Extending the Redshift-Distance Relation in Cosmological General Relativity to Higher Redshifts

The redshift-distance modulus relation, the Hubble Diagram, derived from Cosmological General Relativity has been extended to arbitrarily large redshifts. Numerical methods were employed and a density function was found that results in a valid solution of the field equations at all redshifts. The extension has been compared to 302 type Ia supernova data as well as to 69 Gamma-ray burst data. The latter however do not truly represent a ‘standard candle’ as the derived distance moduli are not independent of the cosmology used. Nevertheless the analysis shows a good fit can be achieved without the need to assume the existence of dark matter. The Carmelian theory is also shown to describe a universe that is always spatially flat. This results from the underlying assumption of the energy density of a cosmological constant Ω_Λ=1, the result of vacuum energy. The curvature of the universe is described by a spacevelocity metric where the energy content of the curvature at any epoch is Ω _K =Ω_Λ−Ω=1−Ω, where Ω is the matter density of the universe. Hence the total density is always Ω _K +Ω=1.     

Hydrodynamic vacuum sources of dark matter self-generation in an accelerating universe without a Big Bang

We have obtained a generalization of the hydrodynamic theory of vacuum in the context of general relativity. While retaining the Lagrangian character of general relativity, the new theory provides a natural alternative to the view that the singularity is inevitable in general relativity and the theory of a hot Universe. We show that the macroscopic source-sink motion as a whole of ordinary (dark) matter that emerges during the production of particles out of the vacuum can be a new source of gravitational vacuum polarization (determining the variability of the cosmological term in general relativity). We have removed the well-known problems of the cosmological constant by refining the physical nature of dark energy associated precisely with this hydrodynamically initiated variability of the vacuum energy density. A new exact solution of the modified general relativity equations that contains no free (fitting) parameter additional to those available in general relativity has been obtained. It corresponds to the continuous and metric-affecting production of ultralight dark matter particles (with mass m ₀ = (ħ/c ²) $ \sqrt {12\rho _0 k} $ \sqrt {12\rho _0 k} ≈ 3 × 10⁻⁶⁶ g, k is the gravitational constant) out of the vacuum, with its density ρ₀, constant during the exponential expansion of a spatially flat Universe, being retained. This solution is shown to be stable in the regime of cosmological expansion in the time interval −∞ < t < t _max, when t = 0 corresponds to the present epoch and t _max= 2/3H ₀ cΩ_0m ≈ 38 × 10⁹ yr at Ω_0m = ρ₀/ρ_c ≈ 0.28 (H ₀ is the Hubble constant, ρ_c is the critical density). For t > t _max, the solution becomes exponentially unstable and characterizes the inverse process of dark matter particle absorption by the vacuum in the regime of contraction of the Universe. We consider the admissibility of the fact that scalar massive photon pairs can be these dark matter particles. Good quantitative agreement of this exact solution with the cosmological observations of SnIa, SDSS-BAO, and the decrease in the acceleration of the expansion of the Universe has been obtained.     

A Cyclic Model of Universe with Energy Exchange between Radiation,Matter and Vacuum Energy

We further extend the cosmological scenario with energy exchange by Barrow and Clifton and our previous work to the more complex case with energy exchange between three fluids: radiation, matter and vacuum energy. By prescribing the form of energy exchange function, we construct an infinitely cyclic cosmological model, in which the universe undergoes an endless sequence of cosmic epoch and each consisting of expansion and contraction, and the cosmological parameters, such as the Hubble parameter H, deceleration parameter q, transition red-shift Z _T, and densities ρ _r ,ρ _m , and ρ _Λ are consistent with the present observed values.     

Dark energy degeneracies in the background dynamics

We discuss degeneracies between dark energy and cosmic parameters using a fully non-perturbative and non-parametric approach. This allows us to examine the knock-on bias induced in the reconstructed dark energy equation of state, w(z), if there is a bias in the cosmic curvature or dark matter content. Assuming perfect Hubble, distance and volume measurements, we show that for z > 1, the bias in w(z) is up to two orders of magnitude larger than the corresponding errors in Ω _k or Ω _m .     

The Distance Modulus Determined from Carmeli’s Cosmology Fits the Accelerating Universe Data of the High-redshift Type Ia Supernovae Without Dark Matter

The velocity of the Hubble expansion has been added to General Relativity by Moshe Carmeli and this resulted in new equations of motion for the expanding universe. For the first time the observational magnitude–redshift data derived from the high-z supernova teams has been analysed in the framework of the Carmeli theory and the fit to that theory is achieved without the inclusion of any dark matter. Best fits to the data yield an averaged matter density for the universe at the present epoch Ω_m ≈ 0.021, which falls well within the measured values of the baryonic matter density. And the best estimate of Ω_Λ+ Ω_m ≈ 1.021 at the present epoch. The analysis also clearly distinguishes that the Hubble expansion of the universe is speed-limited.     

Cosmology with galaxy correlations

In this review, I outline the use of galaxy correlations to constrain cosmological parameters. As with the cosmic microwave background (CMB), the density of dark and baryonic matter imprints important scales on the fluctuations of matter and thus the clustering of galaxies, e.g., the particle horizon at matter-radiation equality and the sound horizon at recombination. Precision measurements of these scales from the baryon acoustic oscillations (BAO) and the large scale shape of the power spectrum of galaxy clustering provide constraints on Ω _m h ². Recent measurements from the Sloan Digital Sky Survey (SDSS) and 2dF Galaxy Redshift Survey (2dFGRS) strongly suggest that Ω _m < 0.3. This forms the basic evidence for a flat Universe dominated by a Cosmological Constant (Λ) today (when combined with results from the CMB and supernova surveys). Further evidence for this cosmological model is provided by the late-time Integrated Sachs–Wolfe (ISW) effect, which has now been detected using a variety of tracers of the large scale structure in the Universe out to redshifts of z > 1. The ISW effect also provides an opportunity to discriminate between Λ, dynamical dark energy models and the modification of gravity on large scales.     

Features of holographic dark energy under combined cosmological constraints

We investigate the observational signatures of the holographic dark-energy models, including both the original model and a model with an interaction term between the dark energy and dark matter. We first delineate the dynamical behavior of such models, especially considering whether they would have a “big rip” for different parameters; then we use several recent observations, including 182 high-quality type Ia supernovae data observed with the Hubble Space Telescope, the SNLS and ESSENCE surveys, 42 latest Chandra X-ray cluster gas mass fraction, 27 high-redshift gamma-ray burst samples, the baryon acoustic oscillation measurement from the Sloan Digital Sky Survey, and the CMB shift parameter from the WMAP three-year result to give more reliable and tighter constraints on the holographic dark-energy models. The results of our constraints for the holographic dark-energy model without interaction is c=0.748_−0.009^+0.108, Ω _m0=0.276_−0.016^+0.017, and for the model with interaction (c=0.692_−0.107^+0.135, Ω _m0=0.281_−0.017^+0.017, α=−0.006_−0.024^+0.021, where α is an interacting parameter). As these models have more parameters than the ΛCDM model, we use the Bayesian Evidence as a model-selection criterion to make comparisons. We found that the holographic dark-energy models are mildly favored by the observations as compared to the ΛCDM model.     

Running coupling: does the coupling between dark energy and dark matter change sign during the cosmological evolution?

In this paper we put forward a running coupling scenario for describing the interaction between dark energy and dark matter. The dark sector interaction in our scenario is free of the assumption that the interaction term Q is proportional to the Hubble expansion rate and the energy densities of dark sectors. We only use a time-variable coupling b(a) (with a the scale factor of the universe) to characterize the interaction Q. We propose a parametrization form for the running coupling b(a)=b ₀ a+b _e (1−a) in which the early-time coupling is given by a constant b _e , while today the coupling is given by another constant, b ₀. For investigating the feature of the running coupling, we employ three dark energy models, namely, the cosmological constant model (w=−1), the constant w model (w=w ₀), and the time-dependent w model (w(a)=w ₀+w ₁(1−a)). We constrain the models with the current observational data, including the type Ia supernova, the baryon acoustic oscillation, the cosmic microwave background, the Hubble expansion rate, and the X-ray gas mass fraction data. The fitting results indicate that a time-varying vacuum scenario is favored, in which the coupling b(z) crosses the noninteracting line (b=0) during the cosmological evolution and the sign changes from negative to positive. The crossing of the noninteracting line happens at around z=0.2–0.3, and the crossing behavior is favored at about 1σ confidence level. Our work implies that we should pay more attention to the time-varying vacuum model and seriously consider the phenomenological construction of a sign-changeable or oscillatory interaction between dark sectors.     

Cosmological Consequences of Scale-Related Comoving Masses for Cosmic Pressure, Mass, and Vacuum Energy Density

According to ideas of Mach, Whitrow, Dirac, or Hoyle, inertial masses of particles should not be a genuine, predetermined quantity; rather they should represent a relational quantity which by its value somehow reflects the deposition and constellation of all other objects in their cosmic environment. In this paper we want to pick up suggestions given by Thirring and by Hoyle of how, due to requirements of the equivalence of rotations and of general relativistic conformal scale invariance, the particle masses of cosmic objects should vary with the cosmic length scale. We study cosmological consequences of comoving cosmic masses which co-evolve by mass with the expansion of the universe. The vanishing of the covariant divergence of the cosmic energy-momentum tensor under the new prerequisite that matter density only falls off with the reciproke of the squared cosmic scale S(t) then leads to the astonishing result that cosmic pressuredoes not fall off adiabatically but rather falls off in a quasi-isothermal behaviour, varying with S(t) as matter density does. Hence, as a new cosmological fact, it arises that, even in the late phases of cosmic expansion, pressure cannot be neglected what concerns its gravitational action on the cosmic dynamics. We then show that under these conditions the cosmological equations can, however, only be solved if, in addition to matter, also pressure and energy density of the cosmic vacuum are included in the calculation. An unaccelerated expansion with a Hubble parameter falling off with S(t)⁻¹ is obtained for a vacuum energy density decay according to S(t)⁻² with a well-tuned proportion of matter and vacuum pressures. As it appears from these results, a universe with particle masses increasing with the cosmic sale S(t) is in fact physically conceivable in an energetically consistent manner, if vacuum energy at the expansion of the universe is converted into mass density of real matter with no net energy loss occuring. This universe in addition also happens to be an economical one which has and keeps a vanishing total energy.     

The cosmological constant revisited

I briefly review the observational evidence for a small cosmological constant at the present epoch. This evidence mainly comes from high redshift observations of Type 1a supernovae, which, when combined with CMB observations strongly support a flat Universe with Ω _m + Ω_A ⋍ 1. Theoretically a cosmological constant can arise from zero point vacuum fluctuations. In addition ultra-light scalar fields could also give rise to a Universe which is accelerating driven by a time dependent Λ-term induced by the scalar field potential. Finally a Λ dominated Universe also finds support from observations of galaxy clustering and the age of the Universe.     

Equation of state for the Universe from similarity symmetries

In this paper we proposed to use the group of analysis of symmetries of the dynamical system to describe the evolution of the Universe. This method is used in searching for the unknown equation of state. It is shown that group of symmetries enforce the form of the equation of state for noninteracting scaling multifluids. We showed that symmetries give rise to the equation of state in the form p =-Λ + w ₁ρ(a) + w ₂ a ^β + 0 and energy density ρ = Λ+ρ₀₁ a ^-3(1+w) +ρ₀₂ a ^α +ρ₀₃ a ^-3, which is commonly used in cosmology. The FRW model filled with scaling fluid (called homological) is confronted with the observations of distant type Ia supernovae. We found the class of model parameters admissible by the statistical analysis of SNIa data.We showed that the model with scaling fluid fits well to supernovae data. We found that Ω_m,0 ≃ 0.4 and n ≃ -1 (β = -3n), which can correspond to (hyper) phantom fluid, and to a high density universe. However if we assume prior that Ω_m,0 = 0.3 then the favoured model is close to concordance ΛCDM model. Our results predict that in the considered model with scaling fluids distant type Ia supernovae should be brighter than in the ΛCDM model, while intermediate distant SNIa should be fainter than in the ΛCDM model. We also investigate whether the model with scaling fluid is actually preferred by data over ΛCDM model. As a result we find from the Akaike model selection criterion: it prefers the model with noninteracting scaling fluid.     

Spacetime Curvature is Important for Cosmology Constrained with Supernova Emissions

We investigate universe expansion models as functions of emission frequency ratio decline rather than redshift z, using the latest on-line, self-consistent data from 192 supernovae. We present results for simpler and some current models of cosmology, including those with dark energy (standard model) and a recent model correcting for the effect of a small time-dependent, emission frequency increase with lookback. This new model, with a gentle lookback decline of the Planck constant, and the standard model fit the data with similar confidence according to Bayesian Information Criteria. The standard model tends towards solutions high in matter density while remaining flat, but models without dark energy tend towards dilute universes with significant spacetime and curvature and a smaller Hubble constant. We conclude the normalized spacetime parameter, Ω _k , should not be ignored and it includes the combined contributions of huge spacetime magnitude and curvature.     

Anisotropic Universe Models with Perfect Fluid and Dark Energy with Time Varying G and Λ

We have investigated general Bianchi type I cosmological models which containing a perfect fluid and dark energy with time varying G and Λ that have been presented. The perfect fluid is taken to be one obeying the equation of state parameter, i.e., p=ωρ; whereas the dark energy density is considered to be either modified polytropic or the Chaplygin gas. Cosmological models admitting both power-law which is explored in the presence of perfect fluid and dark energy too. We reconstruct gravitational parameter G, cosmological term Λ, critical density ρ _c , density parameter Ω, cosmological constant density parameter Ω _Λ and deceleration parameter q for different equation of state. The present study will examine non-linear EOS with a general nonlinear term in the energy density.     

f(R) theories of gravity in the Palatini approach matched with observations

We investigate the viability of f(R) theories in the framework of the Palatini approach as solutions to the problem of the observed accelerated expansion of the universe. Two physically motivated popular choices for f(R) are considered,: power law, f(R) = β R ⁿ , and logarithmic, f(R) = α ln R. Under the Palatini approach, both Lagrangians give rise to cosmological models comprising only standard matter and undergoing a present phase of accelerated expansion. We use the Hubble diagram of type Ia Supernovae and the data on the gas mass fraction in relaxed galaxy clusters to see whether these models are able to reproduce what is observed and to constrain their parameters. It turns out that they are indeed able to fit the data with values of the Hubble constant and of the matter density parameter in agreement with some model independent estimates, but the today deceleration parameter is higher than what is measured in the concordance ΛCDM model.     

Carmeli's Cosmology Fits Data for an Accelerating and Decelerating Universe Without Dark Matter or Dark Energy

A new relation for the density parameter Ω is derived as a function of expansion velocity υ based on Carmeli's cosmology. This density function is used in the luminosity distance relation D _L. A heretofore neglected source luminosity correction factor (1 − (υ/c)²)^−1/2 is now included in D _L. These relations are used to fit type Ia supernovae (SNe Ia) data, giving consistent, well-behaved fits over a broad range of redshift 0.1 < z < 2. The best fit to the data for the local density parameter is Ω_m = 0.0401 ± 0.0199. Because Ω_m is within the baryonic budget there is no need for any dark matter to account for the SNe Ia redshift luminosity data. From this local density it is determined that the redshift where the universe expansion transitions from deceleration to acceleration is z _t = 1.095^+0.264 _−0.155. Because the fitted data covers the range of the predicted transition redshift z _t, there is no need for any dark energy to account for the expansion rate transition. We conclude that the expansion is now accelerating and that the transition from a closed to an open universe occurred about 8.54 Gyr ago.     

Smoothening of a random surface as it results from the edwards-wilkinson kinetic equation

The time evolution of a random surfacez=h(r, t) (r=x, y) formed by a deposition process of the Edwards-Wilkinson type is discussed. The discussion is based on the author’s former derivation of the autocorrelation functionA _h(|r − r′|,t, t′)=〈h(r,t)h(r′,t′)〉 of the height functionh(r,t) under the assumption of a stochastic initial condition [V. Bezák: Acta Physica Univ. Comenianae39 (1998) 135]. Under the assumption of a steady (non-zero) deposition rate, the varianceσ _h ² (t)=〈[h(r,t)]²〉 increases logarithmically in time whilst the correlation lengthl _h(t) of the height functionh(r,t) increases as ∼t ^1/2. Therefore, the ratioσ _h(t)/l _h (t) tends to zero and the surfacez=h(r,t) does always tend towards a smoothened appearance. This work has been supported by the Slovak Grant Agency VEGA under contract No. 1/4319/97.     

Constraints on accelerating universe using ESSENCE and Gold supernovae data combined with other cosmological probes

We use recent data: the 192 ESSENCE type Ia supernovae (SNe Ia), the 182 Gold SNe Ia, the three-year WMAP, the SDSS baryon acoustic peak, the X-ray gas mass fraction in clusters and the observational H(z) data, to constrain models of the accelerating universe. Combining the 192 ESSENCE data with the observational H(z) data to constrain the parameterized deceleration parameter, we obtain the best-fit values of the transition redshift and current deceleration parameter z _T=0.632_−0.127^+0.256 and q ₀=−0.788_−0.182^+0.182. Furthermore, using the ΛCDM model and two model-independent equations of state of the dark energy, we find that the combined constraint from the 192 ESSENCE data and four other cosmological observations gives smaller values for Ω _0m and q ₀, but a larger value for z _T than the combined constraint from the 182 Gold data with four other observations. Finally, according to the Akaike information criterion it is shown that the recently observed data equally support three dark energy models: ΛCDM, w _de(z)=w ₀ and w _de(z)=w ₀+w ₁ln (1+z).     

LRS Bianchi Type II Bulk Viscous Fluid Universe with?Decaying Vacuum Energy Density Λ

The present study deals with spatially homogeneous and locally rotationally symmetric (LRS) Bianchi type II cosmological models with bulk viscous fluid distribution of matter and decaying vacuum energy density Λ. To get the deterministic models of the universe, we assume that the expansion (θ) in the model is proportional to the shear (σ). This leads to condition R=mS ⁿ , where R and S are metric potentials, m and n are constants. We have obtained two types of models of the universe for two different values of n. The vacuum energy density Λ for both models is found to be a decreasing function of time and it approaches a small positive value at late time which is supported by recent results from the observations of (SN Ia). Some physical and geometric behaviour of these models are also discussed.     

Can Inflation, Dark Matter and Dark Energy Be Described in Terms of a Single, Real Scalar Field?

In this article, our aim is to consider inflation, dark energy and dark matter in the framework of a real scalar field. To this end, we use the quintessence approach. We have tried a real scalar field with a specific self-interaction potential in a spacially flat universe. Numerical results indicate that this potential can drive the expansion of the universe in three distinct phases. The first phase behaves as an inflationary expansion. For this stage, setting the scalar field’s initial value to ϕ ₀≥1.94 leads to N 3 68\mathcal{N}\geq 68 favored by observation. After the inflationary phase, the scalar field starts an oscillatory behavior which averages to a =0\bar{w}=0 fluid. This stage can be taken as a cold dark matter (p≈0) epoch expected from works on the structure formation issue. Observations and cosmological models indicate that t _inf ≈10⁻³⁵ s and the matter dominated lasts for t _m ≈10¹⁷ s, hence (\fract_mt_inf)_obs ? 10⁵²(\frac{t_{m}}{t_{inf}})_{obs}\approx10^{52}. We have shown that the present model can satisfy such a constraint. Finally, the scalar field leaves the oscillatory behavior and once again enters a second inflationary stage which can be identified with the recent accelerated expansion of the universe. We have also compared our model with the ΛCDM model and have found a very good agreement between the equation of state parameter of both of models during the DM and DE era.