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.

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.

Dark energy in five-dimensional Brans-Dicke cosmology with dimensional reduction

We explore a 5D Brans-Dicke scalar cosmology by conjecturing that the four-dimensional Hubble parameter varies as H = εФ^s, ε ∈ R and s is some unknown power index and that the extra-dimensions compactify as the visible dimensions expand as b（t） ≈ a^x （t）, x ∈R^-. We mainly discuss the case x = - 1. For critical values of e close to unity, it was observed that the acceleration of the universe occurs at red- shift close to z = 0.8 which indicates that in our model, accelerated expansion of the universe began only recently. Several interesting points are revealed and discussed in some detail.

Interacting viscous entropy-corrected holographic scalar field models of dark energy with time-varying G in modified FRW cosmology

We study the entropy-corrected version of the holographic dark energy （HDE） model in the framework of modified Friedmann-Robertson-Walker cosmology. We consider a non-flat universe filled with an interacting viscous entropy-corrected HDE （ECHDE） with dark matter. Also included in our model is the case of the variable gravitational constant G. We obtain the equation of state and the deceleration param- eters of the interacting viscous ECHDE. Moreover, we reconstruct the potential and the dynamics of the quintessence, tachyon, K-essence and dilaton scalar field models according to the evolutionary behavior of the interacting viscous ECHDE model with time-varying G.

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.

An interacting two-fluid scenario for dark energy in a Bianchi type-I cosmological model

We study the evolution of the dark energy parameter within a Bianchi type-I cosmological model filled with barotropic fluid and dark energy. The solutions have been obtained for power law and exponential forms of the expansion parameter （they correspond to a constant deceleration parameter in general relativity）. After a long time, the models tend to be isotropic under certain conditions.

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 Inverse Gravity Inflationary Theory of Cosmology

Cosmological expansion or inflation is mathematically described by the theoretical notion of inverse gravity whose variations are parameterized by a factor that is a function of the distance to which cosmological expansion takes prominence over gravity. This assertion is referred to as the inverse gravity inflationary assertion. Thus, a correction to Newtonian gravitational force is introduced where a parameterized inverse gravity force term is incorporated into the classical Newtonian gravitational force equation where the inverse force term is negligible for distances less than the distance to which cosmological expansion takes prominence over gravity. Conversely, at distances greater than the distance to which cosmological expansion takes prominence over gravity. The inverse gravity term is shown to be dominant generating universal inflation. Gravitational potential energy is thence defined by the integral of the difference (or subtraction) between the conventional Newtonian gravitational force term and the inverse gravity term with respect to radius (r) which allows the formulation, incorporation, and mathematical description to and of gravitational redshift, the Walker-Robertson scale factor, the Robinson-Walker metric, the Klein-Gordon lagrangian, and dark energy and its relationship to the energy of the big bang in terms of the Inverse gravity inflationary assertion. Moreover, the dynamic pressure of the expansion of a cosmological fluid in a homogeneous isotropic universe is mathematically described in terms of the inverse gravity inflationary assertion using the stress-energy tensor for a perfect fluid. Lastly, Einstein’s field equations for the description of an isotropic and homogeneous universe are derived incorporating the mathematics of the inverse gravity inflationary assertion to fully show that the theoretical concept is potentially interwoven into the cosmological structure of the universe.

Quark-Novae Ia in the Hubble diagram: implications for dark energy

The accelerated expansion of the Universe was proposed through the use of Type-Ia supernovae （SNe） as standard candles. The standardization depends on an empirical correlation between the stretch/color and peak luminosity of the light curves. The use of Type-Ia SNe as standard candles rests on the assumption that their properties （and this correlation） do not vary with redshift. We consider the possibility that the majority of Type-Ia SNe are in fact caused by a Quark-Nova detonation in a tight neutron-star-CO-white-dwarf binary system, which forms a Quark-Nova Ia （QN-Ia）. The spin-down energy injected by the Quark-Nova remnant （the quark star） contributes to the post-peak light curve and neatly explains the observed correlation between peak luminosity and light curve shape. We demonstrate that the parameters describing QN-Ia are NOT constant in redshift. Simulated QN-Ia light curves provide a test of the stretch/color correlation by comparing the true distance modulus with that determined using SN light curve fitters. We determine a correction between the true and fitted distance moduli, which when applied to Type-Ia SNe in the Hubble diagram recovers the ΩM = 1 cosmology. We conclude that Type-Ia SNe observations do not necessitate the need for an accelerating expansion of the Universe （if the observed SNe Ia are dominated by QNe Ia） and by association the need for dark energy.

An interacting scenario for dark energy in a Bianchi type-I universe

We study the interaction between dark energy （DE） and dark matter in the scope of anisotropic Bianchi type-I space-time. First we derive the general form of the DE equation of state （EoS） parameter in both non-interacting and interacting cases and then we examine its future by applying a hyperbolic scale factor. It is shown that in the non-interacting case, depending on the value of the anisotropy parameter K, the DE EoS parameter varies from phantom to quintessence whereas in the interacting case the EoS parameter varies in the quintessence region. However, in both cases, the DE EoS parameter ωde ultimately （i.e. at z ： -1） tends to the cosmological constant （ωde = -1）. Moreover, we fix the cosmological bound on the anisotropy parameter K by using recent observational data about the Hubble parameter.

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 brief review on cosmological analysis of galaxy surveys with multiple tracers

Galaxy redshift surveys are one of the key probes in modern cosmology.In the data analysis of galaxy surveys,the precision of the statistical measurement is primarily limited by the cosmic variance on large scales.Fortunately,this limitation can in principle be mitigated by observing multiple types of biased tracers.In this brief review,we present the idea of the multi-tracer method,outline key steps in the data analysis and show several worked examples based on the GAMA,BOSS and e BOSS galaxy surveys.This work is a part of a special issue dedicated to the 20 th anniversary of RAA(2001–2020),which is prefaced in Wang&Ip(2020).

Probing dynamics of dark energy with latest observations

We examine the validity of the ACDM model and probe the dynamics of dark energy with the latest astronomical observations. Using the Ore（z） diagnosis, we find that various kinds of observational data are in tension within the ACDM framework. We then allow for dynamics of dark energy and investigate the constraint on dark energy parameters. We find that for two different kinds of parametri- sations of the equation of state parameter w, a combination of current data mildly favours an evolving w, although the significance is not sufficient for it to be supported by Bayesian evidence. A forecast of the DESI survey shows that the dynamics of dark energy could be detected at the 7σ confidence level and would be decisively supported by Bayesian evidence, if the best-fit model of w derived from current data is the true model.

Constraints on smoothness parameter and dark energy using observational H(z) data

With large-scale homogeneity,the universe is locally inhomogeneous,clustering into stars,galaxies and larger structures.Such property is described by the smoothness parameter α which is defined as the proportion of matter in the form of intergalactic medium.If we consider the inhomogeneities over a small scale,there should be modifications of the cosmological distances compared to a homogenous model.Dyer and Roeder developed a second-order ordinary differential equation（D-R equation） that describes the angular diameter distance-redshift relation for inhomogeneous cosmological models.Furthermore,we may obtain the D-R equation for observational H（z） data（OHD）.The density-parameter ΩM,the state of dark energy ω,and the smoothness-parameter α are constrained by a set of OHD in a spatially flat XCDM universe as well as a spatially flat XCDM universe.By using a χ2 minimization method,we get α = 0.81＋0.19-0.20 and ΩM = 0.32＋0.12-0.06 at the 1σ confidence level.If we assume a Gaussian prior of ΩM = 0.26 ± 0.1,we get α = 0.93＋0.07-0.19 and ΩM = 0.31＋0.06-0.05.For the XCDM model,α is constrained to α≥ 0.80 but ω is weakly constrained around-1,where ω describes the equation of state of the dark energy（pX = ωρX）.We conclude that OHD constrains the smoothness parameter more effectively than the data of SNe Ia and compact radio sources.

Comparison of cosmological models using standard rulers and candles

In this paper, we used standard rulers and standard candles （separately and jointly） to explore five popular dark energy models under the assumption of the spatial flatness of the Universe. As standard rulers, we used a data set comprised of 118 galactic scale strong lensing systems （individual standard rulers if properly calibrated for the mass density profile） combined with BAO diagnostics （statistical standard ruler）. Type Ia supernovae served as standard candles. Unlike most previous statistical studies involving strong lensing systems, we relaxed the assumption of a singular isothermal sphere （SIS） in favor of its generalization： the power-law mass density profile. Therefore, along with cosmological model parameters, we fitted the power law index and its first derivative with respect to the redshift （thus allowing for mass density profile evolution）. It turned out that the best fitted ~/parameters are in agreement with each other, irrespective of the cosmological model considered. This demonstrates that galactic strong lensing systems may provide a complementary probe to test the properties of dark energy. The fits for cosmological model parameters which we obtained are in agreement with alternative studies performed by other researchers. Because standard rulers and standard candles have different parameter degeneracies, a combination of stan- dard rulers and standard candles gives much more restrictive results for cosmological parameters. Finally, we attempted an analysis based on model selection using information theoretic criteria （AIC and BIC）. Our results support the claim that the cosmological constant model is still best and there is no （at least statistical） reason to prefer any other more complex model.

Interacting two-fluid viscous dark energy models in a non-flat universe

We study the evolution of the dark energy parameter within the scope of a spatially non-fiat and isotropic Friedmann-Robertson-Walker model filled with barotropic fluid and bulk viscous stresses. We have obtained cosmological solutions that do not have a Big Rip singularity, and concluded that in both non-interacting and interacting cases the non-fiat open Universe crosses the phantom region. We find that during the evolution of the Universe, the equation of state for dark energy ωD changes from ωDeff 〉 - 1 to ωDeff 〈 - 1, which is consistent with recent observations.

FLRW non-singular cosmological model in general relativity

A singularity free cosmological model is obtained in a homogeneous and isotropic background with a specific form of the Hubble parameter in the presence of an interacting dark energy represented by a time-varying cosmological constant in general relativity. Different cases that arose have been extensively studied for different values of the curvature parameter. Some interesting results have been found with this form of the Hubble parameter to meet the possible negative value of the decelera- tion parameter （- 1/3≤ q 〈 0） as the current observations reveal. For some particular values of these parameters, the model reduces to Berman＇s model.

Accelerating dark energy models with anisotropic fluid in Bianchi type Ⅵ_0 space-time

Motivated by the increasing evidence for the need of a geometry that re- sembles Bianchi morphology to explain the observed anisotropy in the WMAP data, we have discussed some features of Bianchi type VI0 universes in the presence of a fluid that has an anisotropic equation of state （EoS） parameter in general relativity. We present two accelerating dark energy （DE） models with an anisotropic fluid in Bianchi type VI0 space-time. To ensure a deterministic solution, we choose the scale factor a（t） = √tnet, which yields a time-dependent deceleration parameter, representing a class of models which generate a transition of the universe from the early decelerating phase to the recent accelerating phase. Under suitable conditions, the anisotropic mod- els approach an isotropic scenario. The EoS for DE co is found to be time-dependent and its existing range for derived models is in good agreement with data from recent observations of type Ia supernovae （SNe Ia） （Knop et al. 2003）, SNe Ia data com- bined with cosmic microwave background （CMB） anisotropy and galaxy clustering statistics （Tegmark et al. 2004a）, as well as the latest combination of cosmological datasets coming from CMB anisotropies, luminosity distances of high redshift SNe Ia and galaxy clustering. For different values of n, we can generate a class of physically viable DE models. The cosmological constant A is found to be a positive decreasing function of time and it approaches a small positive value at late time （i.e. the present epoch）, which is corroborated by results from recent SN Ia observations. We also ob- serve that our solutions are stable. The physical and geometric aspects of both models are also discussed in detail.

Interaction of Gravitational field and Brans-Dicke field in R/W universe containing Dark Energy like fluid

On studying some new models of Robertson-Walker universes with a Brans-Dicke scalar field, it is found that most of these universes contain a dark energy like fluid which confirms the present scenario of the expansion of the universe. In one of the cases, the exact solution of the field equations gives a universe with a false vacuum, while in another it reduces to that of dust distribution in the Brans-Dicke cosmology when the cosmological constant is not in the picture. In one particular model it is found that the universe may undergo a Big Rip in the future, and thus it will be very interesting to investigate such models further.

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.