Classical Cosmology II. The Einstein Ring

The Einstein ring is usually explained in the framework of the gravitational lens. Conversely here we apply the framework of the expansion of a superbubble (SB) in order to explain the spherical appearance of the ring. Two classical equations of motion for SBs are derived in the presence of a linear and a trigonometric decrease for density. A relativistic equation of motion with an inverse square dependence for the density is derived. The angular distance, adopting the minimax approximation, is derived for three relativistic cosmologies: the standard, the flat and the wCDM. We derive the relation between redshift and Euclidean distance, which allows fixing the radius of the Einstein ring. The details of the ring are explained by a simple version of the theory of images.

The Tension Cosmology, Largest Cosmic Structures and Explosions of Supernovae from SST

Here, using the Scale-Symmetric Theory (SST) we explain the cosmological tension and the origin of the largest cosmic structures. We show that a change in value of strong coupling constant for cold baryonic matter leads to the disagreement in the galaxy clustering amplitude, quantified by the parameter S8. Within the same model we described the Hubble tension. We described also the mechanism that transforms the gravitational collapse into an explosion—it concerns the dynamics of virtual fields that lead to dark energy. Our calculations concern the Type Ia supernovae and the core-collapse supernovae. We calculated the quantized masses of the progenitors of supernovae, emitted total energy during explosion, and we calculated how much of the released energy was transferred to neutrinos. Value of the speed of sound in the strongly interacting matter measured at the LHC confirms that presented here model is correct. Our calculations show that the Universe is cyclic.

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.

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.

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.

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.

Cosmology of a Chaplygin Gas Model Under f(T)Gravity and Evolution of Primordial Perturbations

This paper reports a detailed study of generalized Chaplygin gas(GCG)with power law form of scale factor and truncated form of the scale factor using binomial expansion in both interacting and non-interacting scenarios along with its cosmological consequences,studied in terms of equation of state(EoS)parameter.In the non-interacting scenario,the EoS parameter behaves as quintessence in both forms of the scale factor.In the interacting scenario,the EoS parameter behaves as phantom and for the truncated form of the scale factor,it violates the constraints of the positive parameterα.The cosmological implementation of GCG interacting with pressureless dark matter is investigated in the framework of f(T)modified gravity,where T is the torsion scalar in teleparallelism.The interaction term is directly proportional to the GCG density with positive coupling constant.In f(T)gravity,the EoS is behaving like phantom.The stability of the reconstructed model is investigated and it is found to be stable against small gravitational perturbations,i.e.,the squared speed of sound is non-negative and an increasing function of cosmic time t.We have observed that our reconstructed f(T)model satisfies one of the sufficient conditions of a realistic reconstructed model and it is consistent with the CMB constraints and primordial nucleosynthesis.Cosmology of primordial perturbations has also been analyzed and the self-interacting potential has been found to be an increasing function of cosmic time t.

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.

Redshift drift reconstruction for some cosmological models from observations

Redshift drift is a tool to directly probe the expansion history of the uni- verse. Based on the Friedmann-Robertson-Walker framework, we reconstruct the ve- locity drift and deceleration factor for several cosmological models using observa- tional H（z） data from the differential ages of galaxies and baryon acoustic oscillation peaks, luminosity distance of Type Ia supernovae, cosmic microwave background shift parameter, and baryon acoustic oscillation distance parameter. They can, for the first time, provide an objective and quantifiable measure of the redshift drift. We find that reconstructed velocity drift with different peak values and corresponding redshifts can potentially provide a method to distinguish the quality of competing dark energy mod- els at low redshifts. Better fitting between models and observational data indicate that current data are insufficient to distinguish the quality of these models. However, by comparing with the simulated velocity drift from Liske et al, we find that the Dvali- Gabadadze-Porrati model is inconsistent with the data at high redshift, which origi- nally piqued the interest of researchers in the topic of redshift drift. Considering the deceleration factor, we are able to give a stable instantaneous estimation of a transition redshift of zt ~ 0.7 from joint constraints, which incorporates a more complete set of values than the previous study that used a single data set.

Measurements of the Cosmological Parameters &Omega;_mand <i>H</i>₀

From Baryon Acoustic Oscillation measurements with Sloan Digital Sky Survey SDSS DR14 galaxies, and the acoustic horizon angle measured by the Planck Collaboration, we obtain Ωm=0.2724±0.0047, and h+0.020&sdot;∑mv=0.7038±0.0060, assuming flat space and a cosmological constant. We combine this result with the 2018 Planck “TT, TE, EE + lowE + lensing” analysis, and update a study of ∑mv with new direct measurements of σ8, and obtain ∑mv=0.27±0.08 eV assuming three nearly degenerate neutrino eigenstates. Measurements are consistent with Ωk=0, and Ωde(a)=ΩΛ constant.

Confidence Level Estimator of Cosmological Parameters

Cosmological Models frequently suggest the existence of physical, quantities, e.g. dark energy, we cannot yet observe and measure directly. Their values are obtained indirectly setting them equal to values and accuracy of the associated model parameters which best fit model and observation. Apparently results are so accurate that some researchers speak of precision cosmology. The accuracy attributed to these indirect values of the physical quantities however does not include the uncertainty of the model used to get them. We suggest a Confidence Level Estimator to be attached to these indirect measurements and apply it to current cosmological models.

A critique of supernova data analysis in cosmology

Observational astronomy has shown significant growth over the last decade and has made important contributions to cosmology. A major paradigm shift in cosmology was brought about by observations of Type Ia supernovae. The notion that the universe is accelerating has led to several theoretical challenges. Unfortunately, although high-quality supernovae data-sets are being produced, their statistical anal- ysis leaves much to be desired. Instead of using the data to directly test the model, several studies seem to concentrate on assuming the model to be correct and limiting themselves to estimating model parameters and internal errors. As shown here, the important purpose of testing a cosmological theory is thereby vitiated.

The Ring Produced by an Extra-Galactic Superbubble in Flat Cosmology

A superbubble which advances in a symmetric Navarro-Frenk-White density profile or in an auto-gravitating density profile generates a thick shell with a radius that can reach 10 kpc. The application of the symmetric and asymmetric image theory to this thick 3D shell produces a ring in the 2D map of intensity and a characteristic “U” shape in the case of 1D cut of the intensity. A comparison of such a ring originating from a superbubble is made with the Einstein’s ring. A Taylor approximation of order 10 for the angular diameter distance is derived in order to deal with high values of the redshift.

A new interpretation of zero Lyapunov exponents in BKL time for Mixmaster cosmology

A global relationship between cosmological time and Belinskii-Khalatnikov -Lifshitz （BKL） time during the entire evolution of the Mixmaster Bianchi IX universe is used to explain why all the Lyapunov exponents are zero at the BKL time. The actual reason is that the domain of the cosmological time is finite as the BKL time runs from minus infinity to infinity.

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.

Cosmology using long gamma-ray bursts: statistical analysis of errors in calibrated data

We investigate direction dependence and non-Gaussian features in high-z cosmological data using ?_(χ~2) and ?_χ statistics and the Kolmogorov-Smirnov test. These techniques are applied on a set of calibrated long gamma-ray bursts(GRBs) and its combination with recent Type Ia supernovae data(Union2). Our statistical analysis shows a weak but consistent direction dependence in both the data sets.The analysis also indicates a non-Gaussian nature of errors in both data sets.

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.

Observational constraints on the accelerating universe in the framework of a 5D bounce cosmological model

In the framework of a five-dimensional （5D） bounce cosmological model, a useful function f（z） is obtained by giving a concrete expression of deceleration parameter q（z） = q1 ＋q2/1＋1n（1＋z） Then using the obtained Hubble parameter H（z） according to the function f（z）, we constrain the accelerating universe from recent cosmic observations： the 192 ESSENCE SNe Ia and the 9 observational H（z） data. The best fitting values of transition redshift zT and current deceleration parameter q0 are given as zT =0.65-0.12^＋0.25 and q0=-0.76-0.15^＋0.15（1σ）. Furthermore, in the 5D bounce model it can be seen that the evolution of equation of state （EOS） for dark energy Wde can cross over -1 at about z = 0.23 and the current value W0de ： =-1.15 〈 -1. On the other hand, by giving a concrete expression of model-independent EOS of dark energy Wde, in the 5D bounce model we obtain the best fitting values zT = 0 .66-0.08^＋0.11 and q0=-0.69-0.10^＋0.10（1σ） from the recently observed data： the 192 ESSENCE SNe Ia, the observational H（z） data, the 3-year Wilkinson Microwave Anisotropy Probe （WMAP）, the Sloan Digital Sky Survey （SDSS） baryon acoustic peak and the x-ray gas mass fraction in clusters.