Geodesic
Scalar perturbations in f(R) cosmologies in the late Universe
Archivum mathematicum, Tome 53 (2017) no. 5, pp. 313-324
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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.
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.
DOI : 10.5817/AM2017-5-313
Classification : 83C55, 83D05, 83F05
Keywords: mechanical approach; Hubble law; Friedmann equation; Einstein equation; scalar perturbation; tensor of energy-momentum 
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Novák, Jan. Scalar perturbations in f(R) cosmologies in the late Universe. Archivum mathematicum, Tome 53 (2017) no. 5, pp. 313-324. doi: 10.5817/AM2017-5-313

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