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$w = 1 / 3$ to $w = - 1$ evolution in a Robertson–Walker space-time with constant scalar curvature

Luca Guido Molinari

http://orcid.org/0000-0002-5023-787X

Dipartimento di Fisica “A. Pontremoli”, Università degli Studi di Milano, via Celoria 16, I-20133 Milano, Italy

INFN sez. di Milano, Via Celoria 16, I-20133 Milano, Italy

E-mail Address: luca.molinari@unimi.it

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and

Carlo Alberto Mantica

Dipartimento di Fisica “A. Pontremoli”, Università degli Studi di Milano, via Celoria 16, I-20133 Milano, Italy

INFN sez. di Milano, Via Celoria 16, I-20133 Milano, Italy

E-mail Address: carlo.mantica@mi.infn.it

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https://doi.org/10.1142/S0219887819500610Cited by:5 (Source: Crossref)

Abstract

The Ricci tensor of a Robertson–Walker (RW) space-time is here specified by requiring constancy of the scalar curvature and a vanishing spatial curvature. By entering this Ricci tensor in Einstein’s equations (without cosmological constant), the cosmological fluid shows a transition from a pure radiation to a Lambda equation of state. In other words, the RW geometry with constant scalar curvature and flat space fixes the limit values $w = 1 / 3$ and $w = - 1$ , without any hypothesis on the cosmological fluid. The value of the scalar curvature fixes the time-scale for the transition.

For this reason, we investigate the ‘toy-universe’ with Hubble parameter $h = 0.673$ and temperature $T_{CMB} = 2.72$ K. The model predicts an age of the universe in the range 7.3–13.7Gyr.

Keywords:

AMSC: 83C15, 83F05

References

1. Planck Collab., Planck 2018 results. I. Overview and the cosmological legacy of Planck, arXiv:1807.06205. See also https://www.cosmos.esa.int/web/planck. Google Scholar
2. J.-H. He, L. Guzzo, B. Li and C. M. Baugh, No evidence for modifications of gravity from galaxy motions on cosmological scales, Nature Astronomy 2 (2018) 967–972. Crossref, Web of Science, Google Scholar
3. S. Weinberg, Cosmology (Oxford University Press, 2008). Crossref, Google Scholar
4. M. S. Longair, Galaxy Formation (Springer, 2008). Google Scholar
5. C. A. Mantica and L. G. Molinari, Generalized Robertson–Walker space-times, a survey, Int. J. Geom. Meth. Mod. Phys. 14(3) (2017) 1730001 (27pp). Link, Web of Science, Google Scholar
6. C. A. Mantica and L. G. Molinari, Twisted Lorentzian manifolds: A characterization with torse-forming time-like unit vectors, Gen. Relativ. Grav. 49 (2017) 51. Crossref, Web of Science, Google Scholar
7. B.-Y. Chen, A simple characterization of generalized Robertson–Walker space-times, Gen. Relativ. Grav. 46 (2014) 1833. Crossref, Web of Science, Google Scholar
8. B.-Y. Chen, Rectifying submanifolds of Riemannian manifolds and torqued vector fields, Kragujev. J. Math. 41(1) (2017) 93103. Crossref, Google Scholar
9. B.-Y. Chen, Differential Geometry of Warped Product Manifolds and Submanifolds (World Scientific, 2017). Link, Google Scholar
10. C. A. Mantica, L. G. Molinari and U. C. De, A condition for a perfect fluid space-time to be a generalized Robertson–Walker space-time, J. Math. Phys. 57(2) (2016) 022508, Erratum JMP 57 (2016) 022508. Google Scholar
11. C. A. Mantica and L. G. Molinari, On the Weyl and the Ricci tensors of generalized Robertson–Walker space-times, J. Math. Phys. 57(10) (2016) 102502. Crossref, Web of Science, Google Scholar
12. A. Kamenshchik, U. Moschella and V. Pasquier, An alternative to quintessence, Phys. Lett. B 511 (2001) 265–268. Crossref, Web of Science, Google Scholar
13. S. Capozziello, C. A. Mantica and L. G. Molinari, Cosmological perfect-fluids in $f (R)$ gravity, Int. J. Geom. Meth. Mod. Phys. 16(1) (2019) 1950008 (14pp). Link, Web of Science, Google Scholar
14. S. Capozziello, S. Nojiri, S. D. Odintsov and A. Troisi, Cosmological viability of $f (R)$ -gravity as an ideal fluid and its compatibility with a matter dominated phase, Phys. Lett. B 639 (2006) 135–143. Crossref, Web of Science, Google Scholar
15. K. Kleidis and V. K. Oikonomou, Autonomous dynamical system description of de Sitter evolution in scalar assisted $f (R)$ — $ϕ$ gravity, Int. J. Geom. Meth. Mod. Phys. 15(12) (2018) 1850212 (9pp). Link, Web of Science, Google Scholar
16. V. Mukhanov, Physical Foundations of Cosmology (Cambridge University Press, 2005). Crossref, Google Scholar