Address: Vysoká škola ekonomická v Praze, náměstí Winstona Churchilla 1938/4, Praha 3, Czech Republic
E-mail: jan.janno.novak@gmail.com
Abstract: Standard approach in cosmology is hydrodynamical approach, when galaxies are smoothed distributions of matter. Then we model the Universe as a fluid. But we know, that the Universe has a discrete structure on scales 150 - 370 MPc. Therefore we must use the generalized mechanical approach, when is the mass concentrated in points. Methods of computations are then different. We focus on $f(R)$-theories of gravity and we work in the cell of uniformity in the late Universe. We do the scalar perturbations and we use 3 approximations. First we neglect the time derivatives and we do the astrophysical approach and we find the potentials $\Phi $ and $\Psi $ in this case. Then we do the large scalaron mass approximation and we again obtain the potentials. Final step is the quasi-static approximation, when we use the equations from astrophysical approach and the result are the potentials $\Phi $ and $\Psi $. The resulting potentials are combination of Yukawa terms, which are characteristic for $f(R)$-theories, and standard potential.
AMSclassification: primary 83C55; secondary 83D05, 83F05.
Keywords: mechanical approach, Hubble law, Friedmann equation, Einstein equation, scalar perturbation, tensor of energy-momentum.
DOI: 10.5817/AM2017-5-313