ANISOTROPIC BRANE COSMOLOGIES WITH EXPONENTIAL POTENTIALS

We study Bianchi I type brane cosmologies with scalar matter self-interacting through combinations of exponential potentials. Such models correspond in some cases to inflationary universes. We discuss in detail the conditions for accelerated expansion to occur: in particular, we show that the condition which is necessary and sufficient for inflation in the relativistic version of the models is not sufficient in the brane case. Another peculiar feature of the models is that the relationship between the value of the scale factor at the beginning of inflation and the equation of state is very different from what one finds in the relativistic framework. We also analyze the influence of the value of the anisotropy and the brane tension, and show that the associated effects become negligible in the late time limit, those related to the anisotropy disappearing earlier. This study focuses mainly on single field models, but we also consider a generalization yielding models with multiple non-interacting fields and examine their features briefly. We conclude that, in the brane scenario, an increase in the number of fields assists inflation, as happened in general relativity.