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

Abstract

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

Scale-Covariant Theory of Gravitation Through Self-Similarity

“…(2) For the Bianchi VII 0 and IX models [34] we have obtained the same results, and for this reason we show them together. The solution is as follows: ℎ = 3, i.e.…”

Bianchi I in scalar and scalar-tensor cosmologies

“…(16). The solution behaves as (17). We find the following solutions and G = but we do not regain the previous solution.…”

“…In particular, observations of Hulse-Taylor binary pulsar [11,12], Type Ia supernova observations [13]. For an extensive review see Uzan [14] In a series of recent papers [15][16][17] we have considered three theoretical models in order to study and compare how the "constants" G and Λ may vary under the self-similar hypothesis. These different theoretical frameworks are: general relativity with time varying constants (TVC), scalar cosmological models with interacting and non-interacting scalar and matter fields and TVC and different scalar-tensor theories.…”

Scalar-Tensor Bianchi VI Models

“…Furthermore working under the hypothesis of selfsimilarity allows us to find exact power-law solutions in such a way that we may compare the obtained solution for each studied model. By applying the theoretical results obtained in [20] we have studied how may vary and Λ in the described theoretical models using different geometries as Bianchi I [25], Bianchi II [26], Bianchi V, VII ℎ and IX [27] and Kantowsky-Sach [20]. In this paper, enlarging the program, we would like to study the case of family of Bianchi VI geometry, that is, Bianchi III, VI 0 , and VI ℎ .…”