Scalar perturbations in f(R) cosmologies in the late Universe

Jan Novák

Archivum Mathematicum (2017)

  • Volume: 053, Issue: 5, page 313-324
  • ISSN: 0044-8753

Abstract

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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 Φ and Ψ 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 Φ and Ψ . The resulting potentials are combination of Yukawa terms, which are characteristic for f ( R ) -theories, and standard potential.

How to cite

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Novák, Jan. "Scalar perturbations in f(R) cosmologies in the late Universe." Archivum Mathematicum 053.5 (2017): 313-324. <http://eudml.org/doc/294621>.

@article{Novák2017,
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.},
author = {Novák, Jan},
journal = {Archivum Mathematicum},
keywords = {mechanical approach; Hubble law; Friedmann equation; Einstein equation; scalar perturbation; tensor of energy-momentum},
language = {eng},
number = {5},
pages = {313-324},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Scalar perturbations in f(R) cosmologies in the late Universe},
url = {http://eudml.org/doc/294621},
volume = {053},
year = {2017},
}

TY - JOUR
AU - Novák, Jan
TI - Scalar perturbations in f(R) cosmologies in the late Universe
JO - Archivum Mathematicum
PY - 2017
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 053
IS - 5
SP - 313
EP - 324
AB - 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.
LA - eng
KW - mechanical approach; Hubble law; Friedmann equation; Einstein equation; scalar perturbation; tensor of energy-momentum
UR - http://eudml.org/doc/294621
ER -

References

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  1. Berry, C.P.L., Gair, J.R., Linearized f ( R ) gravity: gravitational radiation and solar system tests, Phys. Rev. D 83 1004022 (2011), arXiv:1104.0819. (2011) 
  2. Burgazli, A., Eingorn, M., Zhuk, A., 10.1140/epjc/s10052-015-3335-7, Eur. Phys. J. C 75 118 (2015), arXiv:1301.0418. (2015) DOI10.1140/epjc/s10052-015-3335-7
  3. Eingorn, M., First-order cosmological perturbationsengendered by point-like masses, arXiv:1509.03835v3. 
  4. Eingorn, M., Novák, J., Zhuk, A., 10.1140/epjc/s10052-014-3005-1, Eur. Phys. J. C 74 3005 (2014), arXiv:astro-ph/1401.5410. (2014) DOI10.1140/epjc/s10052-014-3005-1
  5. Eingorn, M., Zhuk, A., Hubble flows and gravitational potentials in observable Universe, arXiv:1205.2384. MR2989879
  6. Eingorn, M., Zhuk, A., 10.1103/PhysRevD.84.024023, Phys. Rev. D 84 024023 (2011), arXiv:1104.1456 [gr-qc]. (2011) DOI10.1103/PhysRevD.84.024023
  7. Eingorn, M., Zhuk, A., Remarks on mechanical approach to observable universe, JCAP 05 024 (2014), arXiv: 1309.4924. (2014) MR3219178
  8. Garcia-Bellido, J., Cosmology and astrophysics, arXiv: astro-ph/0502139. 
  9. Hu, W., Sawicky, I., Models of f ( R ) cosmic acceleration that evade solar system test, Phys. Rev. D 76 064004 (2007), arxiv:0705.1158 [astro-ph]. (2007) 
  10. Jaime, L.G., Patino, L., Salgado, M., f ( R ) cosmology revisted, arXiv:1206.1642 [gr-qc]. 
  11. Jaime, L.G., Patino, L., Salgado, M., 10.1103/PhysRevD.89.084010, Phys. Rev.D 89 084010 (2014), arXiv:gr-qc/1312.5428. (2014) DOI10.1103/PhysRevD.89.084010
  12. Miranda, V., Joras, S., Waga, I., Quartin, M., 10.1103/PhysRevLett.102.221101, Phys. Rev. Lett. 102 221101 (2009), arXiv: 0905.1941 [astro-ph]. (2009) DOI10.1103/PhysRevLett.102.221101
  13. Naf, J., Jetzer, P., On the 1 / c expansion of f ( R ) gravity, Phys. Rev. D 81 104003 (2010), arXiv:1004.2014 [gr-qc]. (2010) 
  14. Riess, A.G. et al.,, 10.1086/300499, Astronom. J. 116 (1998), 1009–1038. (1998) DOI10.1086/300499
  15. Starobinsky, A.A., 10.1134/S0021364007150027, JETP Lett 86 (2007), 157–163, arXiv:0706.2041. (2007) DOI10.1134/S0021364007150027
  16. Tsujikawa, S., Udin, K., Tavakol, R., 10.1103/PhysRevD.77.043007, Phys. Rev. D 77 043007 (2008), arXiv:0712.0082v2. (2008) MR2421223DOI10.1103/PhysRevD.77.043007

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