A New Self Creation Cosmology

A theory is described which produces continuous creation by adapting that of Brans-Dicke. The universe is seen to be created out of the zero point energy field by self-contained gravitational, scalar, and matter fields. The theory is conformally equivalent to General Relativity in vacuo.Both the Jordan and the Einstein frames are physical and they conserve energy and four-momentum respectively. The conformal equivalence has the consequence that predictions of the theory in solar system experiments are identical with General Relativity, but definitive experiments exist which distinguish between the two theories. The cosmological solution yields a linear expansion with a dynamical density parameter Omega of anda cold matter density parameter of , but the universe is closed. The theory is free of the horizon, smoothness and density problems of GR and therefore does not need Inflation. It does however require an exotic equation of state with negative pressure and it is suggested that this is provided by a false vacuum or zero point energy determined, and there forelimited by, its field equations thereby overcoming the ‘lambda problem’. This revised version was published online in July 2006 with corrections to the Cover Date.     

Density perturbations in the Brans-Dicke theory

We give here the calculation of density perturbations in a gravitation theory with a scalar field non-minimally coupled to gravity, i.e., the Brans-Dicke theory of gravitation. The purpose is to show the influence of this scalar field on the dynamic behaviour of density perturbations along the eras where the equation of state for the matter can be put under the formp=, where is a constant. We analyse the asymptotic behaviour of this perturbations for the cases =0, =–1, =1/3 and =0. In general, we obtain a decaying and growing modes. In the very important case of inflation, =–1, there is no density perturbation, as it is well known. In the vacuum phase the perturbations on the scalar field and the gravitational field present growing modes at the beginning of the expansion and decaying modes at the end of this phase. In the case =0 it is possible, for some negative values of , to have an amplification of the perturbations with a superluminal expansion of the scale factor. We can also obtain strong growing modes for the density contrast for the case where there is a contraction phase which can have physical interest in some primordial era.     

Vacuum energy in cosmic dynamics

The analysis of the Th/U ratio in meteorites and the evolutionary ages of globular clusters favour values of the cosmic age of (19±5)×10⁹ yr. This evidence together with a Hubble parameterH ₀>70 km s^–1 Mpc^–1=(14×10⁹ yr)^–1 cannot be reconciled in a Friedmann model with =0. It requires a cosmological constant in the order of 10^–56 cm^–2, equivalent to a vacuum density _v =10^–29 g cm^–3 The Friedmann-Lemaître models (>0) with a hot big-bang have been calculated. They are based on a present value of the baryonic matter density of ₀=0.5×10^–30 g cm^–3 as derived from the primordial⁴He and²H abundances.For a Hubble parameter ofH ₀=75 km s^–1 Mpc^–1, our analysis favours a set of models which can be represented by a model with Euclidean metric (density parameter ₀=1.0, deceleration parameterq ₀=–0.93, aget ₀=19.7×10⁹ yr) and by a closed model with perpetual expansion (₀=1.072,q ₀=–1.0, aget ₀=21.4×10⁹ yr). A present density parameter close to one can indeed be expected if the conjecture of an exponential inflation of the very early universe is correct.The possible behaviour of the vacuum density is demonstrated with the help of Streeruwitz' formula in the context of the closed model with an inflationary phase at very early times.     

Verification of maximum limit of density variation parameter λ for a stable neutron star using Reissner-Nordström interior solution

A static spherically-symmetric model, based on an exact solution of Einstein's equation, gives the permissible matter density ~2 × 10¹⁴ g cm^–3. By use of the change in radius density (i.e., central density per unit radius) minimum, Parui and Sarma (1991) have estimated the upper limit of the density variation parameter = 0.68 for a superdense star such as a neutron star withK = –2. In this paper we have verified this upper limit using the Reissner-Nordström interior solution of the Einstein-Maxwell's field equations withK = - 3.     

Bianchi type-III bulk viscous string cosmological model in Brans-Dicke theory of gravitation

A spatially homogeneous and anisotropic Bianchi type-III space-time is considered in the framework of a scalar-tensor theory of gravitation proposed by Brans and Dicke (Phys. Rev. 124:925, 1961) in the presence of bulk viscous fluid containing one dimensional cosmic strings. We have found a determinate solution of the field equations using the plausible physical conditions (i) a barotropic equation state for the pressure and density, (ii) special law of variation for Hubble’s parameter proposed by Berman (Nuovo Cimento B74:182, 1983), (iii) shear scalar is proportional to scalar expansion and (iv) the trace of the energy tensor of the fluid vanishes. We have also assumed that bulk viscous pressure is proportional to energy density. Some physical and kinematical properties of the model are, also, discussed.     

The maximum limit of the density variation parameter λ for a stable neutron star

A static spherically-symmetric model, based on an exact solution of Einstein's equation, gives the permissible matter density 2×10¹⁴ g cm^–3. If we use the change in the ratio of central density to the radiusr=a (i.e., central density per unit radius (₀/a), we call it radius density) minimum, we have estimated the upper limit of the density variation parameter () and minimum mass limit of a superdense star like a neutron star. This limit gives an idea of the domain where the neutron abundance with negligible number of electrons and protons (may be treated as pure neutrons) and equilibrium in neutrons begins.     

Kaluza-Klein dark energy cosmological model in scale Co-variant Theory of Gravitation

A five dimensional Kaluza-Klein dark energy model with variable EoS parameter is investigated in the scale co-variant theory of gravitation proposed by Canuto et al. (in Phys. Rev. 39:429, 1977) in a five dimensional Kaluza-Klein space-time in the presence of perfect fluid source. Using the special law of variation for Hubble’s parameter proposed by Berman (in Nuovo Cimento B 74:183, 1983), we have obtained a determinate solution which represents a dark energy cosmological model in the theory. We have also used the result that the scalar expansion is proportional to shear scalar of the space-time. It is observed that the EoS parameter, skewness parameter in the model turn out to be functions of cosmic time. Some physical and Kinematical properties of the model are also discussed.     

The Friedmann universe and the world potential

In Section 1 of the paper the energy equation of the Friedmann universe, when matter dominates over radiation, is discussed. It is known that the value of the world potential is constant everywhere in the Universe, despite the pulsation motion of the Universe or a possible transformation of pulsation energy into matter or vice versa. The condition for the Universe being closed is deduced. Furthermore, the possibility to define the mass-energy of the Universe is discussed; and the conclusion is arrived at that the mass-energy of the Universe relative to an observer in the non-metric space outside the Universe is equal to zero; i.e. the Universe originated as a vacuum fluctuation. Finally, the view-point of an external observer is described. Such an observer can claim that our closed Universe is a black hole in a non-metric empty space. Besides, the differences between such a black hole and the astrophysical black holes are indicated.In Section 2 the origin of the gravitational force retarding the expansion is discussed, using the properties of the relativistic gravitational potential. In contradiction to Section 1, the view-point of an inner observer (inside the Universe) is used here. It is concluded that the boundary of the closed Universe is an unlocalizable potential barrier.In Section 3 of the paper the apparent discrepancy between Mach's principle and the general theory of relativity is resolved. The solution is based on the fact that, for the Euclidean open universe, the concept of mass is related to the potential of the background equal to –1, but the concept of the mass-energy is related to the zero-potential of the non-metric background. Because the universe is open and a potential barrier (a boundary of the universe) can be localized-i.e. is geometrically existing — by solution of the field equation, we have to refer to the background with zero-potential. The principal idea of the solution is then that the zero-density means the density of mass-energy, when simultaneously the mass density is equal to the critical value for which the Robertson-Walker metric becomes the Euclidean metric of the Minkowski (i.e., flat) space-time. Further a generalization of Newton's law of inertia is formulated, and the properties of nullgeodesics are touched upon. As a conclusion it is stated that this paper and the two previous ones (see Voráek, 1979a, b)de facto express Mach's principle.     

Can Brans-Dicke universes in five dimensions be interpreted as 4-dimensional general relativity cosmologies?

The 5-dimensional Jordan-Brans-Dicke cosmologies in vacuum are found for the Bianchi type I metric, their relation with general relativity cosmologies is studied. Two solutions are possible, both produce effective pressure and energy density in the 4-dimensional G.R.-universes. One is a power-law relation, with two cases, the first one is forp _eff=_eff and the other forp _eff=_eff(– 1 < < 1) has a behaviour as the open flat universe. The second solution is an exponential only valid forp _eff=–_eff. In all cases the three-space expansion reaches infinity ast and the fifth dimension can be made to decrease approaching zero. The scalar field can increase or decrease with time.     

A note on the equation of state of a scalar field

The energy momentum tensor of a scalar field is considered as being that of a perfect fluid with equation of statep=p(). In the extreme case that the field energy is purely kinetic,p=p, whereas if it is purely potential,p=–.     

The evolution of nonlinear hydrodynamical density fluctuations of the photon-plasma gas during the recombination era of the Universe

On the basis of the hydrodynamical equations of a two-component gas (photons and hydrogen with coupling via Thomson scattering) in the recombination era of the Universe (standard model), the evolution of the density perturbations up to second order are calculated. It is shown, that the generated second-order amplitudes of the density fluctuations of the matter reach values of the same order as the first-order amplitudes within only one tenth of the expansion time for fluctuations with wavelengths corresponding to 10⁷ M . Upper limits in the density fluctuations (for the gravitationally instable modes) up to which first-order calculations are valid, are given. This calculation indicates that the linear perturbation analysis is very restricted, especially at wavelengths near the lower limit of the Jeans length.The linear analysis would be a good approximation only for density fluctuations of the matter with the density contrast less than 10^–5–10^–4 at the recombination era. Therefore, a nonlinear analysis which is not based on a perturbation series is required for studying the evolution of the density perturbations, because for this we need a density contrast of 10^–2–10^–3 at the end of the recombination era.     

Inflationary solutions for anisotropic model in scalar-tensor theory

In this paper we have studied B-D theory and general scalar tensor theory of Gravitation for anisotropic cosmological model in the false vacuum state. The possibility of both exponential inflation and power function inflation are examined for constant or variable coupling parameter . Also asymptotic limit of the scalar field and are discussed.     

The cosmological model of Brans-Dicke theory

We use the generalized Brans-Dicke theory, in which the Pauli metric is identified to be the physical space-time metric, to study the Universe in different epochs. Exact analytical expressions for dilaton field , cosmological radiusR and density parameter are obtained fork=+1,0,–1 Universe in the radiation-dominated epoch. For matter dominated Epoch, exact analytical expressions for Hubble parameterH, cosmological radius, dilaton field, deceleration factorq, density parameter and the gravitational coupling of the ordinary matter are obtained for the flat Universe. Other important results are: (1) the density parameter is always less than unity for the flat Universe because the dilaton field plays a role as an effective dark matter, and (2) the new Brans-Dicke parameter must be larger than 31.75 in order to consistent with the observed data.     

A direct hydrodynamical approach to the evolution of the density correlations in an expanding flat Friedmann Universe

A direct approach of the dynamical equation for the evolution of the two-point density correlation function is given in an expanding flat Friedmann Universe in the Newtonian approximation. If the third and higher moments are neglected, a wave-like equation of third-order for the two-point density correlation function is found. The exact solution of this equation shows, in the large time limit, the usual Jeans instability t ^4/3. It is suggested that the highern-point correlation function of the density grow liket ^2n/3 in the same approximation. This indicates that every truncation procedure of the hierarchy of the equations is inapplicable at least for large timest.     

Bianchi type-V bulk viscous string cosmological model in Saez-Ballester scalar-tensor theory of gravitation

In this paper, a spatially homogeneous and anisotropic Bianchi type-V cosmological model is considered in a scalar-tensor theory of gravitation proposed by Saez and Ballester (in Phys. Lett. A 113:467, 1986) when the source for energy momentum tensor is a bulk viscous fluid containing one dimensional cosmic strings. The field equations being highly non-linear, we obtain a determinate solution using the plausible physical conditions (i) the scalar of expansion of the space-time is proportional to shear scalar (ii) the baratropic equation of state for pressure and density and (iii) the bulk viscous pressure is proportional to the energy density. It is interesting to observe that cosmic strings do not survive in this model. Some physical and kinematical properties of the model are also discussed.     

Sensitivity plots for WIMP direct detection using the annual modulation signature

Annual modulation due to the Earth's motion around the Sun is a well-known signature of the expected weakly interacting massive particle (WIMP) signal induced in a solid state underground detector. In the present paper, we discuss the prospects of this technique on statistical grounds, introducing annual-modulation sensitivity plots for the WIMP–nucleon scalar cross-section for different materials and experimental conditions. The highest sensitivity to modulation is found in the WIMP mass interval 10m_W130 GeV, the actual upper limit depends on the choice of the astrophysical parameters, while the lowest values of the explorable WIMP–nucleon elastic cross-sections fall in most cases within one order of magnitude of the sensitivities of the present direct detection WIMP searches.     

On the interior of the neutron star (II)

With the assumption, the physical 3-spacet = constant in a superdense star is spheroidal and the matter-density on the boundary surface of the configurationa = 2 × 10¹⁴ g cm^–3( the average matter density in a neutron star) Vaidya and Tikekar (1982) proposed an exact relativistic model for a neutron star. They suggested that their model can describe the hydrostatic equilibrium conditions in such a superdense star with densities in the range of 10¹⁴-10¹⁶ g cm^–3. Based on this model Parui and Sarma (1991) estimated the maximum limit of the density variation parameter for a stable neutron star (both for charged and uncharged) which is equal to 0.68, i.e. _max = 0.68.In this paper we have shown variation of central density per unit equilibrium radius (0/a), variation of mass, upper limit of density variation parameter both for charged and uncharged neutron stars at densities 10¹⁵ and 10¹⁶ g cm^–3, respectively. We have obtained _max = 0.68, i.e. the same as before. The important is that the duration of stability among the neutron star's constituents around _max will be shorter and shorter at higher densities as we proceed near the centre of the neutron star. In case of a charged neutron star, once stability among the constituents has been established, then unstability appears gradually maintaining linear relation between change in central density per unit equilibrium radius and change in mass whereas in case of uncharged neutron star, linear relation does not maintain.     

Variable constant of gravitation and celestial mechanics

In the present paper the celestial mechanics consequences (light deflection, radar ranging of the planet, geodetic precession and secular effects in the orbital elements in the two-body problem) for the class of the theories based on the vacuum Jordan's Lagrangian has been considered. In these theories the gravitational constantG is proportional to ^–, being a scalar field and , some dimensionless parameter and the local law of conservation of the energy-momentum tensor holds. Of all these theories with different the most interesting one is that corresponding to =0. In the postnewtonian approximation this gravitational theory is completely equivalent to the general theory of relativity.     

Cosmological Scalar in the Jordan-Brans-Dicke Theory. I

A variant of the Jordan-Brans-Dicke (JBD) theory is examined which contains a cosmological scalar that is written so that on going to the Einstein representation it becomes the ordinary cosmological constant of general relativity theory. This paper is divided into two parts. In Part I we examine the cosmological solutions for the Einstein representation of the JBD theory, i.e., in the presence of a minimally coupled scalar field. In Part II we shall study the cosmological solutions in the proper representation of the JBD theory with a self consistent scalar field. The analysis of these solutions is of interest in connection with modern concepts of the evolution of the universe, in particular, with the observed acceleration of cosmological expansion and estimates of the density of dark matter and dark energy.__________Translated from Astrofizika, Vol. 48, No. 3, pp. 455–462 (August 2005).