrophysics: V. The Truncated Weibull Distribution

We demonstrate that certain astrophysical distributions can be modelled with the truncated Weibull distribution, which can lead to some insights: in particular, we report the average value, the rth moment, the variance, the median, the mode, the generation of random numbers, and the evaluation of the two parameters with maximum likelihood estimators. The first application of the Weibull distribution is the initial mass function for stars. The magnitude version of the Weibull distribution is applied to the luminosity function for the Sloan Digital Sky Survey (SDSS) galaxies and to the photometric maximum of the 2MASS Redshift Survey (2MRS) galaxies. The truncated Weibull luminosity function allows us to model the average value of the absolute magnitude as a function of the redshift for the 2MRS galaxies.

An optimal method for the power spectrum measurement

An aliasing effect brought up by mass assignment onto Fast Fourier Transformation （FFT） grids may bias measurement of the power spectrum of large scale structures. In this paper, based on the Beylkin＇s unequally spaced FFT technique, we propose a new precise method to extract the true power spectrum of a large discrete data set. We compare the traditional mass assignment schemes with the new method using the Daub6 and the 3rd-order B-spline scaling functions. Our measurement of Poisson samples and samples of N-body simulations shows that the B-spline scaling function is an optimal choice for mass assignment in the sense that （1） it has a compact support in real space and thus yields an efficient algorithm （2） without any extra corrections. The Fourier space behavior of the 3rd-order B-spline scaling function enables it to be able to accurately recover the true power spectrum with errors less than 5% up to k 〈 kN. It is expected that such a method can be applied to higher order statistics in Fourier space and will enable us to have a precision capture of the non-Gaussian features in the large scale structure of the universe.

New Probability Distributions in Astrophysics: VI. The Truncated Sujatha Distribution

The truncated version of the two-parameter Sujatha distribution is analysed. In particular, its probability density function and distribution function are obtained. The results are applied to the initial mass function for stars, to the luminosity function for galaxies, to the number of galaxies as a function of the redshift and to the average absolute magnitude of a galaxy as a function of its redshift.

Can we constrain the evolution of HI bias using configuration entropy?

We study the evolution of the configuration entropy of HI distribution in the post-reionization era assuming different time evolution of HI bias.We describe time evolution of linear bias of HI distribution using a simple form b(a)=b_(0)a^(n) with different index n.The derivative of the configuration entropy rate is known to exhibit a peak at the scale factor corresponding to theΛ-matter equality in the unbiasedΛCDM model.We show that in theΛCDM model with time-dependent linear bias,the peak shifts to smaller scale factors for negative values of n.This is related to the fact that the growth of structures in the HI density field can significantly slow down even before the onset ofΛdomination in the presence of a strong time evolution of the HI bias.We find that the shift is linearly related to the index n.We obtain the best fit relation between these two parameters and propose that identifying the location of this peak from observations would allow us to constrain the time evolution of HI bias within the framework of theΛCDM model.

A transitioning universe with time varying G and decaying Λ

We present a model of a universe that transitions from an early deceleration phase to the current acceleration phase under the framework of general relativity, in the presence of gravitational coupling G（t） and cosmological terms A（t）. Einstein＇s field equations have been solved by considering the time dependent deceleration parameter （DP） which renders the scale factor e = （thekt）1/m where m, n and k are positive con- stants. The cosmological term （A （t）） is found to be positive and a decreasing function of time, which supports the result obtained from observations of type Ia supernovae. The geometrical and kinematical features of the model are examined in detail.

New Probability Distributions in Astrophysics: VIII. The Truncated Weibull—Pareto Distribution

We derive the truncated version of the Weibull—Pareto distribution, deriving the probability density function, the distribution function, the average value, the rth moment about the origin, the media, the random generation of values and the maximum likelihood estimator which allows deriving the three parameters. The astrophysical applications of the Weibull—Pareto distribution are the initial mass function for stars, the luminosity function for the galaxies of the Sloan Digital Sky Survey, the luminosity function for QSO and the photometric maximum of galaxies of the 2 MASS Redshift Survey.

Improving constraint onΩ_(m)from SDSS using marked correlation functions

Large-scale structure(LSS)surveys will increasingly provide stringent constraints on our cosmological models.Recently,the density-marked correlation function(MCF)has been introduced,offering an easily computable density-correlation statistic.Simulations have demonstrated that MCFs offer additional,independent constraints on cosmological models beyond the standard two-point correlation(2PCF).In this study,we apply MCFs for the first time to SDSS CMASS data,aiming to investigate the statistical information regarding clustering and anisotropy properties in the Universe and assess the performance of various weighting schemes in MCFs,and finally obtain constraints onΩ_(m).Upon analyzing the CMASS data,we observe that,by combining different weights(α=[-0.2,0,0.2,0.6]),the MCFs provide a tight and independent constraint on the cosmological parameterΩ_(m),yieldingΩ_(m)=0.293±0.006 at the 1σlevel,which represents a significant reduction in the statistical error by a factor of 3.4 compared to that from 2PCF.Our constraint is consistent with recent findings from the small-scale clustering of BOSS galaxies(Zhai et al.Astronphys.J.948,99(2023))within the 1σlevel.However,we also find that our estimate is lower than the Planck measurements by about 2.6σ,indicating the potential presence of new physics beyond the standard cosmological model if all the systematics are fully corrected.The method outlined in this study can be extended to other surveys and datasets,allowing for the constraint of other cosmological parameters.Additionally,it serves as a valuable tool for forthcoming emulator analysis on the Chinese Space Station Telescope(CSST).

Using Cartesian Slice Plots of a Cosmological Simulation as Input of a Convolutional Neural Network

Using a uniform partitioning of cubic cells,we cover the total volume of aΛCDM cosmological simulation based on particles.We define a visualization cell as a spatial extension of the cubic cell,so that we collect all simulation particles contained in this visualization cell to create a series of Cartesian plots in which the overdensity of matter is clearly visible.We then use these plots as input to a convolutional neural network(CNN)based on the Keras library and TensorFlow for image classification.To assign a class to each plot,we approximate the Hessian of the gravitational potential in the center of the cubic cells.Each selected cubic cell is then assigned a label of 1,2 or 3,depending on the number of positive eigenvalues obtained for the Householder reduction of the Hessian matrix.We apply the CNN to several models,including two models with different visualization volumes,one with a cell size of type L(large)and the other with a cell type S(small).A third model combines the plots of the previous L and S cell types.So far,we have mainly considered a slice parallel to the XY plane to make the plots.The last model is considered based on visualizations of cells that also include slices parallel to the ZX and ZY planes.We find that the accuracy in classification plots is acceptable,and the ability of the models to predict the class works well.These results allow us to demonstrate the aim of this paper,namely that the usual Cartesian plots contain enough information to identify the observed structures of the cosmic web.

Generalized Kibble-Zurek mechanism for defects formation in trapped ions

The Kibble-Zurek(KZ)mechanism has played a fundamental role in defect formation with universal scaling laws in nonequilibrium phase transitions.However,this theory may not accurately predict the scaling laws in inhomogeneous systems and slow quenching processes.Here,we present a generalized KZ mechanism for the defect formation in trapped ions with the freeze-out condition gt=b0τ(t),where g is a universal quenching velocity function and b0 is a constant.We derived a differential equationφ(x,t)to account for the frozen correlation length of a kink in an inhomogeneous system and demonstrated a smooth crossover from a fast quenching process to a slow quenching process,which agrees well with the experiments performed by Ulm et al.[Nat.Commun.4,2290(2013)]and Pyka et al.[Nat.Commun.4,2291(2013)].Furthermore,we confirmed our theoretical model using molecular dynamics simulation by solving the stochastic differential equation,showing excellent agreement with the results from the differential equation.Our theory provides a general theoretical framework for studying KZ physics in inhomogeneous systems,which has applications in other nonequilibrium platforms studied experimentally.

Renormalization-group theory of first-order phase transition dynamics in field-driven scalar model

Through a detailed study of the mean-field approximation, the Gaussian approximation, the perturbation expansion, and the field-theoretic renormalization-group analysis of a φ^3 theory, we show that the instability fixed points of the theory, together with their associated instability exponents, are quite probably relevant to the scaling and universality behavior exhibited by the first-order phase transitions in a field-driven scalar Ca model, below its critical temperature and near the instability points. Finite- time scaling and leading corrections to the scaling are considered. We also show that the instability exponents of the first-order phase transitions are equivalent to those of the Yang-Lee edge singularity, and employ the latter to improve our estimates of the former. The outcomes agree well with existing numerical results.

Renormalization group theory for temperature-driven first-order phase transitions in scalar models

We study the scaling and universal behavior of temperature-driven first-order phase transitions in scalar models. These transitions are found to exhibit rich phenomena, though they are controlled by a single complex-conjugate pair of imaginary fixed points of φ3 theory. Scaling theories and renormalization group theories are developed to account for the phenomena, and three universality classes with their own hysteresis exponents are found： a field-like thermal class, a partly thermal class, and a purely thermal class, designated, respectively, as Thermal Classes I, II, and III. The first two classes arise from the opposite limits of the scaling forms proposed and may cross over to each other depending on the temperature sweep rate. They are both described by a massless model and a purely massive model, both of which are equivalent and are derived from φ3 theory via symmetry. Thermal Class III characterizes the cooling transitions in the absence of applied external fields and is described by purely thermal models, which include cases in which the order parameters possess different symmetries and thus exhibit different universality classes. For the purely thermal models whose free energies contain odd-symmetry terms, Thermal Class III emerges only at the mean-field level and is identical to Thermal Class II. Fluctuations change the model into the other two models. Using the extant three- and two- loop results for the static and dynamic exponents for the Yang-Lee edge singularity, respectively, which falls into the same universality class as φ3 theory, we estimate the thermal hysteresis exponents of the various classes to the same precision. Comparisons with numerical results and experiments are briefly discussed.

Elucidating galaxy assembly bias in SDSS

We investigate the level of galaxy assembly bias in the Sloan Digital Sky Survey (SDSS) main galaxy sample using ELUCID,a state-of-the-art constrained simulation that accurately reconstructed the initial density perturbations within the SDSS volume.On top of the ELUCID haloes,we develop an extended HOD model that includes the assembly bias of central and satellite galaxies,parameterized as Q_(cen)and Q_(sat),respectively,to predict a suite of one-and two-point observables.In particular,our fiducial constraint employs the probability distribution of the galaxy number counts measured on 8 h^(-1)Mpc scales N_8^(g) and the projected cross-correlation functions of quintiles of galaxies selected by N_(8)^(g) with our entire galaxy sample.We perform extensive tests of the efficacy of our method by fitting the same observables to mock data using both constrained and non-constrained simulations.We discover that in many cases the level of cosmic variance between the two simulations can produce biased constraints that lead to an erroneous detection of galaxy assembly bias if the non-constrained simulation is used.When applying our method to the SDSS data,the ELUCID reconstruction effectively removes an otherwise strong degeneracy between cosmic variance and galaxy assembly bias in SDSS,enabling us to derive an accurate and stringent constraint on the latter.Our fiducial ELUCID constraint,for galaxies above a stellar mass threshold M_(*)=10^(10.2)h^(-2)M_(⊙),is Q_(cen)=-0.09±0.05 and Q_(sat)=0.09±0.10,indicating no evidence for a significant (>2σ) galaxy assembly bias in the local Universe probed by SDSS.Finally,our method provides a promising path to the robust modelling of the galaxy-halo connection within future surveys like DESI and PFS.