An Analytical Solution in the Complex Plane for the Luminosity Distance in Flat Cosmology

We present an analytical solution for the luminosity distance in spatially flat cosmology with pressureless matter and the cosmological constant. The complex analytical solution is made of a real part and a negligible imaginary part. The real part of the luminosity distance allows finding the two parameters H0 and ΩM . A simple expression for the distance modulus for SNs of type Ia is reported in the framework of the mini-max approximation.

Sparse Formulae for the Distance Modulus in Cosmology

We review the distance modulus in twelve different cosmologies: the ΛCDM model, the wCDM model, the Cardassian model, the flat case, the øCDM cosmology, the Einstein—De Sitter model, the modified Einstein—De Sitter model, the simple GR model, the flat expanding model, the Milne model, the plasma model and the modified tired light model. The above distance moduli are processed for three different compilations of supernovae and a supernovae + GRBs compilation: Union 2.1, JLA, the Pantheon and Union 2.1 + 59 GRBs. For each of the 48 analysed cases we report the relative cosmological parameters, the chi-square, the reduced chi-square, the AIC and the Q parameter. The angular distance as function of the redshift for five cosmologies is reported in the framework of the minimax approximation.

Cosmological Distances in Closed Model of the Universe

Four Cosmological distances were determined in the light of the closed cosmic model which was presented in a previous study. Each of these distances was obtained in terms of the redshift of an extragalactic object. It is found that the luminosity distance of the extragalactic object in the closed cosmic model, the observed model and model are approximately the same up to z = 0.1535. However, the luminosity distance in the close cosmic model approximately agrees with its value in the observed model up to z = 0.6442. Estimations of the horizon distance of the universe, the total mass and the mass of matter within the horizon distance, the equivalent numbers of the Milky Way-like galaxies and the Coma-like clusters of galaxies to the mass of matter were computed in the closed cosmic model at the present time.

The Distance Modulus in Dark Energy and Cardassian Cosmologies via the Hypergeometric Function

The presence of the dark energy allows both the acceleration and the expansion of the universe. In the case of a constant equation of state for dark energy we derived an analytical solution for the Hubble radius in terms of the hypergeometric function. An approximate Taylor expansion of order seven is derived for both the constant and the variable equation of state for dark energy. In the case of the Cardassian cosmology, we also derived an analytical solution for the Hubble radius in terms of the hypergeometric function. The astronomical samples of the distance modulus for Supernova (SN) of type Ia allows the derivation of the involved cosmological in the case of constant equation of state, variable equation of state and Cardassian cosmology.

Application of a Space-based Optical Interferometer Toward Measuring Cosmological Distances of Quasars

Measuring quasar distance through joint analysis of spectroastrometry and reverberation mapping observations is a new method for driving the development of cosmology.In this paper,we carry out detailed simulation and analysis to study the effect of four basic observational parameters(baseline length,exposure time,equivalent diameter and spectral resolution)on the data quality of differential phase curves(DPCs),and furthermore on the accuracy of distance measurement.In our simulation,we adopt an axisymmetrical disk model of a broad line region(BLR)to generate differential phase signals.We find that the differential phases and their Poisson errors could be amplified by extending the baseline,while the influence of optical path difference errors can be reduced during fitting the BLR model.Longer exposure time or larger equivalent diameter helps reduce the absolute Poisson error.Therefore,the relative error of DPCs could be reduced by increasing any of the above three parameters,then the accuracy of distance measurement could be improved.In contrast,the uncertainty of absolute angular distances(D_(A))could be improved with higher spectral resolution,although the relative error of DPCs would be amplified.We show how the uncertainty of distance measurement varies with the relative error of DPCs.For our specific set of model parameters,without considering more complicated structures and kinematics of BLRs in our simulation,it is found that the relative error of DPCs<20%is a limit for accurate distance measurement.The relative error of DPCs has a lower limit(roughly 5%)and the uncertainty in distance measurement can be better than 2%.

Cosmological Distances in Five General Cosmic Models

Four cosmological distances were investigated in the light of the five general cosmic models which were developed in a previous study. These are the proper distance, luminosity distance, angular diameter distance and distance modulus. Each of these distances was studied in terms of the redshift of the extragalactic objects. Estimations of the horizon distance of the universe, the total mass and the mass of matter within the horizon distance, the equivalent numbers of the Milky Way-like galaxies and the Coma-like clusters of galaxies to the mass of matter were determined in the general models at the present time.

Are Type Ia Supernovae Reliable Distance Indicators?

Recent applications of type Ia supernovae （SNe Ia） in cosmology have successfully revealed the accelerating expansion of the universe. However, as distance indicators used in measuring the expansion history of the universe and probing the nature of dark energy, these objects must pass more strict tests. We propose a K-S test to investigate if there exists any systematic bias when deriving the luminosity distances under the standard candle assumption. Two samples, one comprising 71 high-redshift SNe Ia and the other, 44 nearby ones, are used in our investigation. We find that it is likely there exists a bias in the adopted samples, which is probably caused by a systematic error, e.g. in the color parameter used in the luminosity calibration and a bias may be caused by the SN evolution or by varying properties of the dust surrounding the SNe Ia.

A New Consistency Test forΛCDM Cosmology Using Galaxy Surveys

We propose a new consistency test for theΛCDM cosmology using baryonic acoustic oscillations(BAO)and redshift space distortion(RSD)measurements from galaxy redshift surveys.Specifically,we determine the peak position of fσ8(z)in redshift z offered by an RSD measurement,and compare it to the one predicted by the BAO observables assuming a flatΛCDM cosmology.We demonstrate this new test using the simulated data for the DESI galaxy survey,and argue that this test complements those using the background observables alone,and is less subject to systematics in the RSD analysis,compared to traditional methods using values of fσ8(z)directly.

Testing X-ray measurements of galaxy cluster gas mass fraction using the cosmic distance-duality relation

We propose a consistency test for some recent X-ray gas mass fraction （fgas） measurements in galaxy clusters, using the cosmic distance-duality relation, Ttneory = DL（1 ＋ Z）-2/DA, with luminosity distance （DL） data from the Union2 compilation of type Ia supernovae. We set Z/theory = 1, instead of assigning any red- shift parameterizations to it, and constrain the cosmological information preferred by fga8 data along with supernova observations. We adopt a new binning method in the reduction of the Union2 data, in order to minimize the statistical errors. Four data sets of X-ray gas mass fraction, which are reported by Allen et al. （two samples）, LaRoque et al. and Ettori et al., are analyzed in detail in the context of two theoretical models of fgas. The results from the analysis of Alien et al.＇s samples demonstrate the feasibility of our method. It is found that the preferred cosmology by LaRoque et al.＇s sample is consistent with its reference cosmology within the 1σ confidence level. However, for Ettori et al.＇s fgas sample, the inconsistency can reach more than a 3σ confidence level and this dataset shows special preference to an ΩA = 0 cosmology.

Concordance of Kinematics and Lensing of Elliptical Galaxies with WMAP Cosmology

We explore degeneracies in strong lensing model so to make time delay data consistent with the WMAP （Wilkinson Microwave Anisotropy Probe） cosmology. Previous models using a singular isothermal lens often yield a time delay between the observed multiple images too small than the observed value if we ＂hardwire＂ the now widely quoted post-WMAP ＂high＂ value of the Hubble constant （Ho ～71 ± 4km s^-1 Mpc^-1）. Alternatively, the lens density profile （star plus dark matter） is required to be locally steeper than r-2 （isothermal） profile near the Einstein radius （of the order 3 kpc） to fit the time delays; a naive extrapolation of a very steep profile to large radius would imply a lens halo with a scale length of the order only 3 kpc, too compact to be consistent with CDM. We explore more sophisticated, mathematically smooth, positive lens mass density profiles which are consistent with a large halo and the post-WMAP H0. Thanks to the spherical monopole degeneracy, the ＂reshuffling＂ of the mass in a lens model does not affect the quality of the fit to the image positions, amplifications, and image time delays. Even better, unlike the better-known mass sheet degeneracy, the stellar mass-to-light and the H0 value are not affected either. We apply this monopole degeneracy to the quadruple imaged time-delay system PG 1115＋080. Finally we discuss the implications of the time delay data on the newly proposed relativistic MOND theory.

The distance duality relation test from the ACT cluster and type Ia supernova data

The validity of the cosmic distance-duality （DD） relation is investigated by using 91 measure- ments of the gas mass fraction of galaxy clusters recently reported by the Atacama Cosmology Telescope （ACT） and the luminosity distance from the Union2.1 type Ia supernova （SNIa） sample independent of any cosmological models and the value of the Hubble constant. We consider four different approaches to derive the gas mass function and two different parameterizations of the DD relation, and find that they have very slight influences on the DD relation test and the relation is valid at the la confidence level. We also discuss the constraints on a andβ, which represent the effects of the shapes and colors of the light curves of SNIa, respectively. Our results on a and β are different from those obtained from the ACDM model and the galaxy cluster plus SNIa data.

Method of determining cosmological parameter ranges with samples of candles with an intrinsic distribution

In this paper, the effect of the intrinsic distribution of cosmological candles is investigated. We find that in the case of a narrow distribution the deviation of the observed modulus of sources from the expected central value can be estimated within a ceratin range. We thus introduce lower and upper limits of X^2, X^2min and X^2max to estimate cosmological parameters by applying the conventional minimizing X^2 method. We apply this method to a gammaray burst （GRB） sample as well as to a combined sample including this GRB sample and an SN Ia sample. Our analysis shows that： a） in the case of assuming an intrinsic distribution of candles of the GRB sample, the effect of the distribution is obvious and should not be neglected; b） taking into account this effect would lead to a poorer constraint of the cosmological parameter ranges. The analysis suggests that in the attempt of constraining the cosmological model with current GRB samples, the results tend to be worse than was previously anticipated if the mentioned intrinsic distribution does exist.

Constraining Dark Energy and Cosmological Transition Redshift with Type Ia Supernovae

The property of dark energy and the physical reason for the acceleration of the present universe are two of the most difficult problems in modern cosmology. The dark energy contributes about two-thirds of the critical density of the present universe from the observations of type-Ia supernovae （SNe Ia） and anisotropy of cosmic microwave background （CMB）. The SN Ia observations also suggest that the universe expanded from a deceleration to an acceleration phase at some redshift, implying the existence of a nearly uniform component of dark energy with negative pressure. We use the ＂Gold＂ sample containing 157 SNe Ia and two recent well-measured additions, SNe Ia 1994ae and 1998aq to explore the properties of dark energy and the transition redshift. For a fiat universe with the cosmological constant, we measure ΩM=0.28-0.05^＋0.04 which is consistent with Riess et al. The transition redshift is zT=0.60-0.08^＋0.04. We also discuss several dark energy models that define w（z） of the parameterized equation of state of dark energy including one parameter and two parameters （w（z） being the ratio of the pressure to energy density）. Our calculations show that the accurately calculated transition redshift varies from zT =0.29-0.06^＋0.07 to zT =0.60-0.08^＋0.06 across these models. We also calculate the minimum redshift zc at which the current observations need the universe to accelerate.

A Cosmological Model without Singularity Based on RW Metric (1)

A new conjecture is proposed that there are two sorts of matter called s-matter and v-matter which are symmetric, whose masses are positive, but whose gravitational masses are opposite to each other. Based on the conjecture and the SUS(5) × SUV(5) gauge group, a cosmological model has been constructed and the following inferences have been derived. There are two sorts of symmetry breaking called V-breaking and S-breaking. In theV-breaking, SUV(5) breaks finally to SUV(3) × UV(1) so that v-particles get their masses and form v-atoms andv-galaxies etc., while SUS(5) still holds so that s-fermions and s-gauge bosons are massless and form SUS(5)color-singlets. There is no interaction among the SUS(5) color-singlets except gravitation so that they distribute loosely in space, cannot be observed, and cause space to expand with an acceleration. Evolution of the universe is explained. There is no space-time singularity. There are the highest temperature and the least scale in the universe. It is impossible that the Plank temperature and length are arrived. A formula is obtained which describes the relation between a luminous distance and its redshift. A huge void is not empty, and is equivalent to a huge concave lens. The densities of hydrogen in the huge voids must be much less than that predicted by the conventional theory. The gravitation between two galaxies whose distance is long enough will be less than that predicted by the conventional theory. A black hole with its big enough mass will transform into a white hole.

哈勃常数危机

哈勃常数定量刻画了当前宇宙的膨胀速率,精确测定哈勃常数是现代宇宙学的一个重要科学问题.近年来,哈勃常数的局域直接测量值与全局模型拟合值之间出现了越来越严重的偏差,其中局域直接测量值来自于晚期宇宙的局域距离阶梯测量结果,而全局模型拟合值来自于早期宇宙的微波背景辐射对宇宙学标准模型的观测限制.如果该偏差不是由其中任何一种观测手段的观测误差和系统误差所致,那么很有可能意味着存在超出宇宙学标准模型的新物理.本文从观测和模型两方面简述该哈勃常数危机问题,并结合作者近年来对此问题的研究从观测和模型两方面进行展望.

Constraining the Spatial Curvature of the Local Universe with Deep Learning

We use the distance sum rule method to constrain the spatial curvature of the Universe with a large sample of 161strong gravitational lensing systems,whose distances are calibrated from the Pantheon compilation of typeⅠa supernovae using deep learning.To investigate the possible influence of mass model of the lens galaxy on constraining the curvature parameterΩ_(k),we consider three different lens models.Results show that a flat Universe is supported in the singular isothermal sphere(SIS)model with the parameterΩ_(k)=0.049_(-0.125)^(+0.147).While in the power-law(PL)model,a closed Universe is preferred at the~3σconfidence level,with the parameterΩ_(k)=-0.245_(-0.071)^(+0.075).In the extended PL model,the 95%confidence level upper limit ofΩ_(k)is<0.011.As for the parameters of the lens models,constraints on the three models indicate that the mass profile of the lens galaxy could not be simply described by the standard SIS model.

HⅠGalaxy Detections in the Zone of Avoidance with FAST

The Zone of Avoidance(ZoA)is a region of low galactic latitude that is heavily obscured by the Milky Way.Observations with radio telescopes are basically unaffected by dust extinction and can unveil the structure behind it through the Milky Way.One of the scientific goals of the Five-hundred-meter Aperture Spherical radio Telescope(FAST)is to search for the neutral hydrogen and understand the large-scale physics to explore the origin and evolution of the universe.We take the 15,500 IRAS(the Infrared Astronomical Satellite)galaxies from PSCz(“Point Source Catalog”)survey to reconstruct the density field of the local universe,obtain the distribution of the relative density of galaxies in the ZoA region with a redshift z below 0.07,and the number of detectable galaxies with FAST is estimated by using the neutral hydrogen mass function of the ALFA(Arecibo L-band Feed Array)survey.We conclude that FAST can observe more than 2000 ZoA galaxies within a distance of 300 Mpc h_(70)^(-1),and present preliminary results of the partial GPPS(the FAST Galactic Plane Pulsar Snapshot survey)data,compared with ALFA ZoA(The Arecibo L-band Feed Array Zone of Avoidance),show that FAST has a higher detection sensitivity to search for HI galaxies in the ZoA area.

Ia超新星在宇宙学中的应用

对Ia超新星在宇宙学中的应用作了述评．蓝Ia超新星具有相对均匀的光谱、光变曲线及峰值光度，是较好的相对距离指示器．利用峰值光度同光变曲线形状或其它与距离无关的可观测量的关系可进一步将Ia超新星校准成精确的距离指示器。一旦它们的绝对光度得到标定，就可以定出哈勃常数H0。基于对邻近星系Ia超新星的理解，高红移Ia超新星的数据可对宇宙密度参数ΩM、ΩA及减速因子q0作出限制，并对膨胀宇宙的最终命运作出判定。

Ia超新星与哈勃常数(英文)

蓝 Ia超新星是迄今天文学家已知的校准得最好的标准烛光 ,峰值光度弥散仅为 0 .11mag.将近处距离已知的蓝 Ia超新星匹配到远处哈勃流样本中 ,便可获得哈勃常数的估计值 .当前的数据显示哈勃常数为H0 =( 55.3± 5.3) km· s-1· Mpc-1.

Ia超新星:理论与宇宙学

Ｉａ超新星作为测量遥远星系距离（从而测定宇宙膨胀速率）的“标准烛光”，已经成为具有重要意义的天体。主要介绍当前Ｉａ超新星研究的理论和观测进展．光谱分光及测光证据表明，Ｉａ超新星是由吸积碳氧白矮星热核爆炸产生，但有关Ｉａ超新星前身星双星系统及流体动力学模型仍是有争议的。蓝Ｉａ超新星具有相对均匀的峰值光度，它是天文学家已知的校准得最好的示距天体．近年来，人们在利用Ｉａ超新星测量时空方面已取得了巨大进展．