Eur. Phys. J. C (2014) 74: 3005
https://doi.org/10.1140/epjc/s10052-014-3005-1

Regular Article - Theoretical Physics

gravity: scalar perturbations in the late Universe

¹ Physics Department, North Carolina Central University, Fayetteville st. 1801, Durham, NC, 27707, USA
² Institute for Theoretical Physics, University of Cologne, Zülpicher st. 77, 50937 , Cologne, Germany
³ Department of Theoretical Physics, Faculty of Mathematics and Physics, Charles University, V Holesovickach 2, 180 00 , Prague 8, Czech Republic
⁴ Institute of Mathematics AS CR, Zitna st. 25, 115 67 , Prague 1, Czech Republic
⁵ Astronomical Observatory, Odessa National University, Dvoryanskaya st. 2, Odessa, 65082, Ukraine

^* e-mail: maxim.eingorn@gmail.com

Received: 13 March 2014
Accepted: 28 July 2014
Published online: 22 August 2014

Abstract

In this paper we study scalar perturbations of the metric for nonlinear models. We consider the Universe at the late stage of its evolution and deep inside the cell of uniformity. We investigate the astrophysical approach in the case of Minkowski spacetime background and two cases in the cosmological approach, the large scalaron mass approximation and the quasi-static approximation, getting explicit expressions for scalar perturbations for both these cases. In the most interesting quasi-static approximation, the scalar perturbation functions depend on both the nonlinearity function and the scale factor . Hence, we can study the dynamical behavior of the inhomogeneities (e.g., galaxies and dwarf galaxies) including into consideration their gravitational attraction and the cosmological expansion, and also taking into account the effects of nonlinearity. Our investigation is valid for functions which have stable de Sitter points in future with respect to the present time, which is typical for the most popular models.