Four-Dimensional Mathematics Creates the Super Universe

In the common theory of the Universe, the redshift of the light wavelength from distant stars indicates the speed of the star. In this study, the model of the Universe is the surface volume of the four-dimensional sphere, and the shape of the Universe results in the most of the redshift of light wavelength. Therefore, there is no dark energy accelerating the Universe. The surface of the four-dimensional sphere is a volume, and this volume is a good model for the Universe. The surface volume of the four-dimensional sphere has been explained by a model of four-dimensional cube, within which the forming of surface volume can be easily shown. The model of four-dimensional cube containing six side cubes is ingenious for explaining the structure of the four-dimensional Universe, but it is not enough because the four-dimensional cube has not six side cubes, but eight side cubes. Therefore, in this study a better method has been created to construct the four-dimensional cube. Our three-dimensional Universe is the surface of the four-dimensional sphere Universe. The volume of our three-dimensional Universe is finite, and beneath it is the infinite volume four-dimensional Super Universe. Two important basic formulae have been derived: The surface volume of the four-dimensional sphere is π3R3 in which R is the radius of the sphere, and the fourth-power volume of the four-dimensional sphere is 1/4 π3R4. The volume of the Universe has been calculated π3R3 = 62 × 1030 ly3. Time as the fourth dimension of the space takes effect only near the speed of light, and therefore it has been ignored in this study.

The Jiao Tong University Spectroscopic Telescope Project

The Jiao Tong University Spectroscopic Telescope(JUST)is a 4.4-meter f/6.0 segmented-mirror telescope dedicated to spectroscopic observations.The JUST primary mirror is composed of 18 hexagonal segments,each with a diameter of 1.1 m.JUST provides two Nasmyth platforms for placing science instruments.One Nasmyth focus fits a field of view of 10′and the other has an extended field of view of 1.2°with correction optics.A tertiary mirror is used to switch between the two Nasmyth foci.JUST will be installed at a site at Lenghu in Qinghai Province,China,and will conduct spectroscopic observations with three types of instruments to explore the dark universe,trace the dynamic universe,and search for exoplanets:(1)a multi-fiber(2000 fibers)medium-resolution spectrometer(R=4000-5000)to spectroscopically map galaxies and large-scale structure;(2)an integral field unit(IFU)array of 500 optical fibers and/or a long-slit spectrograph dedicated to fast follow-ups of transient sources for multi-messenger astronomy;(3)a high-resolution spectrometer(R~100000)designed to identify Jupiter analogs and Earth-like planets,with the capability to characterize the atmospheres of hot exoplanets.

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.

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.

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.

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.

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.

The S_(8)tension in light of updated redshift-space distortion data and PAge approximation

One of the most prominent challenges to the standard Lambda cold dark matter(ΛCDM) cosmology is the tension between the structure growth parameter S;constrained by the cosmic microwave background(CMB) data and the smaller one suggested by the cosmic shear data. Recent studies show that, for ΛCDM cosmology, redshift-space distortion(RSD) data also prefers a smaller S;that is ~ 2-3σ lower than the CMB value, but the result is sensitive to the cosmological model. In the present work we update the RSD constraint on S;with the most up-to-date RSD data set where the correlation between data points is properly taken into account. To reduce the model dependence, we add in our Monte Carlo Markov Chain calculation the most up-to-date data sets of Type Ia supernovae(SN) and baryon acoustic oscillations(BAO), whose correlation with RSD is also taken into account, to constrain the background geometry. For ΛCDM cosmology we find S_(8)= 0.812 ± 0.026, which is ~ 2σ larger than previous studies, and hence is consistent with the CMB constraint. By replacing ΛCDM with the parameterization based on cosmic Age(PAge), an almost model-independent description of the late universe, we find that the RSD + SN + BAO constraint on S;is insensitive to the cosmological model.

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.