http://arxiv.org/abs/1506.01664
We study general gauge-dependent dynamical equations describing homogeneous isotropic cosmologies coupled to a scalar field $\psi$ (scalaron). For flat cosmologies ($k=0$), we analyze in detail the previously proposed gauge-independent equation describing the differential, $\chi(\alpha)$, of the map of the metric $\alpha$ to the scalaron $\psi$, which is the main mathematical characteristic (`portrait’) of cosmologies in $\alpha$-version. In a more habitual $\psi$-version, the similar equation for the differential of the inverse map, $\bar{\chi}(\psi)$, can be solved asymptotically or for special scalaron potentials $v(\psi)$.
In the $\alpha$-version the whole dynamical system is explicitly integrable for $k\neq 0$ and any `potential’ $\bar{v}(\alpha)$ replacing $v(\psi)$. There is no \textit{a priori} relation between the two potentials before deriving $\chi$, which depends on the potential itself, though relations between the two pictures can be found in asymptotic regions. An alternative proposal is to specify a cosmology by assuming a characteristic solution or its phase portrait and then finding the potentials from the solutions of the dynamical equations. Our main subject is the mathematical structure of cosmologies, but possible applications of the results are briefly discussed.
A. Filippov
Fri, 5 Jun 15
39/63
Comments: 27 pages