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

top
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

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.