Growing Time Function Research Articles

Bianchi Type-II Cosmological Model with a Linear Equation of State in Vsl Theory

We study Bianchi type-II model with time varying constant under the self similarity approach. In first part of the paper we have studied the model by considering time variable G and Λ and obtain the solutions of the field equations by using linear equation of state (EOS) of the form ρ = np+ρo where n and ρo are constants. It is observed that G must be time growing function while nature of Λ depends on the nature of γ. In the second part of paper we have studied the model by considering variable speed of light (VSL) and obtain the similar types of solutions as in the first model and all the physical parameters which depends on ∫ cdt. Arriving to the conclusion that c must be growing time function and Λ depends on value γ.

(An)Isotropic models in scalar and scalar-tensor cosmologies

We study how the constants $G$ and $\Lambda$ may vary in different theoretical models (general relativity with a perfect fluid, scalar cosmological models (\textquotedblleft quintessence\textquotedblright) with and without interacting scalar and matter fields and a scalar-tensor model with a dynamical $\Lambda$) in order to explain some observational results. We apply the program outlined in section II to study three different geometries which generalize the FRW ones, which are Bianchi \textrm{V}, \textrm{VII}$_{0}$ and \textrm{IX}, under the self-similarity hypothesis. We put special emphasis on calculating exact power-law solutions which allow us to compare the different models. In all the studied cases we arrive to the conclusion that the solutions are isotropic and noninflationary while the cosmological constant behaves as a positive decreasing time function (in agreement with the current observations) and the gravitational constant behaves as a growing time function.

Bianchi VI0&III models: self-similar approach

We study several cosmological models with Bianchi VI0&III symmetries under the self-similar approach. We find new solutions for the ‘classical’ perfect fluid model as well as for the vacuum model although they are really restrictive for the equation of state. We also study a perfect fluid model with time-varying constants, G and Λ. As in other studied models we find that the behaviour of G and Λ are related. If G behaves as a growing time function then Λ is a positive decreasing time function but if G is decreasing then Λ0 is negative. We end by studying a massive cosmic string model, putting special emphasis in calculating the numerical values of the equations of state. We show that there is no SS solution for a string model with time-varying constants.

Massive cosmic strings in Bianchi type II

We study a massive cosmic strings with BII symmetries cosmological models in two contexts. The first of them is the standard one with a barotropic equation of state. In the second one we explore the possibility of taking into account variable \textquotedblleft constants\textquotedblright ($G$ and $\Lambda ).$Both models are studied under the self-similar hypothesis. We put special emphasis in calculating the numerical values for the equations of state. We find that for $\omega\in(0,1]$, $G$, is a growing time function while $\Lambda$, behaves as positive decreasing time function. If $\omega=0,$ both \textquotedblleft constants\textquotedblright, $G$ and $\Lambda,$ behave as true constants.

Bianchi II with time varying constants. Self-similar approach

We study a perfect fluid Bianchi II models with time varying constants under the self-similarity approach. In the first of the studied model, we consider that only vary $G$ and $\Lambda.$ The obtained solution is more general that the obtained one for the classical solution since it is valid for an equation of state $\omega\in(-1,\infty) $ while in the classical solution $\omega\in(-1/3,1) .$ Taking into account the current observations, we conclude that $G$ must be a growing time function while $\Lambda$ is a positive decreasing function. In the second of the studied models we consider a variable speed of light (VSL). We obtain a similar solution as in the first model arriving to the conclusions that $c$ must be a growing time function if $\Lambda$ is a positive decreasing function.

About Bianchi I with VSL

In this paper we study how to attack, through different techniques, a perfect fluid Bianchi I model with variable G,c and Λ, “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 (∫ 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 Λ is a decreasing time function whose sing depends on the equation of state ω, while the exponents of the scale factor must satisfy the conditions ∑ =1 3 α i =1 and ∑ =1 3 α 2 <1, ∀ ω, 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 ω and e, 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.