Cosmological singularities and higher-order gravitational lagrangians

General relativity is modified by adding terms proportional to R² and R^μνR_μν to the Lagrangian. One class of solutions of the modified field equations is free of singularities but does not lead to asymptotic behaviour (for large time) of the Friedmann type. A second class, which shows the correct asymptotic behaviour, does contain the usual singularities of Friedmann universes, collapse being modulated by small oscillations only. The quantum effects considered here are thus unable to prevent the occurrence of cosmological singularities under physically reasonable conditions.     

Using gravitational lenses to detect gravitational waves

Gravitational lenses could be used to detect gravitational waves, because a gravitational wave affects the travel-time of a light ray. In a gravitational lens, this effect produces time-delays between the different images. Thus the bending of light, which was the first experimental confirmation of Einstein's theory, can be used to search for gravitational waves, which are the most poorly confirmed aspect of that same theory. Applying this method to the gravitational lens 0957+561 gives new upper bounds on the amplitude of low-frequency gravitational waves in the universe, and new limits on the energy-density during an early inflationary phase.This Essay received the First Award from the Gravity Research Foundation, 1990-Ed.     

Cosmological meaning of the gravitational gauge group

It is shown that among the \(R+\beta S^{abc}S_{abc}\) models, only the one with \(\beta =1/2\) has nonvanishing torsion effect in the Robertson–Walker universe filled with a spin fluid, where \(S_{abc}\) denotes torsion. Moreover, the torsion effect in that model is found to be able to replace the big-bang singularity by a big bounce. Furthermore, we find that the model can be obtained under a Kaluza–Klein-like ansatz, by assuming that the gravitational gauge group is the de Sitter group.     

Cosmological tests of gravity

Modifications of general relativity provide an alternative explanation to dark energy for the observed acceleration of the universe. We review recent developments in modified gravity theories, focusing on higher-dimensional approaches and chameleon/f(R) theories. We classify these models in terms of the screening mechanisms that enable such theories to approach general relativity on small scales (and thus satisfy solar system constraints). We describe general features of the modified Friedman equation in such theories.The second half of this review describes experimental tests of gravity in light of the new theoretical approaches. We summarize the high precision tests of gravity on laboratory and solar system scales. We describe in some detail tests on astrophysical scales ranging from ∼ kpc (galaxy scales) to ∼ Gpc (large-scale structure). These tests rely on the growth and inter-relationship of perturbations in the metric potentials, density and velocity fields which can be measured using gravitational lensing, galaxy cluster abundances, galaxy clustering and the integrated Sachs-Wolfe effect. A robust way to interpret observations is by constraining effective parameters, such as the ratio of the two metric potentials. Currently tests of gravity on astrophysical scales are in the early stages — we summarize these tests and discuss the interesting prospects for new tests in the coming decade.     

Characterization of classical Gaussian processes using quantum probes

We address the use of a single qubit as a quantum probe to characterize the properties of classical noise. In particular, we focus on the characterization of classical noise arising from the interaction with a stochastic field described by Gaussian processes. The tools of quantum estimation theory allow us to find the optimal state preparation for the probe, the optimal interaction time with the external noise, and the optimal measurement to effectively extract information on the noise parameter. We also perform a set of simulated experiments to assess the performances of maximum likelihood estimator, showing that the asymptotic regime, where the estimator is unbiased and efficient, is approximately achieved already after few thousands repeated measurements on the probe system.     

Galaxies as gravitational lenses: Realistic models

The gravitational lens effects associated with a transparent mass distribution are quite different from those of the well-known opaque sphere. We have shown that any spherical galaxy whose mass distribution, when projected onto the plane of the sky, decreases outward from the center of the galaxy and diverges less rapidly than 1/h ash0, must always produce an odd number of images, usually one or three, of a source located behind the galaxy. Using optical scalar techniques, the amplification of each image can readily be obtained. For a given source and galaxy, we can define a dimensionless focal length, a function of impact parameter, and a dimensionless distance factor, depending on lens parameters and source distance. The central value of the ratio of these quantities determines the multiplicity of the images. The mass distribution of the galaxy is a crucial function, and we show in some detail how this affects the various focal lengths.     

Gas dynamics in strong gravitational fields

The steady and axially symmetric flow of a perfect fluid is studied in the context of general relativistic gas dynamics. It is assumed that the flow occurs in the background field of a rotating black hole (or any compact object). The hydrodynamic equations are referred to a locally nonrotating frame and their characteristics are found. The equations describing oblique shock waves are also obtained.     

高斯光束经过负球差透镜的聚焦

本文讨论高斯光束经过负球差透镜的聚焦，得到了聚焦光场轴上点的光强分布的表示式，并对其进行数值计算。数值计算结果表明，在负球差的情况下，得到光强的最大点位置（最佳聚焦点）相对于无球差情况，往透镜方向移动，并且，最佳聚焦点的光强较无球差时大，当Ｎｗ＝１，Ｎａ＝５，ｋＳ１＝－０．２时，得到的最佳聚焦点的光强是无球差时的１．３４倍。本文还讨论了透镜的菲涅尔数对聚焦光场分布的影响。结果表明，当透镜的菲涅尔数小于１时，球差对高斯光束的聚焦的影响可以忽略。     

Unification of gravitational and strong nuclear fields

Using the recently derived Evans wave equation of unified field theory, the strong nuclear field is described with an SU(3) representation of the gravitational field and the Gell-Mann color triplet is derived from general relativity as a three-spinor eigenfunction of the Evans wave equation.     

Dirac particle spin in strong gravitational fields

Dynamics of the Dirac particle spin in general strong gravitational fields is discussed. The Hermitian Dirac Hamiltonian is derived and transformed to the Foldy-Wouthuysen (FW) representation for an arbitrary metric. The quantum mechanical equations of spin motion are found. These equations agree with corresponding classical ones. The new restriction on the anomalous gravitomagnetic moment (AGM) by the reinterpretation of Lorentz invariance tests is obtained.     

Cosmological effects of gravitational birefringence in a theory of gravitation with C and P violation

An explanation is given within a previously proposed theory of gravitation with broken conjugation and parity symmetry (C and P violation) for the recently detected effect of non-Faraday rotation of the polarization plane in the propagation of electromagnetic radiation over cosmological distances. Zh. éksp. Teor. Fiz. 113, 1921–1929 (June 1998)     

Self-Similar Cosmological model: Introduction and empirical tests

After calling attention to the empirical and theoretical motivations for considering the hypothesis of a self-similar cosmos, the basic concepts and scaling rules of the Self-Similar Cosmological Model are presented. The results of a diverse set of 20 falsification tests are then shown to provide strong quantitative support for the uniqueness and broad applicability of the self-similar scale transformation equations, which successfully correlate physical parameters of atomic, stellar, and galactic scale systems. Possible implications of these results are discussed.