Zel’dovich Λ and Weinberg’s relation: an explanation for the cosmological coincidences

In 1937 Dirac proposed the large number hypothesis (LNH). The idea was to explain that these numbers were large because the Universe is old. A time variation of certain “constants” was assumed. So far, no experimental evidence has significantly supported this time variation. Here we present a simplified cosmological model. We propose a new cosmological system of units, including a cosmological Planck’s constant that “absorbs” the well known large number 10¹²⁰. With this new Planck’s constant no large numbers appear at the cosmological level. They appear at lower levels, e.g. at the quantum world. We note here that Zel’dovich formula, for the cosmological constant Λ, is equivalent to the Weinberg’s relation. The immediate conclusion is that the speed of light c must be proportional to the Hubble parameter H, and therefore decrease with time. We find that the gravitational radius of the Universe and its size are one and the same constant (Mach’s principle). The usual cosmological Ω’s parameters for mass, lambda and curvature turn out to be all constants of order one. The anthropic principle is not necessary in this theory. It is shown that a factor of 10⁶¹ converts in this theory a Planck fluctuation (a quantum black hole) into a cosmological quantum black hole: the Universe today. General relativity and quantum mechanics give the same local solution of an expanding Universe with the law a(t)≈const?t. This constant is just the speed of light today. Then the Hubble parameter is exactly H=a(t)′/a(t)=1/t.     

Delay of emission from extragalactic gamma-ray burst sources as a test for selecting a model of the universe

We obtained an order-of-magnitude estimate for the dispersion of light caused by the effect of quantum fluctuations on the propagation of electromagnetic waves in four-dimensional spacetime. We calculated the delay of the photons from cosmological gamma-ray bursts (GRBs) for the flat, open, and closed cosmological models. This delay is attributable to the effect of expansion of the Universe on the propagation of a dispersive light wave in space. Analysis shows that the delay of GRB photons contains a regular component related to the expansion of the Universe. We conclude that cosmological models of the Universe can be selected by the delay of emission of various energies from GRBs; the accuracy of measuring the parameter Δt/ΔE _γ must be no lower than 10^?6 s MeV^?1.     

Lymanα forests and the evolution of the universe

The Lyα forest absorption lines in the spectra of quasars are interpreted as caused by the crossings of the light beam with the walls of a bubble structure (expanding with the Hubble flow only). Then, the typical separation between the absorption lines is proportional to the mean size of the bubbles. The variable factor is the expansion rate H[z]. The Friedmann regression analysis of the observed line separations determines the density parameter ω₀ and the normalized cosmological term λ₀ = λc²/3H²₀ of the appropriate cosmological model: ω₀ = 0.014 ± 0.002, λ₀ = 1.080 ± 0.006. Depending on the Hubble parameter this method reveals the values of the present mean matter density pm,0 = 2.6 h² · 10⁻²⁸ kg m⁻³ and of the cosmological constant Λ = 3.77 h² · 10⁻⁵² m⁻² (with h = H₀/(100 km/s·Mpc)). According to our analysis all models with Λ = 0 must be excluded. The curvature of space is positive. The curvature radius R₀ is 3.3 times the Hubble radius (c/H₀). The age t₀ is 2.8 times the Hubble age (H₀⁻¹).     

Two restrictions in the theories that include G(t) and c(t) varying with time

Much work has been done taking into account the possibility that the gravitational constant G may vary with cosmological time t (or with the cosmological scale factor a(t)). The same may be said about the speed of light c. We present here two important remarks on these subject. These remarks include G(t) and c(t) varying with time with the restriction 8πG/c ⁴=constant.     

On the neutrino mass and the Lemaitre model

In the light of the experiments /3,4/ showing that neutrinos may have a non-zero rest-mass, we discuss the constraints placed on the cosmological term Λ and the Hubble constant H_o by such a mass and the age of the universe in the Lemaitre model. An upper limit of Λ of 15 × 10^?57/cm² and possible ranges of H_o are given.     

Time evolution of the unstable two-fluid density fluctuations in Robertson-Walker Universes

We consider density fluctuations of a two-fluid model consisting of hydrogen plasma and radiation prior to the cosmic hydrogen recombination. As investigation method that of the dispersion relations is applied, which have been derived from the general-relativistic sound-wave equations taking into account the coupling between plasma and radiation carefully. We obtain growing unstable acoustic modes within the mass range 2 · 10⁶ M _⊙ < M < 6 · 10 ¹² M _⊙. In a second step the coupled differential equations for the amplitudes of the unstable modes are integrated numerically with respect to time where the integration extends from the initial time prior to the hydrogen recombination up to the present time. We find a significant increase of the amplitudes up to 4 orders of magnitude, if the Universe is described by a cosmological model with a positive cosmological constant (Λ ? 2,2 · 10^-56 cm^-2) and a positive curvature (Lemaître-Universe) without an essential amount of cold dark matter. We conclude that the existence of galaxies confirm these statements.     

Physical constants and evolution of the Universe

A cosmological model is discussed which is based on interpretation of the red shift by decrease of the light speed with time everywhere in the Universe beginning with a certain moment of time in the past. The model is described by a metric in which the light speed depends on time and the radius of the curvature of three-dimensional space remains constant (c-metric). It is shown that this metric leads to the same observed facts and formulas of different characteristics that the metric of standard cosmology does but with essentially different physical interpretation. Such a property is the consequence of conformity of spaces being defined by both metrics. The agreement with the fundamental physics laws is achieved by introducing the evolution of a number of other fundamental constants synchronously with the variation of the light speed. The model considered connected the evolution of the Universe with evolution of physical constants and permits explaining some unclear cosmological phenomena — for example, a high isotropy of the relict background and superluminal speed in quasars.     

A new class of Bianchi cosmological models in f(R,T) gravity

The new class of cosmological model of the early Universe is considered with f(R,T) modified theories of gravity (Harko et al. in Phys. Rev. D 84:024020, 2011). The exact solutions to the corresponding field equations are obtained in quadrature form. The cosmological parameters have been discussed in detail. We have also discussed the well-known astrophysical phenomena, namely the Hubble parameter H(z), luminosity distance (d _L ) and distance modulus μ(z) with redshift.     

A two-dimensional study for cooling and self-gravitating accretion discs

A solution to the coincidence and Big Rip problems on the bases of an anisotropic space-time is proposed. To do so, we study the interaction between viscous dark energy and dark matter in the scope of the Bianchi type-I Universe. We parameterize the viscosity and the interaction between the two fluids by constants ζ ₀ and σ respectively. A detailed investigation on the cosmological implications of this parametrization has been made. We have also performed a geometrical diagnostic by using the statefinder pairs {s,r} and {q,r} in order to differentiate between different dark energy models. Moreover, we fit the coupling parameter σ as well as the Hubble’s parameter H ₀ of our model by minimizing the χ ² through the age differential method, involving a direct measurement of H.     

Measurements of the Matter Density Perturbation Amplitude from Cosmological Data

The various measurements of the linear matter density perturbation amplitude obtained from the observations of the cosmic microwave background (CMB) anisotropy, weak gravitational lensing, galaxy cluster mass function, matter power spectrum, and redshift space distortions are compared. The Planck data on the CMB temperature anisotropy spectrum at high multipoles, ? > 1000 (where the effect of gravitational lensing is most significant), are shown to give a measurement of the matter density perturbation amplitude that contradicts all other measurements of this quantity from both Planck CMB anisotropy data and other data at a significance level of about 3.7σ. Thus, at present these data should not be combined together for the calculations of constraints on cosmological parameters. Except for the Planck data on the CMB temperature anisotropy spectrum at high multipoles, all the remaining measurements of the density perturbation amplitude agree well between themselves and give the following constraints: σ₈ = 0.792± 0.006 on the linear matter density perturbation amplitude, Ω_m = 0.287± 0.007 on the matter density parameter, and H₀ = 69.4 ± 0.6 km s^?1 Mpc^?1 on the Hubble constant. Various constraints on the sum of neutrino masses and the number of neutrino flavors can be obtained by additionally taking into account the data on baryon acoustic oscillations and (or) direct Hubble constant measurements in the local Universe.     

Cosmological scalar fields that mimic the ΛCDM cosmological model

We look for cosmologies with a scalar field (dark energy without cosmological constant), which mimic the standard ΛCDM cosmological model yielding exactly the same large-scale geometry described by the evolution of the Hubble parameter (i.e. photometric distance and angular diameter distance as functions on z). Asymptotic behavior of the field solutions is studied in the case of spatially flat Universe with pressureless matter and separable scalar field Lagrangians; the cases of power-law kinetic term and power-law potential are considered. Exact analytic solutions are found in some special cases. A number of models have the field solutions with infinite behavior in the past or even singular behavior at finite redshifts. We point out that introduction of the cosmological scalar field involves some degeneracy leading to lower precision in determination of Ω _m . To remove this degeneracy additional information is needed besides the data on large-scale geometry. The article is published in the original.     

Absorption of Photons from Distant Gamma-Ray Sources

Being the largest gravitationally bound structures in the Universe, galaxy clusters are huge reservoirs of photons generated by the bremsstrahlung of a hot cluster gas. We consider the absorption of high-energy photons from distant cosmological gamma-ray sources by the bremsstrahlung of galaxy clusters. The magnitude of this effect is the third in order of smallness after the effects of absorption by the cosmic microwave background and absorption by the extragalactic background light. Our calculations of the effect of absorption by the bremsstrahlung of galaxy clusters have shown that this effect manifests itself in the energy range ~1–100 GeV and can be τ ~ 10^?5 in optical depth.     

Non-expanding universe: a cosmological system of units

The product of two empirical constants, the dimensionless fine-structure constant (α) and the von Klitzing constant (R _k, an electrical resistance), turns out to be an exact dimensionless number. Then the accuracy and cosmological time variation (if any) of these two constants can be tied together. Also this product defines a natural unit of the electrical resistance, the inverse of a quantum of conductance. When the speed of light c is taken away from α, as has been shown elsewhere, the constancy of α implies the constancy of the ratio e ²/h (the inverse of the von Klitzing constant), e being the charge of the electron and h the Planck constant. This forces the charge of the electron e to be constant as long as the action h (an angular momentum) is a true constant too. From the constancy of the Rydberg constant the Compton wavelength, h/mc, is then a true constant and consequently there is no expansion at the quantum mechanical level. The momentum mc is also a true constant and then general relativity predicts that the universe is not expanding, as shown elsewhere. The time variation of the speed of light explains the observed Hubble red shift. And there is a mass-boom effect. From this a coherent cosmological system of constant units can be defined.     

On possible cosmic origin of the 11-year solar cycle

In order to test Dicke??s idea of a clock hidden inside the Sun and determine the initial phase of the solar cycle, the epochs of the extrema of the Wolf numbers observed over the past 400 years are examined. It is shown that extrema that obey the period P _W equaled 11.07(4) years retain the initial phase, which cannot be explained in terms of local physics and concepts of the past century regarding the mechanism of the solar cycle based on the theory of a magnetic dynamo and the phenomenological model of the Babcock-Leighton cycle. It is suggested that the cycle has a cosmic (cosmological) origin. This is clearly indicated by the correlation of the cycle period with a holographic time-scale of the Universe, (a ₀ R ³)^1/4/c ?? 11.0(4) years, where a ₀ and R are the radii of the first Bohr orbit of a hydrogen atom and the observable Universe, respectively, and c is the speed of light. It is noted that there are other strict holographic relations that include a ₀, R, P _W , the wavelength of the microwave background radiation (with a temperature of 2.7 K), and a period of the global solar pulsations equal to 9600.6 s. The true physical nature of the governing mechanism for the 11-year cycle can perhaps only be understood based on modern concepts about the nonlocality of our world, which follows from Bell??s theorem, which is grounded on the achievements of quantum mechanics at the turn of the 20th and 21st centuries, as well as using a model of a holographic Universe free of c.     

The Ionization Rate During the Decoupling Period in a Universe with Nonzero Cosmological Constant

Nonzero cosmological constant favours cosmological models with larger Hubble constant. The evolution of ionization during decoupling period in a universe with nonzero cosmological constant is computed by using a corrected recombination coefficient. Also presented in this paper is the redshift distribution of the last scattering surfaces of the cosmic background photons while the cosmological constant is nonvanishing. Finally, we give a brief estimation about the influence of H_e on the last scattering surfaces. This revised version was published online in July 2006 with corrections to the Cover Date.     

Anisotropic universe and observational constraint on the dark energy models with the cosmological redshift drift

This study set out to examine the effect of anisotropy on the various dark energy models by using the observational data, including the Sandage-Loeb test, Strongly gravitationally lensing, observational Hubble data, and Baryon Acoustic Oscillations data. In particular, we consider three cases of dark energy models: the cosmological constant model, which is most favored by current observations, the wCDM model where dark energy is introduced with constant w equation of state parameter and in Chevalier-Polarski-Linder parametrization where ω is allowed to evolve with redshift. With an anisotropy framework, a maximum likelihood method to constrain the cosmological parameters was implemented. With an anisotropic universe, we also study the behavior of different cosmological parameters such as Hubble parameter, EoS parameter, and deceleration parameter of dark energy models mentioned. The results indicate that the Bianchi type I model for the dark energy models are consistent with the combined observational data.     

The influence of host galaxy morphology on the properties of Type Ia supernovae from the JLA compilation

The observational cosmology with distant Type Ia supernovae (SNe) as standard candles claims that the Universe is in accelerated expansion, caused by a large fraction of dark energy. In this paper we investigate the SN Ia environment, studying the impact of the nature of their host galaxies on the Hubble diagram fitting. The supernovae (192 SNe) used in the analysis were extracted from Joint-Light-curves-Analysis (JLA) compilation of high-redshift and nearby supernovae which is the best one to date. The analysis is based on the empirical fact that SN Ia luminosities depend on their light curve shapes and colors. We confirm that the stretch parameter of Type Ia supernovae is correlated with the host galaxy type. The supernovae with lower stretch are hosted mainly in elliptical and lenticular galaxies. No significant correlation between SN Ia colour and host morphology was found. We also examine how the luminosities of SNe Ia change depending on host galaxy morphology after stretch and colour corrections. Our results show that in old stellar populations and low dust environments, the supernovae are slightly fainter. SNe Ia in elliptical and lenticular galaxies have a higher α (slope in luminosity-stretch) and β (slope in luminosity-colour) parameter than in spirals. However, the observed shift is at the 1-σ uncertainty level and, therefore, can not be considered as significant. We confirm that the supernova properties depend on their environment and that the incorporation of a host galaxy term into the Hubble diagram fit is expected to be crucial for future cosmological analyses.     

Generalized holographic dark energy model in the Hubble length

We generalize the holographic dark energy model described in Hubble length IR cutoff by assuming a slowly time varying function for holographic parameter c ². We calculate the evolution of EoS parameter and the deceleration parameter as well as the evolution of dark energy density parameter of the model in flat FRW universe. We show that in this model the phantom line is crossed from quintessence regime to phantom regime which is in agreement with observation. The evolution of deceleration parameter of the model indicates the transition from decelerated to accelerated expansion consistently with observation. Eventually, we show that the holographic dark energy model with Hubble horizon IR cutoff can interpret the pressureless dark matter era at the early time and dark energy dominated phase later. The singularity of the model is also calculated.     

General class of Bianchi cosmological models with Λ in creation-field cosmology

The solutions of Einstein’s equations with cosmological constant (Λ) in the presence of a creation field have been obtained for general class of anisotropic cosmological models. We have obtained the cosmological solutions for two different scenarios of average scale factor. In first case, we have discussed three different types of physically viable cosmological solutions of average scale factor for the general class of Bianchi cosmological models by using a special law for deceleration parameter which is linear in time with a negative slope. In second case, we have discussed another three different forms of cosmological solutions by using the average scale factor in three different scenarios like Intermediate scenario, Logamediate scenario and Emergent scenario. All physical parameters are calculated and discussed in each physical viable cosmological model. We examine the nature of creation field and cosmological constant is dominated the early Universe but they do not survive for long time and finally tends to zero for large cosmic time t. We have also discussed the all energy conditions in each cases.     

Molecules in the early universe

The formation of first molecules, negative Hydrogen ions, and molecular ions in a model of the Universe with cosmological constant and cold dark matter is studied. The cosmological recombination is described in the framework of modified model of the effective 3-level atom, while the kinetics of chemical reactions is described in the framework of the minimal model for Hydrogen, Deuterium, and Helium. It is found that the uncertainties of molecular abundances caused by the inaccuracies of computation of cosmological recombination are approximately 2–3%. The uncertainties of values of cosmological parameters affect the abundances of molecules, negative Hydrogen ions, and molecular ions at the level of up to 2%. In the absence of cosmological reionization at redshift z = 10, the ratios of abundances to the Hydrogen one are 3.08 × 10^–13 for H^–, 2.37 × 10^–6 for H₂, 1.26 × 10^–13 for H₂⁺, 1.12 × 10^–9 for HD, and 8.54 × 10^–14 for HeH⁺.