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.

Dynamical Dark Energy in Light of Cosmic Distance Measurements.Ⅱ.A Study Using Current Observations

We extract key information on dark energy from current observations of BAO,OHD and H_(0),and find hints of dynamical behavior of dark energy.In particular,a dynamical dark energy model whose equation of state crosses-1 is favored by observations.We also find that the Universe has started accelerating at a lower redshift than expected.

Quantized Redshift and its Significance for Recent Observation

With the recent observational evidence in extragalactic astronomy,the interpretation of the nature of quasar redshift continues to be a research interest.Very high redshifts are being detected for extragalactic objects that are presumably very distant and young while also exhibiting properties that are characteristic of a more mature galaxy such as ours.According to Halton Arp and Geoffrey Burbidge,redshift disparities consist of an intrinsic component and are related to an evolutionary process.Karlsson observed redshift periodicity at integer multiples of0.089 in log scale and Burbidge observed redshift periodicity at integer multiples of 0.061 in linear scale.Since Singular Value Decomposition based periodicity estimation is known to be superior for noisy data sets,especially when the data contain multiple harmonics and overtones,mainly irregular in nature,we have chosen it to be our primary tool for analysis of the quasar-galaxy pair redshift data.We have observed a fundamental periodicity of0.051 with a confidence interval of 95%in linear scale with the site-available Sloan Digital Sky Survey Data Release 7(SDSS DR7)quasar-galaxy pair data set.We have independently generated quasar-galaxy pair data sets from both 2d F and SDSS and found fundamental periodicities of 0.077 and 0.089,respectively,in log scale with a confidence interval of 95%.

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.

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.

Testing the Coincidence Problem with Strong Gravitational Lens,Type Ia Supernovae and Hubble Parameter Observational Data

In this paper,we use three different kinds of observational data,including 130 strong gravitational lensing(SGL)systems,type Ia supernovae(SNeIa:Pantheon and Union2.1)and 31 Hubble parameter data points(H(z))from cosmic chronometers to constrain the phenomenological model(ρ_(x)∝ρ_(m)a^(ξ)).By combining these three kinds of data(Union2.1+SGL+H(z)),we get the parameter value at the confidence interval of 2σ,Ω_(X,0)=0.69±0.34,ω_(x)=−1.24±0.61,ξ=3.8±3.9 and H_(0)=70.22±0.86 kms^(−1) Mpc^(−1).According to our results,we find that theΛCDM model is still the model which is in best agreement with the observational data at present,and the coincidence problem is not alleviated.In addition,the Ω_(X) and Ω_(m) have the same order of magnitude in 0<z<1.26.Finally,we obtain the transition redshift z_(T)=0.645.If the transition occurs in z>0.645,it is necessary to introduce the dark energy interacting with dark matter.

The Chromatic Point-spread Function of Weak Lensing Measurement in the Chinese Space Station Survey Telescope

Weak gravitational lensing is a powerful tool in modern cosmology.To accurately measure the weak lensing signal,one has to control the systematic bias on a small level.One of the most difficult problems is how to correct the smearing effect of the Point-Spread Function(PSF)on the shape of the galaxies.The chromaticity of PSF for a broad-band observation can lead to new subtle effects.Since the PSF is wavelength-dependent and the spectrum energy distributions between stars and galaxies are different,the effective PSF measured from the star images will be different from those that smear the galaxies.Such a bias is called color bias.We estimate it in the optical bands of the Chinese Space Station Survey Telescope from simulated PSFs,and show the dependence on the color and redshift of the galaxies.Moreover,due to the spatial variation of spectra over the galaxy image,another higher-order bias exists:color gradient bias.Our results show that both color bias and color gradient bias are generally below 0.1%in CSST.Only for small-size galaxies,one needs to be careful about the color gradient bias in the weak lensing analysis using CSST data.

A Simulation of Calibration and Map-making Errors of the Tianlai Cylinder Pathfinder Array

The Tianlai cylinder array is a pathfinder for developing and testing 21 cm intensity mapping techniques.In this paper,we use numerical simulation to assess how its measurement is affected by thermal noise and the errors in calibration and map-making process,and the error in the sky map reconstructed from a drift scan survey.Here we consider only the single frequency,unpolarized case.The beam is modeled by fitting to the electromagnetic simulation of the antenna,and the variations of the complex gains of the array elements are modeled by Gaussian processes.Mock visibility data are generated and run through our data processing pipeline.We find that the accuracy of the current calibration is limited primarily by the absolute calibration,where the error comes mainly from the approximation of a single dominating point source.We then studied the m-mode map-making with the help of Moore-Penrose inverse.We find that discarding modes with singular values smaller than a threshold could generate visible artifacts in the map.The impacts of the residue variation of the complex gain and thermal noise are also investigated.The thermal noise in the map varies with latitude,being minimum at the latitude passing through the zenith of the telescope.The angular power spectrum of the reconstructed map show that the current Tianlai cylinder pathfinder,which has a shorter maximum baseline length in the North-South direction,can measure modes up to l■2πb_(NS)/λ~200 very well,but would lose a significant fraction of higher angular modes when noise is present.These results help us to identify the main limiting factors in our current array configuration and data analysis procedure,and suggest that the performance can be improved by reconfiguration of the array feed positions.

Neutrino Mass Constraints from Reconstructing the Large-scale Structure:Systematic Uncertainty

We examine the possibility of applying the baryonic acoustic oscillation reconstruction method to improve the neutrino massΣm_νconstraint.Thanks to the Gaussianization of the process,we demonstrate that the reconstruction algorithm could improve the measurement accuracy by roughly a factor of two.On the other hand,the reconstruction process itself becomes a source of systematic error.While the algorithm is supposed to produce the displacement field from a density distribution,various approximations cause the reconstructed output to deviate on intermediate scales.Nevertheless,it is still possible to benefit from this Gaussianized field,given that we can carefully calibrate the“transfer function”between the reconstruction output and theoretical displacement divergence from simulations.The limitation of this approach is then set by the numerical stability of this transfer function.With an ensemble of simulations,we show that such systematic error could become comparable to statistical uncertainties for a DESI-like survey and be safely neglected for other less ambitious surveys.

Expanding or Static Universe: Emergence of a New Paradigm

The no-evolution, concordance expanding universe cosmology and no-evolution, static universe tired light model are compared against observational data on eight cosmology tests. The no-evolution tired light model is found to make a superior fit on all tests. Any attempts to introduce evolutionary corrections to improve the concordance cosmology fit on one test often worsen its fit on other tests. Light curve data of high redshift gamma ray bursts and quasars fail to support claims for cosmological time dilation due to expansion. Also, the SCP supernova light curve test results are considered to be flawed by selection effect biases. The big bang theory also has difficulty accounting for redshift quantization, for the multi-megaparsec periodicity seen in the distribution of galaxy superclusters, and for the discovery of galaxies at redshifts as high as z ~11.9. In overview, it is concluded that a static universe cosmology must be sought to explain the origin of the universe. One possible choice is a cosmology that predicts nonconservative tired-light redshifting in intergalactic space, the continuous creation of neutrons in space, the rate of matter creation scaling with both celestial body mass and temperature, galaxies growing progressively in size, and changing their morphology in the manner suggested by Jeans and Hubble.

Observational Constraints on Varying Alpha in Λ(α)CDM Cosmology

In this work, we consider the so-called Λ(α)CDM cosmology with Λ∝α^(-6) while the fine-structure"constant" α is varying. In this scenario, the accelerated expansion of the universe is driven by the cosmological"constant" Λ(equivalently the vacuum energy), and the varying α is driven by a subdominant scalar field ? coupling with the electromagnetic field. The observational constraints on the varying α and Λ∝α^(-6) models with various couplings BF(?) between the subdominant scalar field ? and the electromagnetic field are considered.

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.

A cosmological model with negative energy photons

According to recent investigations of states of quantum fields, we postulate that there exist negative energy photons in the universe. With this assumption, we find a solution of Einstein＇s equation without introducing the cosmological constant. A new and sizable type Ia supernovae sample is employed to perform a fit with our model and the conventional model. Both models can well account for the current type Ia supernovae observation and they are not distinguishable. With the new model, the cause of the accelerated expansion of the universe and the mechanism of the negative pressure existing in outer space can be explained in ordinary physical terms.

The spatial distribution of dark matter annihilation originating from a gamma-ray line signal

The GeV-TeV -γ-ray line signal is the smoking gun signature of dark matter annihilation or decay. The detection of such a signal is one of the main targets of some space-based telescopes, including Fermi-LAT and the upcoming missions CALET, DAMPE and Gamma-400. An important feature of γ-ray line photons that originate from dark-matter-annihilation is that they are concentrated at the center of the Galaxy. So far, no reliable γ-ray line has been detected by Fermi-LAT, and the upper limits on the cross section of annihilation into ＂y-rays have been reported. We use these upper limits to estimate the ＂maximal＂ number of -y-ray line photons detectable for Fermi- LAT, DAMPE and Gamma-400, and then investigate the spatial distribution of these photons. We show that the center of the distribution will usually be offset from the Galactic center （Sgr A＊） due to the limited statistics. Such a result is almost indepen- dent of models of the dark matter distribution, and will render the reconstruction of the dark matter distribution with the γ-ray line signal very challenging for foreseeable space-based detectors.

Feasible region and stability analysis for hovering around elongated asteroids with low thrust

This paper investigates properties of low-thrust hovering, including the feasible region and stability, in terms of the dynamical parameters for elongated asteroids. An approximate rotating mass dipole model, by which the description of the rotational gravitational field is reduced to two independent parameters, is employed to construct normalized dynamical equations. The boundaries of the feasible region are determined by contours representing the magnitude of the active control. The effects of a rotating gravitational field and maximal magnitude of the low thrust on the feasible hovering regions are analyzed with numerical results. The stability conditions are derived according to the forms of the eigenvalues of the linearized equation near the hovering position. The stable regions are then determined by a grid search and the effects of the relevant parameters are analyzed in a parametric way. The results show that a close hovering can be easier to realize near the middle of the asteroid than near the two ends in the sense of both required control magnitude and stability.

New applications of the H-reversal trajectory using solar sails

Advanced solar sailing has been an increasingly attractive propulsion system for highly non-Keplerian orbits.Three new applications of the orbital angular momentum reversal（H-reversal） trajectories using solar sails are presented：space observation,heliocentric orbit transfer and collision orbits with asteroids.A theoretical proof for the existence of double H-reversal trajectories（referred to as‘H2RTs’） is given,and the characteristics of the H2RTs are introduced before a discussion of the mission applications.A new family of H2RTs was obtained using a 3D dynamic model of the two-body frame.In a time-optimal control model,the minimum period H2RTs both inside and outside the ecliptic plane were examined using an ideal solar sail.Due to the quasi-heliostationary property at its two symmetrical aphelia,the H2RTs were deemed suitable for space observation.For the second application,the heliocentric transfer orbit was able to function as the time-optimal H-reversal trajectory,since its perihelion velocity is a circular or elliptic velocity.Such a transfer orbit can place the sailcraft into a clockwise orbit in the ecliptic plane,with a high inclination or displacement above or below the Sun.The third application of the H-reversal trajectory was simulated impacting an asteroid passing near Earth in a head-on collision.The collision point can be designed through selecting different perihelia or different launch windows.Sample orbits of each application were presented through numerical simulation.The results can serve as a reference for theoretical research and engineering design.

Alternative kind of hydrogen atoms as a possible explanation for the latest puzzling observation of the 21 cm radio line from the early Universe

There is a puzzling astrophysical result concerning the latest observation of the absorption profile of the redshifted radio line 21 cm from the early Universe(as described in Bowman et al.). The amplitude of the profile was more than a factor of two greater than the largest predictions. This could mean that the primordial hydrogen gas was much cooler than expected. Some explanations in the literature suggested a possible cooling of baryons either by unspecified dark matter particles or by some exotic dark matter particles with a charge a million times smaller than the electron charge. Other explanations required an additional radio background. In the present paper, we entertain a possible different explanation for the above puzzling observational result: the explanation is based on the alternative kind of hydrogen atoms(AKHA),whose existence was previously demonstrated theoretically, as well as by the analysis of atomic experiments. Namely, the AKHA are expected to decouple from the cosmic microwave background(CMB) much earlier(in the course of the Universe expansion) than usual hydrogen atoms, so that the AKHA temperature is significantly lower than that of usual hydrogen atoms. This seems to lower the excitation(spin) temperature of the hyperfine doublet(responsible for the 21 cm line) sufficiently enough for explaining the above puzzling observational result. This possible explanation appears to be more specific and natural than the previous possible explanations. Further observational studies of the redshifted 21 cm radio line from the early Universe could help to verify which explanation is the most relevant.

Extracting 21 cm signal by frequency and angular filtering

Extracting the neutral hydrogen （HI） signal is a great challenge for cosmological 21 cm experiments; both the astrophysical foregrounds and receiver noise are typically several orders of magnitude greater than the 21 cm signal. However, the different properties of the 21 cm signal, foreground and noise can be exploited to separate these components. The foregrounds are generally smooth or correlated over the frequency space along a line of sight （LOS）, while both the 21 cm signal and noise vary stochastically along the same LoS. The foreground can be removed by filtering out the smooth component in frequency space. The receiver noise is basically uncorrelated for observations at different times, hence for surveys it is also uncorrelated in different directions, while the 21 cm signal, which traces the large scale structure, is correlated up to certain scales. In this exercise, we apply Wiener filters in frequency and angular space to extract the 21 cm signals. We found that the method works well. Inaccurate knowl- edge about the beam could degrade the reconstruction, but the overall result is still good, showing that the method is fairly robust.

Sky reconstruction for the Tianlai cylinder array

We apply our sky map reconstruction method for transit type interferometers to the Tianlai cylin- der array. The method is based on spherical harmonic decomposition, and can be applied to a cylindrical array as well as dish arrays and we can compute the instrument response, synthesized beam, transfer func- tion and noise power spectrum. We consider cylinder arrays with feed spacing larger than half a wavelength and, as expected, we find that the arrays with regular spacing have grating lobes which produce spurious images in the reconstructed maps. We show that this problem can be overcome using arrays with a different feed spacing on each cylinder. We present the reconstructed maps, and study the performance in terms of noise power spectrum, transfer function and beams for both regular and irregular feed spacing configura- tions.