Exact interior and exterior solutions to Einstein's field equations are derived for vacuum strings. The exterior solution for a uniform density vacuum string corresponds to a conical space while the interior solution is that of a spherical cap. For Mu equals 0-1/4 the external metric is ds-squared = -dt-squared + dr-squared + (1-4 Mu)-squared r-squared dphi-squared + dz-squared, where Mu is the mass per unit length in the string in Planck masses per Planck length. A maximum mass per unit length for a string is 6.73 x 10 to the 27th g/cm. It is shown that strings cause temperature fluctuations in the cosmic microwave background and produce equal brightness double QSO images separated by up to several minutes of arc. Formulae for lensing probabilities, image splittings, and time delays are derived for strings in a realistic cosmological setting. String searches using ST, the VLA, and the COBE satellite are discussed.

Gravitational Lensing Effects of Vacuum Strings: Exact Solutions

Der speziellen Relativitatstheorie liegt folgendes Postulat zugrunde, welchem auch durch die Galilei-Newtonsche Mechanik Genuge geleistet wird: Wird ein Koordinatensystem K so gewahlt, das in bezug auf dasselbe die physikalischen Gesetze in ihrer einfachsten Form gelten, so gelten dieselben Gesetze auch in Bezug auf jedes andere Koordinatensystem K′, das relativ zu K in gleichformiger Translationsbewegung begriffen ist. Dieses Postulat nennen wir „spezielles Relativitatsprinzip“. Durch das Wort „speziell“ soll angedeutet werden, das das Prinzip auf den Fall beschrankt ist, das K′ eine gleichformige Translationsbewegung gegen K ausfuhrt, das sich aber die Gleichwertigkeit von K′ und K nicht auf den Fall ungleichformiger Bewegung von K′ gegen K erstreckt.

Die Grundlage der allgemeinen Relativitätstheorie

Phase transitions in the early universe can give rise to microscopic topological defects: vacuum domain walls, strings, walls bounded by strings, and monopoles connected by strings. This article reviews the formation, physical properties and the cosmological evolution of various defects. A particular attention is paid to strings and their cosmological consequences, including the string scenario of galaxy formation and possible observational effects of strings.

Cosmic Strings and Domain Walls

In this paper, we investigate the generalized Saez–Ballester scalar–tensor theory of gravity via Noether gauge symmetry (NGS) in the background of Bianchi type I cosmological spacetime. We start with the Lagrangian of our model and calculate its gauge symmetries and corresponding invariant quantities. We obtain the potential function for the scalar field in the exponential form. For all the symmetries obtained, we determine the gauge functions corresponding to each gauge symmetry which include constant and dynamic gauge. We discuss cosmological implications of our model and show that it is compatible with the observational data.

Bianchi type I cosmology in generalized Saez–Ballester theory via Noether gauge symmetry

In this paper, we investigate the dark energy phenomenon by studying the Tsallis holographic dark energy within the framework of Brans–Dicke (BD) scalar–tensor theory of gravity (Brans and Dicke in Phys. Rev. 124:925, 1961). In this context, we choose the BD scalar field $$\phi $$ as a logarithmic function of the average scale factor a(t) and Hubble horizon as the IR cutoff ($$L=H^{-1}$$). We reconstruct two cases of non-interacting and interacting fluid (dark sectors of cosmos) scenario. The physical behavior of the models are discussed with the help of graphical representation to explore the accelerated expansion of the universe. Moreover, the stability of the models are checked through squared sound speed $$v_s^2$$. The well-known cosmological plane i.e., $$\omega _{de}-\omega ^{\prime }_{de}$$ is constructed for our models. We also include comparison of our findings of these dynamical parameters with observational constraints. It is also quite interesting to mention here that the results of deceleration, equation of state parameters and $$\omega _{de}-\omega ^{\prime }_{de}$$ plane coincide with the modern observational data.

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Observational constraint on interacting Tsallis holographic dark energy in logarithmic Brans–Dicke theory

Exact Bianchi type II, VIII and IX String cosmological models are obtained in the Saez-Ballester theory of gravitation. Some physical and geometrical properties of the models are studied.

Exact Bianchi type II, VIII and IX string cosmological models in Saez-Ballester theory of gravitation

An exact Bianchi type-V perfect fluid cosmological model is obtained in a scalar tensor theory proposed by Sen (Z. Phys. 149:311, 1957) based on Lyra Manifold in case of β is a constant and it is shown that this cosmological model exists only in the case of Radiation Universe (ρ=3p) if β is a function of ‘t’ using negative constant deceleration parameter. Some physical and geometrical properties of these models are discussed.

Bianchi type-V cosmological model with perfect fluid using negative constant deceleration parameter in a scalar tensor theory based on Lyra Manifold

In this paper, we consider Bianchi type-
 $\mathit{III}$
 , $V$
 and $\mathit{VI}_{0}$
 space-times filled with generalized ghost pilgrim dark energy (GGPDE) in general relativity. Here we assume the anisotropic distribution of GGPDE by introducing skewness parameters. To get deterministic solutions, we consider the scale factor $a(t)=(t^{n}e^{t})^{ \frac{1}{k}}$
 , so called hybrid expansion, which yields a time dependent deceleration parameter, and exhibits a transition of the Universe from early decelerated phase to the recent accelerating phase. To describe the behavior of the obtained models we construct equation of state (
 $\omega_{\varLambda }$
 ), squared sound speed (
 $v_{s}^{2}$
 ) parameters and $\omega_{\varLambda }$
 –
 $\dot{\omega }_{\varLambda }$
 , $r$
 –
 $s$
 planes. It is worth mentioning here that the analysis of evolution parameters supports the concept of pilgrim dark energy (PDE). Also, these models remain stable for PDE parameter $\beta =-0.5$
 . Moreover, the cosmological planes correspond to $\varLambda \mathit{CDM}$
 limit as well as different well-known dark energy models.

Some Bianchi type generalized ghost piligrim dark energy models in general relativity

In this paper, we consider Bianchi type-VI0 space–time filled with anisotropic modified holographic Ricci dark energy in a scalar–tensor theory proposed by Brans–Dicke (Phys. Rev. 124, 925 (1961))....

/pdf/bianchi-type-vi0-modified-holographic-ricci-dark-energy-apdxu4pztv.pdf

Bianchi type-VI0 modified holographic Ricci dark energy model in a scalar-tensor theory

In this paper, we have considered spatially homogeneous and anisotropic Bianchi type-III space–time filled with matter and anisotropic modified holographic Ricci dark energy in general relativity. ...

/pdf/anisotropic-magnetized-holographic-ricci-dark-energy-3enbm0u1t5.pdf

M. Vijaya Santhi

Papers

Exact Bianchi type II, VIII and IX string cosmological models in Saez-Ballester theory of gravitation

Bianchi type-V cosmological model with perfect fluid using negative constant deceleration parameter in a scalar tensor theory based on Lyra Manifold

Some Bianchi type generalized ghost piligrim dark energy models in general relativity

Bianchi type-VI0 modified holographic Ricci dark energy model in a scalar-tensor theory

Anisotropic magnetized holographic Ricci dark energy cosmological models