About Bianchi I with VSL

Abstract

In this paper we study how to attack, through different techniques, a perfect fluid Bianchi I model with variable G,c and Lambda, but taking into account the effects of a $c$-variable into the curvature tensor. We study the model under the assumption,div(T)=0. These tactics are: Lie groups method (LM), imposing a particular symmetry, self-similarity (SS), matter collineations (MC) and kinematical self-similarity (KSS). We compare both tactics since they are quite similar (symmetry principles). We arrive to the conclusion that the LM is too restrictive and brings us to get only the flat FRW solution. The SS, MC and KSS approaches bring us to obtain all the quantities depending on \int c(t)dt. Therefore, in order to study their behavior we impose some physical restrictions like for example the condition q<0 (accelerating universe). In this way we find that $c$ is a growing time function and Lambda is a decreasing time function whose sing depends on the equation of state, w, while the exponents of the scale factor must satisfy the conditions $\sum_{i=1}^{3}\alpha_{i}=1$ and $\sum_{i=1}^{3}\alpha_{i}^{2}<1,$ $\forall\omega$, i.e. for all equation of state$,$ relaxing in this way the Kasner conditions. The behavior of $G$ depends on two parameters, the equation of state $\omega$ and $\epsilon,$ a parameter that controls the behavior of $c(t),$ therefore $G$ may be growing or decreasing.We also show that through the Lie method, there is no difference between to study the field equations under the assumption of a $c-$var affecting to the curvature tensor which the other one where it is not considered such effects.Nevertheless, it is essential to consider such effects in the cases studied under the SS, MC, and KSS hypotheses.Comment: 29 pages, Revtex4, Accepted for publication in Astrophysics & Space Scienc

Behavior of Time-Varying Constants in Relativity

“…We found that the cosmological constant Λ turned out to be a time decreasing function for Λ 0 > 0 while the gravitational constant G was a time increasing function when G 0 > 0 for all values of k > 0. It is worth mentioning here that our results verify the results obtained by Belinchon [29]. For these behaviors of G and Λ, the time-dependent vacuum energy density relation is also satisfied, according to which both these constants are changing in a reciprocal way [26].…”

“…At the present status of the universe, however, the vacuum energy is vanishing due to the time variations of both Λ and G. Belinchon and Dvila [27] discussed time-varying constants in different spacetimes by using different symmetric techniques. In recent papers [28,29], the same author analyzed the behaviors of time-varying G and Λ for a Bianchi type I model and made comparison of different techniques, including self-similarity, matter collineations, kinematic self-similar similarity, and the Lie method.…”

Bianchi Type I Cosmological Model with Viscous Fluid in the Framework of VSL Theory

“…We consider viscosity coefficient (Sheykhi and Setare [9]) as ξ = ξ 0 ρH −1 , where ξ 0 is constant. As per the procedure given by Belinchón [3], for the metric (2.1), the Einstein field equations can be written as:…”

Kantowski-Sachs Universe in the Varying Speed of Light Theory

“…The Einstein field equations for FRW spacetime in the VSL theory have been solved by Barrow (1999Barrow ( , 2000 for anisotropic model, who also obtained the rate of variation of the speed of light required to solve flatness and cosmological constant problems. Some other mentionalable works in this field are as follows: (i) By assuming energy conservation of observed matter Gopakumar & Vijayagovindam (2001) have solved the flatness cosmological constant problem with varying speed of light c, gravitational coupling strength G and cosmological parameter Λ, (ii) Chimento & Jakubi (2001) have found exact constant solutions for cosmological density parameter using generalization of general relativity that incorporates a cosmic time variation of velocity of light in vacuum and Newtonian gravitation constant, and (iii) Belinchon (2005Belinchon ( , 2006Belinchon ( , 2007 studied perfect fluid Bianchi type I model with variable G, c and Λ. Besides all the above mentioned major works on VSL theory it is observed that some authors (Harko & Mak 1999;Shojaie & Farhoudi 2006) have proposed a new generalization of general relativity which also allows arbitrary changes in the speed of light c and the gravitational constant G. However, this has been done in such a way that variation in the speed of light introduces corrections to the curvature tensor in the Einstein equations in the cosmological frame.…”