Abstract
We study the models and their particular case, the so-called -models under the self-similarity hypothesis. In particular, we calculate the exact form that each quantity may take in order that field equations (FEs) admit self-similar solutions. The methods employed allow us to obtain general results that are valid not only for the FRW metric, but also for all the Bianchi types as well as for the Kantowski-Sachs model (under the self-similarity hypothesis and the power-law hypothesis for the scale factors).
Highlights
E physical and mathematical importance of the modi ed gravitational models has been recently pointed out for several authors, since this kind of theories explains in a better way the dynamics of the very early universe as well as its current acceleration
In a recent paper [5], we have studied some particular cases of the so-called generalized scalar-tensor theories (STTs or FFFFFF models)
We are going to study (4) through the Lie group method (LG) method, that is, we study the kind of functions ff f fffffffff, ZZZZZZ, UUUUUU, and φφ such that the FEs (2) and (4) admit power-law and in particular self-similar solutions
Summary
E physical and mathematical importance of the modi ed gravitational models has been recently pointed out for several authors (see, e.g., [1,2,3,4]), since this kind of theories explains in a better way the dynamics of the very early universe as well as its current acceleration. We study the form that the di erent quantities may take in order that the eld equations (FEs) admit self-similar solutions. We deduce the form that can acquire the function ffffff in order that the FE admit self-similar and power-law solutions (for the scale factors). By studying the trace equation with the Lie group method we proof that fffffffffnn is the unique possible form for the function ffffff under the power-law hypothesis for the scale factors. Since the hypothesis of self-similarity could be strong constraining the form of the function ffffff, we study if under the hypothesis of power-law solutions for the scale factors the function ffffff could take a different form For this purpose, we go next to study the trace equation through the Lie group method
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