https://doi.org/10.1140/epjc/s10052-018-6251-9
Regular Article - Theoretical Physics
Classical evolution of subspaces
1
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Kashirskoe shosse 31, Moscow, 115409, Russia
2
N. I. Lobachevsky Institute of Mathematics and Mechanics, Kazan Federal University, Kremlevskaya street 18, Kazan, 420008, Russia
* e-mail: sergeirubin@list.ru
Received:
20
July
2018
Accepted:
14
September
2018
Published online:
22
September
2018
We study evolution of manifolds after their creation at high energies. Several kinds of gravitational Lagrangians with higher derivatives are considered. It is shown analytically and confirmed numerically that an asymptotic growth of the maximally symmetric manifolds depends strongly on their dimensionality. A number of final metrics describing our Universe is quite poor if we limit ourselves with a maximally symmetric extra space. We show that the initial conditions can be a reason of nontrivial solutions (funnels) and study their properties.
© The Author(s), 2018
