Perfect fluid Bianchi I model with variable G and L

Jose Antonio Belinchon1

Abstract

We study how to attack through different techniques a perfect fluid Bianchi I model with variable G and L. These tactics are: Lie group method (LM), imposing a particular symmetry, self-similarity (SS), matter collineations (MC), and kinematic self-similarity (KSS). We compare the tactics since they are quite similar (symmetry principles). We arrive at the conclusion that the LM is too restrictive and yields only a flat FRW solution with G = const and L = 0. The SS, MC and KSS approaches bring us to a solution where G is a decreasing time function and L ~ t-2, its sign depending on the equation of state while the exponents of the scale factors must satisfy the conditions i=13ai = 1 and i=13ai 2 < 1, "w, i.e., the solution is valid for all equations of state, relaxing in this way the Kasner conditions.

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