I propose a new dynamical system formalism for the analysis of $f(R)$ cosmologies. The new approach eliminates the need for cumbersome inversions to close the dynamical system and allows the analysis of the phase space of $f(R)$-gravity models which cannot be investigated using the standard technique. Differently form previously proposed similar techniques, the new method is constructed in such a way to associate to the fixed points scale factors, which contain four integration constants (i.e. solutions of fourth order differential equations). In this way a new light is shed on the physical meaning of the fixed points. We apply this technique to some $f(R)$ Lagrangians relevant for inflationary and dark energy models.
2015 May 25, 11:00
Faculdade de CiÍncias da Universidade de Lisboa (C6.2.51)
Campo Grande, 1749-016 Lisboa