The expansion field: the value of <Emphasis Type="Italic">H</Emphasis><Subscript>0</Subscript>

Any calibration of the present value of the Hubble constant (H ₀) requires recession velocities and distances of galaxies. While the conversion of observed velocities into true recession velocities has only a small effect on the result, the derivation of unbiased distances which rest on a solid zero point and cover a useful range of about 4–30 Mpc is crucial. A list of 279 such galaxy distances within v < 2,000 km s⁻¹ is given which are derived from the tip of the red-giant branch (TRGB), from Cepheids, and/or from supernovae of type Ia (SNe Ia). Their random errors are not more than 0.15 mag as shown by intercomparison. They trace a linear expansion field within narrow margins, supported also by external evidence, from v = 250 to at least 2,000 km s⁻¹. Additional 62 distant SNe Ia confirm the linearity to at least 20,000 km s⁻¹. The dispersion about the Hubble line is dominated by random peculiar velocities, amounting locally to <100 km s⁻¹ but increasing outwards. Due to the linearity of the expansion field the Hubble constant H ₀ can be found at any distance >4.5 Mpc. RR Lyr star-calibrated TRGB distances of 78 galaxies above this limit give H ₀ = 63.0 ± 1.6 at an effective distance of 6 Mpc. They compensate the effect of peculiar motions by their large number. Support for this result comes from 28 independently calibrated Cepheids that give H ₀ = 63.4 ± 1.7 at 15 Mpc. This agrees also with the large-scale value of H ₀ = 61.2 ± 0.5 from the distant, Cepheid-calibrated SNe Ia. A mean value of H ₀ = 62.3 ± 1.3 is adopted. Because the value depends on two independent zero points of the distance scale its systematic error is estimated to be 6%. Other determinations of H ₀ are discussed. They either conform with the quoted value (e.g. line width data of spirals or the D _n −σ method of E galaxies) or are judged to be inconclusive. Typical errors of H ₀ come from the use of a universal, yet unjustified P–L relation of Cepheids, the neglect of selection bias in magnitude-limited samples, or they are inherent to the adopted models.     

Bianchi type-II space-times with constant deceleration parameter in self creation cosmology

The properties of locally rotationally symmetric Bianchi type-II perfect fluid space-times are analyzed in Barber’s second self-creation theory by using a special law of variation for Hubble’s parameter that yields a constant value of deceleration parameter. By assuming the equation of state p=γ ρ, many new solutions are obtained for different era—Zel’dovich, radiation, vacuum and vacuum energy dominated. The solutions with power-law and exponential expansion are discussed. A detailed study of geometrical and physical parameters is carried out. The nature of singularity is also clarified in each case.     

The redshift revisited

We analyse the history of modern cosmology based on the redshift phenomenon and on the cosmic background radiation (CBR). We show the models of different authors for the interpretation of the redshift and how the tired light models predicted the correct value of 2.7 K temperature previous to Gamow and collaborators.     

How can NASA’s Lunar Reconnaissance Orbiter projects verify the existence of the fifth force

The spring constant of the earth is found to be 1.1 × 10⁻⁸/s² which is based on the famous Pound and Rebka gravitational red-shift experimental data. The spring force, or so-called the fifth force of the earth is then known. This paper suggests how can NASA’s Lunar Reconnaissance Orbiter (LRO) projects verify the existence of the fifth force by simple free fall experiment without man-mission. Such a force, as we have predicted, should be the type of intermediate range.     

Cosmological models with shear and rotation

Cosmological models involving shear and rotation are considered, first in the general relativistic and then in the Newtonian framework with the aim of investigating singularities in them by using numerical and analytical techniques. The dynamics of these rotating models are studied. It is shown that singularities are unavoidable in such models and that the centrifugal force arising due to rotation can never overcome the gravitational and shearing force over a length of time.     

Bianchi type-I,III, V,VIo and Kantowski-Sachs universes in creation-field cosmology

The solutions of Einstein’s equations in the presence of a creation field have been obtained for Bianchi type-I, III, V, VIo and Kantowski-Sachs (KS) universes in the quadrature form. Some physically interesting cases have been studied in detail.     

Shear and vorticity in a combined Einstein-Cartan-Brans-Dicke inflationary lambda-Universe

A combined BCDE (Brans-Dicke and Einstein-Cartan) theory with lambda-term is developed through Raychaudhuri’s equation, for inflationary scenario. It involves a variable cosmological constant, which decreases with time, jointly with energy density, cosmic pressure, shear, vorticity, and Hubble’s parameter, while the scale factor, total spin and scalar field increase exponentially. The post-inflationary fluid resembles a perfect one, though total spin grows, but the angular speed does not (Astrophys. Space Sci. 312: 275, 2007d).      

A Cosmological Model with Negative Constant Deceleration Parameter in a Scalar-Tensor Theory

With the help of a special law of variation for Hubble's parameter presented by Bermann [Nuovo Cimento B (1983), 74, 182], a cosmological model with negative constant deceleration parameter is obtained in the framework of Saez-Ballester [Phys. Lett (1985), Al 13, 467] scalar -- tensor theory of gravitation. Some physical and kinematical properties of the model are, also, discussed.     

Anisotropic Bianchi type-I models with constant deceleration parameter in general relativity

A special law of variation for Hubble’s parameter is presented in a spatially homogeneous and anisotropic Bianchi type-I space-time that yields a constant value of deceleration parameter. Using the law of variation for Hubble’s parameter, exact solutions of Einstein’s field equations are obtained for Bianchi-I space-time filled with perfect fluid in two different cases where the universe exhibits power-law and exponential expansion. It is found that the solutions are consistent with the recent observations of type Ia supernovae. A detailed study of physical and kinematical properties of the models is carried out.