An inflationary cosmological model in Dunn's scalar-tensor theory of gravitation

The gravitational field equations in Dunn's scalar-tensor theory of gravitation are generalized by including a cosmological constant. The resulting equations are solved for a Robertson-Walker line-element with flat three-space. The solution represents a cosmological model that develops into an inflationary era.     

Note concerning gravitation and electromagnetism

The Maxwell equations for gravitational fields previously assumed by Sciama are derived from elementary considerations. The Lagrangian for a gravitating mass in a non-inertial coordinate system yields equations of motion leading to force definitions for a gravitational field intensity and a gravitational induction field. The non-inertial velocity of the coordinate system plays the role of a vector potential contributing to the generalized momenta of bodies moving in the system. A Lagrangian density constructed from the force-defined fields then lead to the source definitions of gravitational fields. It is found that positive field energy densities require repulsive gravitational forces, whereas attractive forces imply the violation of the conservation of energy. This paradox is resolved by representing gravitational quantities as pure-imaginary entities. Thus characterized, the equations which define gravitational fields become identical to Maxwell's equations but are pure-imaginary. This suggests a combined representation for gravitational and electromagnetic fields which, in covariant form, indicates both the well known equivalence of mass and energy and a possible equivalence of charge and energy. From orthogonality considerations, it is conjectured that this latter energy is gravitational, and that, whereas gravitational fields interact with electromagnetic energy, electromagnetic fields interact with gravitational energy. Parts of this work were completed at Air Force Cambridge Research Laboratories, Bedford, Mass., U.S.A.     

Further results for astrophysics from the cosmology within the framework of the Projective Unified Field Theory

Recently the 5‐dimensional Projective Unified Field Theory (PUFT) of the author (Schmutzer 1995a, Schmutzer 1995b) has been applied to a closed homogeneous isotropic cosmological model with the result of a cosmology without big bang (Schmutzer 1999a, Schmutzer 1999b). Continuing this approach, in this paper following subjects are treated: recalculation of numerical values of cosmological quantities, exact solution of the field equations to a point‐like body, motion of a test body in such a field, definition of the empirical effective gravitational factor (“constant”), Einstein effects compared to the empirical situation, adiabatic approximation of the motion of an orbiting testbody under the influence of the expanding cosmos (transition of the ellipses to circles, decrease of the radius of the orbiting bodies, decrease of the excentricity, increase of the frequency of orbiting objects etc.), heat production in a moving body induced by the cosmological expansion with application to various cosmic objects.     

Global Monopole and C-Field

It is well known that a C-field, generated by a certain source equation leads to interesting changes in the cosmological solutions of Einstein's equations. It is argued that different types of topological objects may have been created by the vacuum phase transitions in the early universe. In the cosmological arena, the defects have been put forward as a possible mechanism for structure formation. A global monopole is a heavy object formed in the phase transition of a system composed of a self coupling scalar field triplet φ^a whose original global 0(3) symmetry is spontaneously broken to U(1). In this article, we find a special solution for the space-time of a global monopole in presence of C-field. It is shown that the nature of the solution remains the same as in general relativity case i.e. monopole exerts no gravitational force on the matter surrounding it but space around it has a deficit solid angle. Pacs Nos: 98.80cq, 04.20jb, 04.50     

Some Robertson-Walker models with time dependent <Emphasis Type="Italic">G</Emphasis> and Λ

Einstein field equations with variable gravitational and cosmological constants are considered in the presence of perfect fluid for Robertson-Walker universe by assuming the cosmological term proportional to the Hubble parameter. This variation law for vacuum density has recently been proposed by Schützhold on the basis of quantum field estimations in the curved and expanding background. The cosmological term tends asymptotically to a genuine cosmological constant and the model tends to a deSitter universe. We obtain that the present universe is accelerating with a large fraction of cosmological density in the form of cosmological term.     

Robertson-Walker cosmological models with perfect fluid in general relativity

Einstein's field equations with variable gravitational and cosmological constants are considered in the presence of perfect fluid for a Robertson-Walker universe by assuming the cosmological term to be proportional to R-m(R is a scale factor and m is a constant).A variety of solutions is presented.The physical significance of the cosmological models has also been discussed.     

Black hole solutions in warped DGP brane world

Using the effective gravitational field equations in the warped DGP brane-world scenario (Maeda et al. in Phys. Rev. D 68:024033, 2003), we study spherically symmetric vacuum (static black hole) solutions on the brane. Working with a conformally flat bulk, we have obtained an exact Schwarzschild–de Sitter black hole solution similar to the standard solution in the presence of a cosmological constant, which confirms the idea that an extra term in the effective vacuum field equations on the warped DGP brane can play the role of a positive cosmological constant.     

Cosmological models with time-varying gravitational and cosmological “constants”

The evolution and dynamics of a locally-rotationally-symmetric (LRS) Bianchi type-V space-time cosmological models are discussed with variable gravitational and cosmological “constants” in context of the particle creation. We present the exact solutions of Einstein field equations by using a power-law form of the average scale factor of the metric in the case of the particle creation and in the absence of particle creation. The solution describes the particle and entropy generation in the anisotropic cosmological models. The particle creation rate is uniquely determined by the variation of gravitational and cosmological “constants”. We observe that the variable gravitational constant does not necessarily imply particle creation. In a generic situation, models can be interpolated between different phases of the universe. The dynamical behaviors of the solutions and kinematical parameters of the model are discussed in detail.     

Bianchi type-I cosmological models with time dependent G and Λ

Einstein field equations with variable gravitational and cosmological constants are considered in the presence of perfect fluid for Bianchi type-I universe by assuming the cosmological term proportional to the Hubble parameter. This variation law for vacuum density has recently been proposed by Schützhold on the basis of quantum field estimations in the curved and expanding background. The model obtained approaches isotropy. The cosmological term tends asymptotically to a genuine cosmological constant, and the model tends to a deSitter universe. We obtain that the present universe is accelerating with a large fraction of cosmological density in the form of cosmological term.     

Bianchi type-I cosmological models with perfect fluid in general relativity

Einstein's field equations with variable gravitational and cosmological constants are considered in the presence of perfect fluid for the Bianchi type-Ⅰ universe by assuming that the cosmological term is proportional to R-m(R is a scale factor and m is a constant).A variety of solutions are presented.The physical significance of the respective cosmological models are also discussed.     

The statistics of weak lensing at small angular scales: probability distribution function

Weak gravitational lensing surveys have the potential to probe mass density fluctuation in the Universe directly. Recent studies have shown that it is possible to model the statistics of the convergence field at small angular scales by modelling the statistics of the underlying density field in the highly non-linear regime. We propose a new method to model the complete probability distribution function of the convergence field as a function of smoothing angle and source redshift. The model relies on a hierarchical ansatz for the behaviour of higher order correlations of the density field. We compare our results with ray-tracing simulations and find very good agreement over a range of smoothing angles. Whereas the density probability distribution function is not sensitive to the cosmological model, the probability distribution function for the convergence can be used to constrain both the power spectrum and cosmological parameters.     

Perihel-Bewegung und kosmologische Singularität in TREDERS Gravitationstheorie

In the framework of TREDER 's gravitational theory we elaborate the consequences of a class of field equations for some solar-system effects and their connection to the problem of cosmological singularity. These equations read on special conditions with components of the energy momentum tensor, KRONECKER 's symbol, tetrad components). ω is a real parameter. If we choose the integration constants of the static spherically symmetric vacuum case in such a way that red shift is the same like that of EINSTEIN 's theory and the source of gravitational field is that of a point mass we obtain for the perihelion rotation the expression is EINSTEINS value of the perihelion rotation.) For we obtain But only if ω > 2/5 cosmological models exist which have no cosmological singularity. On the other hand for ω > 2/5 the value is greater than.     

Radial two-fluid cosmological models

Zero-curvature Friedmann-Robertson-Walker cosmological models that are exact solutions of Einstein's field equations and the laws of thermodynamics in which the source of the gravitational field is a comoving radiation field and a radial non-comoving imperfect fluid are investigated.     

Plane-symmetric universes in general relativity

Plane-symmetric solutions of Einstein's field equations in vacuum, in the presence of electromagnetic fields and with cosmological constant are explored in null coordinates. The gravitational field of an infinite plane (uncharged and charged both) is thus obtained in a simple and systematic way. The method adopted for these solutions has possibilities of generalization.     

Cosmological physics with black holes (and possibly white dwarfs)

The notion that microparsec-scale black holes can be used to probe gigaparsec-scale physics may seem counterintuitive, at first. Yet, the gravitational observatory LISA will detect cosmologically-distant coalescing pairs of massive black holes, accurately measure their luminosity distance and help identify an electromagnetic counterpart or a host galaxy. A wide variety of new black hole studies and a gravitational version of Hubble’s diagram become possible, if host galaxies are successfully identified. Furthermore, if dark energy is a manifestation of large-scale modified gravity, deviations from general relativistic expectations could become apparent in a gravitational signal propagated over cosmological scales, especially when compared to the electromagnetic signal from a same source. Finally, since inspirals of white dwarfs into massive black holes at cosmological distances may permit pre-merger localizations, we suggest that careful monitoring of these events and any associated electromagnetic counterpart could lead to high-precision cosmological measurements with LISA.     

Conformally symmetric Abelian Higgs sunspot and non-metricity of the Sun's spacetime

A U(1)-symmetric Yang-Mills-Higgs (i.e., an Abelian Higgs) sunspot's model is recognized to originate from a massless, complex-valued scalar field coupled minimally to electromagnetic gauge potentials in the background of a (globally)conformally symmetric semi-metric spacetime, whose metric structure is described by the generalized Einstein equations with nonvanishing (positive-valued) cosmological constant. It is shown, in particular, that non-linearity (selfcoupling) of the scalar field appears due to a non-zeroness of the cosmological term, whereas its non-zero vacuum amplitude is induced by the (Ricci scalar) curvature of the Sun's spacetime manifold.     

Cosmological models with the variable gravitational and cosmological constants

Cosmology with the gravitational and cosmological constants generalized as coupling scalars in Einsteins theory is considered. A general method of solving the field equations is given. Exact solution for Zeldovich fluid satisfying G=G ₀(R/R ₀) ⁿ is given.     

非微扰的极早期宇宙现象学: 共振的原初扰动与非高斯尾巴

在精确宇宙学的时代, 多信使、高精度、小尺度的宇宙学观测在帮助人们从更加深刻的层面理解宇宙极早期的同时, 也给基于线性近似和微扰展开宇宙学扰动理论带来了新的挑战. 近年来, 对原初引力波和原初黑洞的搜寻使得研究人员们对早期宇宙在小尺度上的非线性非微扰过程产生了浓厚的研究兴趣. 综述了在宇宙学小尺度上关于原初黑洞产生以及引力波研究取得的诸多进展, 重点关注了使用Mathieu方程的共振效应来研究小尺度功率谱放大以及诱导产生可观测的原初引力波的方法. 此外, 还尝试探讨了非高斯尾巴对原初黑洞形成的影响. 发现Mathieu方程所具备的共振效应可以提供一种有效的方法来刻画原初宇宙中小尺度的非微扰动力学过程, 从而能够更好地理解原初黑洞的形成以及相关的引力波产生机制. 同时, 非微扰的非高斯性在原初黑洞形成中可能会产生不可忽视的影响.     

Exact Boltzmann-Gas Filled Bianchi Type V Space-Times

Bianchi type V cosmological models are studied that contain a relativistic ideal Boltzmann gas. The effect of a cosmological constant upon the space-time geometry is also considered. In both high and low temperature limit the general solution of the Einstein gravitational field equations can be expressed in an exact closed parametric form. At final stages, depending on the presence or absence of the cosmological constant, cosmologies are driven to an isotropic inflationary open de Sitter type Universe or to an isotropic open Friedmann era.     

Exact Nonbarotropic Bianchi Type I Universe

Bianchi type I cosmological models are studied that contain a nonbarotropic relativistic Boltzmann gas. The effect of a cosmological constant is considered too. In the limit of small temperatures the general solution of the Einstein gravitational field equations can be expressed in an exact closed parametrical form. At final stages, depending on the presence or absence of the cosmological constant, cosmologies are driven to an isotropic inflationary de Sitter Universe or to an isotropic Friedmann era. This revised version was published online in July 2006 with corrections to the Cover Date.