The universe is so much bigger than the bit we can see in our observable bubble   and we know nothing about what lies out there in the cosmos. The challenge is so  much bigger than is shown on this chart and it is evident that we really only  understand a tiny fraction of the whole cosmos.  Theories ​for Dark Energy have been around for a long time but we still have no  satisfactory explanation. None of the theories are adequate, some are clearly wrong    – an error of 10^120 is a really big miss!  Scott Dodelson of Carnegie Mellon University, one of the lead scientists behind the  Dark Energy Survey’s new map of cosmic structure says:

Dark Energy

Citation: Farooq, O., Madiyar, F. R., Crandall, S., & Ratra, B. (2017). HUBBLE PARAMETER MEASUREMENT CONSTRAINTS ON THE REDSHIFT OF THE DECELERATION-ACCELERATION TRANSITION, DYNAMICAL DARK ENERGY, AND SPACE CURVATURE. Astrophysical Journal, 835(1), 11. doi:10.3847/1538-4357/835/1/26

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Hubble Parameter Measurement Constraints on the Redshift of the Deceleration–acceleration Transition, Dynamical Dark Energy, and Space Curvature

We compile an updated list of 38 measurements of the Hubble parameter $H(z)$ between redshifts $0.07 \leq z \leq 2.36$ and use them to place constraints on model parameters of constant and time-varying dark energy cosmological models, both spatially flat and curved. We use five models to measure the redshift of the cosmological deceleration-acceleration transition, $z_{\rm da}$, from these $H(z)$ data. Within the error bars, the measured $z_{\rm da}$ are insensitive to the model used, depending only on the value assumed for the Hubble constant $H_0$. The weighted mean of our measurements is $z_{\rm da} = 0.72 \pm 0.05\ (0.84 \pm 0.03)$ for $H_0 = 68 \pm 2.8\ (73.24 \pm 1.74)$ km s$^{-1}$ Mpc$^{-1}$ and should provide a reasonably model-independent estimate of this cosmological parameter. The $H(z)$ data are consistent with the standard spatially-flat $\Lambda$CDM cosmological model but do not rule out non-flat models or dynamical dark energy models.

/pdf/hubble-parameter-measurement-constraints-on-the-redshift-of-3md2kl5ep6.pdf

Hubble parameter measurement constraints on the redshift of the deceleration-acceleration transition, dynamical dark energy, and space curvature

From a hydrodynamicist’s point of view the inclusion of viscosity concepts in the macroscopic theory of the cosmic fluid would appear most natural, as an ideal fluid is after all an abstraction (exluding special cases such as superconductivity). Making use of modern observational results for the Hubble parameter plus standard Friedmann formalism, we may extrapolate the description of the universe back in time up to the inflationary era, or we may go to the opposite extreme and analyze the probable ultimate fate of the universe. In this review, we discuss a variety of topics in cosmology when it is enlarged in order to contain a bulk viscosity. Various forms of this viscosity, when expressed in terms of the fluid density or the Hubble parameter, are discussed. Furthermore, we consider homogeneous as well as inhomogeneous equations of state. We investigate viscous cosmology in the early universe, examining the viscosity effects on the various inflationary observables. Additionally, we study viscous cosmology in the late universe, containing current acceleration and the possible future singularities, and we investigate how one may even unify inflationary and late-time acceleration. Finally, we analyze the viscosity-induced crossing through the quintessence-phantom divide, we examine the realization of viscosity-driven cosmological bounces, and we briefly discuss how the Cardy–Verlinde formula is affected by viscosity.

Viscous Cosmology for Early- and Late-Time Universe

Citation: Chen, Y., Kumar, S., & Ratra, B. (2017). DETERMINING THE HUBBLE CONSTANT FROM HUBBLE PARAMETER MEASUREMENTS. Astrophysical Journal, 835(1), 4. doi:10.3847/1538-4357/835/1/86

/pdf/determining-the-hubble-constant-from-hubble-parameter-wvnaui5uqp.pdf

Determining the Hubble constant from Hubble parameter measurements

We constrain the scalar field dark energy model with an inverse power-law potential, i.e., V()  −α (α > 0), from a set of recent cosmological observations by compiling an updated sample of Hubble parameter measurements including 30 independent data points. Our results show that the constraining power of the updated sample of H(z) data with the HST prior on H0 is stronger than those of the SCP Union2 and Union2.1 compilations. A recent sample of strong gravitational lensing systems is also adopted to confine the model even though the results are not significant. A joint analysis of the strong gravitational lensing data with the more restrictive updated Hubble parameter measurements and the Type Ia supernovae data from SCP Union2 indicates that the recent observations still can not distinguish whether dark energy is a time-independent cosmological constant or a time-varying dynamical component.

https://iopscience.iop.org/article/10.1088/1475-7516/2015/02/010/pdf

Constraints on a phiCDM model from strong gravitational lensing and updated Hubble parameter measurements

We constrain the scalar field dark energy model with an inverse power-law potential, i.e., $V(\phi)\propto {\phi}^{-\alpha}$ ($\alpha>0$), from a set of recent cosmological observations by compiling an updated sample of Hubble parameter measurements including 30 independent data points. Our results show that the constraining power of the updated sample of $H(z)$ data with the HST prior on $H_0$ is stronger than those of the SCP Union2 and Union2.1 compilations. A recent sample of strong gravitational lensing systems is also adopted to confine the model even though the results are not significant. A joint analysis of the strong gravitational lensing data with the more restrictive updated Hubble parameter measurements and the Type Ia supernovae data from SCP Union2 indicates that the recent observations still can not distinguish whether dark energy is a time-independent cosmological constant or a time-varying dynamical component.

Constraints on a $\phi$CDM model from strong gravitational lensing and updated Hubble parameter measurements

We investigate the viable exponential $f(R)$ gravity in the metric formalism with $f(R)=-\beta R_s (1-e^{-R/R_s})$. The latest sample of the Hubble parameter measurements with 23 data points is used to place bounds on this $f(R)$ model. A joint analysis is also performed with the luminosity distances of Type Ia supernovae and baryon acoustic oscillations in the clustering of galaxies, and the shift parameters from the cosmic microwave background measurements, which leads to $0.240 1.47$ at 1$\sigma$ confidence level. The evolutions of the deceleration parameter $q(z)$ and the effective equations of state $\omega_{de}^{eff}(z)$ and $\omega_{tot}^{eff}(z)$ are displayed. By taking the best-fit parameters as prior values, we work out the transition redshift (deceleration/acceleration) $z_T$ to be about 0.77. It turns out that the recent observations are still unable to distinguish the background dynamics in the $\Lambda$CDM and exponential $f(R)$ models.

Constraints on the exponential $f(R)$ model from latest Hubble parameter measurements

Constraints on the inverse power-law scalar field dark energy model from strong gravitational lensing data and updated Hubble parameter measurements

https://doi.org/10.1016/j.dark.2023.101234

Yun Chen

Papers

Constraints on a phiCDM model from strong gravitational lensing and updated Hubble parameter measurements

Constraints on a $\phi$CDM model from strong gravitational lensing and updated Hubble parameter measurements

Constraints on the exponential $f(R)$ model from latest Hubble parameter measurements

Constraints on the inverse power-law scalar field dark energy model from strong gravitational lensing data and updated Hubble parameter measurements

Cosmological Application of the Lens-Redshift Probability Distribution with Improved Galaxy-Scale Gravitational Lensing Sample