The Evolving Absolute Magnitude of Type 1a Supernovae and Its Critical Impact on the Cosmological Parameters

In this work, a computer optimization model has been developed that allows one to load the initial data of observations of supernovae 1a into a table and, in simple steps, by searching for the best fit between observations and theory, obtain the values of the parameters of cosmological models. The optimization is carried out assuming that the absolute magnitude of supernovae is not constant, but evolves with time. It is assumed that the dependence of the absolute magnitude on the redshift is linear: M = M( z = 0) + εc z, where εc is the evolution coefficient of the absolute magnitude of type 1a supernovae. In the case of a flat universe ( ΩM + ΩΛ = 1 ), the best fit between theory and observation is εc = 0.304. In this case, for the cosmological parameters we obtain ΩΛ = 0.000, ΩM =1.000. Naturally, this result exactly coincides with the simulation result for the model with zero cosmological constant ( εc = 0.304, q0 = 0.500 ). Within the framework of the ΛCDM model, without restriction on space curvature ( ΩM + ΩΛ+ ΩK = 1 ), we obtain the following values: εc = 0.304, ΩΛ = 0.000, ΩM = 1.000, ΩK =0.000. Those, this case also leads to a flat model of the Universe ( ΩK =0.000 ). In this work, the critical influence of the absolute magnitude M of type 1a supernovae on the cosmological parameters is also shown. In particular, it was found that a change in this value by only 0.4m (from -19.11 to -18.71) leads to a change in the parameters from ΩΛ = 0.7 and ΩM = 0.3 to ΩΛ = 0 and ΩM =1.

Combining optical and X-ray observations of galaxy clusters to constrain cosmological parameters

Galaxy clusters present unique advantages for cosmological study.Here we collect a new sample of 10 lensing galaxy clusters with X-ray observations to constrain cosmological parameters.The redshifts of the lensing clusters lie between 0.1 and 0.6,and the redshift range of their arcs is from 0.4 to 4.9.These clusters are selected carefully from strong gravitational lensing systems which have both X-ray satellite observations and optical giant luminous arcs with known redshifts.Giant arcs usually appear in the central region of clusters,where mass can be traced with luminosity quite well.Based on gravitational lensing theory and a cluster mass distribution model,we can derive a ratio using two angular diameter distances.One is the distance between lensing sources and the other is that between the deflector and the source. Since angular diameter distance relies heavily on cosmological geometry,we can use these ratios to constrain cosmological models.Moreover,X-ray gas fractions of galaxy clusters can also be a cosmological probe.Because there are a dozen parameters to be fitted,we introduce a new analytic algorithm,Powell＇s UOBYQA（Unconstrained Optimization By Quadratic Approximation） ,to accelerate our calculation.Our result demonstrates that this algorithm is an effective fitting method for such a continuous multi-parameter constraint.We find an interesting fact that these two approaches are separately sensitive toΩΛandΩM.By combining them,we can get reasonable fitting values of basic cosmological parameters：ΩM=0.26 ＋0.04 -0.04,andΩΛ=0.82 ＋0.14 -0.16.

Cosmological parameters for spatially flat dust filled Universe in Brans-Dicke theory

We have investigated late time acceleration for a spatially fiat dust filled Universe in Brans- Dicke theory in the presence of a positive cosmological constant A. Expressions for Hubble＇s constant, luminosity distance and apparent magnitude have been obtained for our model. The theoretical results are compared with observed values of the latest 287 high redshift （0.3 ≤ z ≤1.4） Type Ia supernova data taken from the Union 2.1 compilation to estimate present values of matter and dark energy parame- ters, （Ωm）0 and （ΩA）0. We have also estimated the present value of Hubble＇s constant H0 in light of an updated sample of Hubble parameter measurements including 19 independent data points. The results are found to be in good agreement with recent astrophysical observations. We also calculated various physical parameters such as matter and dark energy densities, present age of the Universe and decelera- tion parameter. The value for Brans-Dicke-coupling constant ω is set to be 40 000 based on accuracy of solar system tests and recent experimental evidence.

Joint constraints on cosmological parameters using future multi-band gravitational wave standard siren observations

Gravitational waves(GWs)from compact binary coalescences can be used as standard sirens to explore the cosmic expansion history.In the next decades,it is anticipated that we could obtain the multi-band GW standard siren data(from nanohertz to a few hundred hertz),which are expected to play an important role in cosmological parameter estimation.In this work,we provide,for the first time to the best of our knowledge,joint constraints on cosmological parameters using the future multi-band GW standard siren observations.We simulate the multi-band GW standard sirens based on the SKA-era pulsar timing array(PTA),Taiji observatory,and Cosmic Explorer(CE)to perform cosmological analysis.In theΛCDM model,we find that the joint PTA+Taiji+CE data could provide a tight constraint on the Hubble constant with a 0.5%precision.Moreover,PTA+Taiji+CE could break the cosmological parameter degeneracies generated by CMB,especially in the dynamical dark energy models.When combining the PTA+Taiji+CE data with the CMB data,the constraint precisions of?_(m)and H_(0)are 1.0%and 0.3%,respectively,meeting the standard of precision cosmology.The joint CMB+PTA+Taiji+CE data giveσ(_(w))=0.028 in the wCDM model andσ(w_(0))=0.11 andσ(w_(a))=0.32 in the w_(0)w_(a)CDM model,which are comparable with or close to the latest constraint results by CMB+BAO+SN.In conclusion,the future multi-band GW observations are expected to be used for exploring the nature of dark energy and measuring the Hubble constant.

Cosmological Constraints on Neutrino Masses in Light of JWST Red and Massive Candidate Galaxies

The overabundance of the red and massive candidate galaxies observed by the James Webb Space Telescope(JWST)implies efficient structure formation or large star formation efficiency at high redshift z~10.In the scenario of a low or moderate star formation efficiency,because massive neutrinos tend to suppress the growth of structure of the universe,the JWST observation tightens the upper bound of the neutrino masses.Assuming A cold dark matter cosmology and a star formation efficiency∈[0.05,0.3](flat prior),we perform joint analyses of Planck+JWST and Planck+BAO+JWST,and obtain improved constraints∑m_(ν)<0.196 eV and ∑m_(ν)+<0.111 eV at 95% confidence level,respectively.Based on the above assumptions,the inverted mass ordering,which implies ∑m_(ν)≥0.1 eV,is excluded by Planck+BAO+JWST at 92.7% confidence level.

Quantifying the Tension between Cosmological Models and JWST Red Candidate Massive Galaxies

We develop a Python tool to estimate the tail distribution of the number of dark matter halos beyond a mass threshold and in a given volume in a light-cone.The code is based on the extended Press-Schechter model and is computationally efficient,typically taking a few seconds on a personal laptop for a given set of cosmological parameters.The high efficiency of the code allows a quick estimation of the tension between cosmological models and the red candidate massive galaxies released by the James Webb Space Telescope,as well as scanning the theory space with the Markov Chain Monte Carlo method.As an example application,we use the tool to study the cosmological implication of the candidate galaxies presented in Labbéet al.The standard Λcold dark matter(ΛCDM)model is well consistent with the data if the star formation efficiency can reach~0.3 at high redshift.For a low star formation efficiency ε~0.1,theΛCDM model is disfavored at~2σ-3σconfidence level.

Prospects of the Multi-channel Photometric Survey Telescope in the Cosmological Application of Type Ia Supernovae

The Multi-channel Photometric Survey Telescope(Mephisto)is a real-time,three-color photometric system designed to capture the color evolution of stars and transients accurately.This telescope system can be crucial in cosmological distance measurements of low-redshift(low-z,z■0.1)Type Ia supernovae(SNe Ia).To optimize the capabilities of this instrument,we perform a comprehensive simulation study before its official operation is scheduled to start.By considering the impact of atmospheric extinction,weather conditions,and the lunar phase at the observing site involving the instrumental features,we simulate light curves of SNe Ia obtained by Mephisto.The best strategy in the case of SN Ia cosmology is to take the image at an exposure time of 130 s with a cadence of 3 days.In this condition,Mephisto can obtain hundreds of high-quality SNe Ia to achieve a distance measurement better than 4.5%.Given the on-time spectral classification and monitoring of the Lijiang 2.4 m Telescope at the same observatory,Mephisto,in the whole operation,can significantly enrich the well-calibrated sample of supernovae at low-z and improve the calibration accuracy of high-z SNe Ia.

Prospects for improving cosmological parameter estimation with gravitational-wave standard sirens from Taiji

Taiji,a space-based gravitational-wave observatory,consists of three satellites forming an equilateral triangle with arm length of 3×10^6 km,orbiting around the Sun.Taiji is able to observe the gravitationalwave standard siren events of massive black hole binary(MBHB)merger,which is helpful in probing the expansion of the universe.In this paper,we preliminarily forecast the capability of Taiji for improving cosmological parameter estimation with the gravitational-wave standard siren data.We simulate fiveyear standard siren data based on three fiducial cosmological models and three models of MBHB’s formation and growth.It is found that the standard siren data from Taiji can effectively break the cosmological parameter degeneracies generated by the cosmic microwave background(CMB)anisotropies data,especially for dynamical dark energy models.The constraints on cosmological parameters are significantly improved by the data combination CMB+Taiji,compared to the CMB data alone.Compared to the current optical cosmological observations,Taiji can still provide help in improving the cosmological parameter estimation to some extent.In addition,we consider an ideal scenario to investigate the potential of Taiji on constraining cosmological parameters.We conclude that the standard sirens of MBHB from Taiji will become a powerful cosmological probe in the future.

Cosmological parameter estimation from large-scale structure deep learning

We propose a light-weight deep convolutional neural network(CNN)to estimate the cosmological parameters from simulated 3-dimensional dark matter distributions with high accuracy.The training set is based on 465 realizations of a cubic box with a side length of 256 h-1 Mpc,sampled with 1283 particles interpolated over a cubic grid of 1283 voxels.These volumes have cosmological parameters varying within the flatΛCDM parameter space of 0.16≤?m≤0.46 and 2.0≤109 As≤2.3.The neural network takes as an input cubes with 32^3 oxels and has three convolution layers,three dense layers,together with some batch normalization and pooling layers.In the final predictions from the network we find a 2.5%bias on the primordial amplitudeσ8 that cannot easily be resolved by continued training.We correct this bias to obtain unprecedented accuracy in the cosmological parameter estimation with statistical uncertainties ofδ?m=0.0015 andδσ8=0.0029,which are several times better than the results of previous CNN works.Compared with a 2-point analysis method using the clustering region of 0-130 and 10-130 h-1 Mpc,the CNN constraints are several times and an order of magnitude more precise,respectively.Finally,we conduct preliminary checks of the error-tolerance abilities of the neural network,and find that it exhibits robustness against smoothing,masking,random noise,global variation,rotation,reflection,and simulation resolution.Those effects are well understood in typical clustering analysis,but had not been tested before for the CNN approach.Our work shows that CNN can be more promising than people expected in deriving tight cosmological constraints from the cosmic large scale structure.

Forecast for cosmological parameter estimation with gravitational-wave standard sirens from the LISA-Taiji network

LISA and Taiji are expected to form a space-based gravitational-wave(GW)detection network in the future.In this work,we make a forecast for the cosmological parameter estimation with the standard siren observation from the LISA-Taiji network.We simulate the standard siren data based on a scenario with configuration angle of 40°between LISA and Taiji.Three models for the population of massive black hole binary(MBHB),i.e.,popⅢ,Q3d,and Q3nod,are considered to predict the events of MBHB mergers.We find that,based on the LISA-Taiji network,the number of electromagnetic(EM)counterparts detected is almost doubled compared with the case of single Taiji mission.Therefore,the LISA-Taiji network’s standard siren observation could provide much tighter constraints on cosmological parameters.For example,solely using the standard sirens from the LISA-Taiji network,the constraint precision of H;could reach 1.3%.Moreover,combined with the CMB data,the GW-EM observation based on the LISA-Taiji network could also tightly constrain the equation of state of dark energy,e.g.,the constraint precision of w reaches about 4%,which is comparable with the result of CMB+BAO+SN.It is concluded that the GW standard sirens from the LISA-Taiji network will become a useful cosmological probe in understanding the nature of dark energy in the future.

Prospect for Cosmological Parameter Estimation Using Future Hubble Parameter Measurements

We constrain cosmological parameters using only Hubble parameter data and quantify the impact of future Hubble parameter measurements on parameter estimation for the most typical dark energy models. We first constrain cosmological parameters using 52 current Hubble parameter data including the Hubble constant measurement from the Hubble Space Telescope. Then we simulate the baryon acoustic oscillation signals from WFIRST(Wide-Field Infrared Survey Telescope) covering the redshift range of z ∈ [0.5, 2] and the redshift drift data from E-ELT(European Extremely Large Telescope) in the redshift range of z ∈ [2, 5]. It is shown that solely using the current Hubble parameter data could give fairly good constraints on cosmological parameters. Compared to the current Hubble parameter data, with the WFIRST observation the H(z) constraints on dark energy would be improved slightly, while with the E-ELT observation the H(z) constraints on dark energy is enormously improved.

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.

THE COSMOLOGICAL PARAMETERS

Updated November 2013, by O. Lahav （University College London） and A.R. Liddle （University of Edinburgh）.

Investigating the Hubble Tension Through Hubble Parameter Data

The Hubble constant(H_0),which represents the expansion rate of the universe,is one of the most important cosmological parameters.The recent measurements of H0using the distance ladder methods such as type Ia supernovae are significantly greater than the CMB measurements by Planck.The difference points to a crisis in the standard model of cosmology termed Hubble tension.In this work we compare different cosmological models,determine the Hubble constant and comment on the Hubble tension using the data from differential ages of galaxies.The data we use are free from systematic effects as the absolute age estimation of the galaxies is not needed.We apply the Bayesian approach along with the commonly used maximum likelihood method to estimate H_0 and calculate the AIC scores to compare the different cosmological models.The non-flat cosmological model provides a higher value for matter density as well as the Hubble constant compared to the flatΛCDM model.The AIC score is smaller for the flatΛCDM cosmology compared to the non-flat model indicating the flat model a better choice.The best-fit values of H_0 for both these models are 68.7±3.1 km s^(-1)Mpc^(-1)and 72.2±4km s^(-1)Mpc^(-1),respectively.Our results are consistent with the CCHP measurements.However,the flat model result does not agree with the SH0ES result,while the non-flat result is inconsistent with the Planck value.

Decisive Role of Gravitational Parameter G in Cosmology

In 1937, P. Dirac proposed the Large Number Hypothesis and the Hypothesis of the variable gravitational “constant”, and later added the notion of continuous creation of Matter in the World. The Hypersphere World-Universe Model (WUM) follows these ideas, albeit introducing a different mechanism of Matter creation. In this paper, we show that Gravitational parameter G that can be measured directly makes measurable all Cosmological parameters, which cannot be measured directly.

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.

Effects of the cosmological constant on chaos in an FRW scalar field universe

The dependence of chaos on two parameters of the cosmological constant and the self-interacting coefficient in the imaginary phase space for a closed Friedman- Robertson-Walker （FRW） universe with a conformally coupled scalar field, as the full understanding of the dependence in real phase space, is investigated numerically. It is found that Poincar6 plots for the two parameters less than 1 are almost the same as those in the absence of the cosmological constant and self-interacting terms. For energies below the energy threshold of 0.5 for the imaginary problem in which there are no cosmological constant and self-interacting terms, an abrupt transition to chaos occurs when at least one of the two parameters is 1. However, the strength of the chaos does not increase for energies larger than the threshold. For other situations of the two parameters larger than 1, chaos is weaker, and even disappears as the two parameters increase.

Robertson-Walker cosmological models with perfect fluid in general relativity

Einstein＇s field equations with variable gravitational and cosmological constants are considered in the presence of perfect fluid for a Robertson-Walker universe by assuming the cosmological term to be proportional to R-m（R is a scale factor and m is a constant）.A variety of solutions is presented.The physical significance of the cosmological models has also been discussed.

Bianchi type-I cosmological models with perfect fluid in general relativity

Einstein＇s field equations with variable gravitational and cosmological constants are considered in the presence of perfect fluid for the Bianchi type-I universe by assuming that the cosmological term is proportional to R-m （R is a scale factor and m is a constant）.A variety of solutions are presented.The physical significance of the respective cosmological models are also discussed.

Degeneracy and discreteness in cosmological model fitting

We explore the problems of degeneracy and discreteness in the standard cosmological model（ΛCDM）. We use the Observational Hubble Data（OHD） and the type Ia supernovae（SNe Ia） data to study this issue. In order to describe the discreteness in fitting of data, we define a factor G to test the influence from each single data point and analyze the goodness of G. Our results indicate that a higher absolute value of G shows a better capability of distinguishing models, which means the parameters are restricted into smaller confidence intervals with a larger figure of merit evaluation. Consequently, we claim that the factor G is an effective way of model differentiation when using different models to fit the observational data.