Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 12 (2016), 006, 16 pages      arXiv:1509.08008
Contribution to the Special Issue on Analytical Mechanics and Differential Geometry in honour of Sergio Benenti

Extended Cosmologies

Salvatore Capozziello a b c, Mariafelicia F. De Laurentis c d e f, Lorenzo Fatibene g h, Marco Ferraris g and Simon Garruto g h
a) Dipartimento di Fisica, University of Napoli ''Federico II'', Italy
b) INFN Sezione Napoli - Iniziativa Specifica QGSKY, Italy
c) Gran Sasso Science Institute (INFN), L'Aquila, Italy
d) Tomsk State Pedagogical University, Russia
e) Laboratory of Theoretical Cosmology, Tomsk State University of Control Systems and Radioelectronics (TUSUR), Russia
f) Institut für Theoretische Physik, Goethe-Universität, Max-von-Laue-Str. 1, 60438 Frankfurt, Germany
g) Dipartimento di Matematica, University of Torino, Italy
h) INFN Sezione Torino - Iniziativa Specifica QGSKY, Italy

Received September 29, 2015, in final form January 16, 2016; Published online January 20, 2016

We shall discuss cosmological models in extended theories of gravitation. We shall define a surface, called the model surface, in the space of observable parameters which characterises families of theories. We also show how this surface can be used to compare with observations. The model surface can potentially be used to falsify whole families of models instead reasoning on a single model basis as it is usually done by best fit arguments with observations.

Key words: cosmology; extended theories of gravitation.

pdf (438 kb)   tex (77 kb)


  1. Allemandi G., Borowiec A., Francaviglia M., Accelerated cosmological models in first-order nonlinear gravity, Phys. Rev. D 70 (2004), 043524, 11 pages, hep-th/0403264.
  2. Allemandi G., Borowiec A., Francaviglia M., Accelerated cosmological models in Ricci squared gravity, Phys. Rev. D 70 (2004), 103503, 13 pages, hep-th/0407090.
  3. Barausse E., Sotiriou T.P., Miller J.C., A no-go theorem for polytropic spheres in Palatini $f({\mathcal R})$ gravity, Classical Quantum Gravity 25 (2008), 062001, 7 pages, gr-qc/0703132.
  4. Barreto A.B., Almeida T.S., Romero C., Extending the ADM formalism to Weyl geometry, AIP Conf. Proc. 1647 (2015), 89-93, arXiv:1503.08455.
  5. Benenti S., Rational cosmology, in preparation.
  6. Bojowald M., Loop quantum cosmology, Living Rev. Relativ. 11 (2008), 4, 131 pages, gr-qc/0601085.
  7. Borowiec A., Kamionka M., Kurek A., Szydlowski M., Cosmic acceleration from modified gravity with Palatini formalism, J. Cosmol. Astropart. Phys. 2012 (2012), no. 2, 027, 32 pages, arXiv:1109.3420.
  8. Buchdahl H.A., Quadratic Lagrangians and Palatini's device, J. Phys. A: Math. Gen. 12 (1979), 1229-1234.
  9. Capozziello S., Curvature quintessence, Internat. J. Modern Phys. D 11 (2002), 483-491, gr-qc/0201033.
  10. Capozziello S., De Laurentis M., Extended theories of gravity, Phys. Rep. 509 (2011), 167-320, arXiv:1108.6266.
  11. Capozziello S., Francaviglia M., Extended theories of gravity and their cosmological and astrophysical applications, Gen. Relativity Gravitation 40 (2008), 357-420, arXiv:0706.1146.
  12. De Felice A., Tsujikawa S., $f({\mathcal R})$ theories, Living Rev. Relativ. 13 (2010), 3, 161 pages, arXiv:1002.4928.
  13. Di Mauro M., Fatibene L., Ferraris M., Francaviglia M., Further extended theories of gravitation: Part I, Int. J. Geom. Methods Mod. Phys. 7 (2010), 887-898, arXiv:0911.2841.
  14. Ehlers J., Pirani F.A.E., Schild A., The geometry of free fall and light propagation, in General Relativity (Papers in Honour of J.L. Synge), Clarendon Press, Oxford, 1972, 63-84.
  15. Faraoni V., $f({\mathcal R})$ gravity: successes and challenges, arXiv:0810.2602.
  16. Fatibene L., Ferraris M., Francaviglia M., Mercadante S., Further extended theories of gravitation: Part II, Int. J. Geom. Methods Mod. Phys. 7 (2010), 899-906, arXiv:0911.2842.
  17. Fatibene L., Garruto S., Polistina M., Breaking the conformal gauge by fixing time protocols, Int. J. Geom. Methods Mod. Phys. 12 (2015), 1550044, 14 pages, arXiv:1410.1284.
  18. Fatibene L., Francaviglia M., From the Ehlers-Pirani-Schild analysis on the foundations of gravitational theories to extended theories of gravity and dark matter, PoS Proc. Sci. (2011), PoS(CORFU2011), 054, 16 pages.
  19. Fatibene L., Francaviglia M., Mathematical equivalence versus physical equivalence between extended theories of gravitations, Int. J. Geom. Methods Mod. Phys. 11 (2014), 1450008, 21 pages, arXiv:1302.2938.
  20. Mana A., Fatibene L., Ferraris M., A further study on Palatini $f({\mathcal R})$-theories for polytropic stars, J. Cosmol. Astropart. Phys. 2015 (2015), no. 10, 040, 19 pages, arXiv:1505.06575.
  21. Olmo G.J., Hydrogen atom in Palatini theories of gravity, Phys. Rev. D 77 (2008), 084021, 8 pages, arXiv:0802.4038.
  22. Olmo G.J., Singh P., Covariant effective action for loop quantum cosmology à la Palatini, J. Cosmol. Astropart. Phys. 2009 (2009), no. 1, 030, 10 pages, arXiv:0806.2783.
  23. Perlick V., Characterization of standard clocks by means of light rays and freely falling particles, Gen. Relativity Gravitation 19 (1987), 1059-1073.
  24. Poulis F.P., Salim J.M., Weyl geometry and gauge-invariant gravitation, Internat. J. Modern Phys. D 23 (2014), 1450091, 24 pages, arXiv:1305.6830.
  25. Querella L., Variational principles and cosmological models in higher-order gravity, Ph.D. thesis, Université de Liegè, 1998, gr-qc/9902044.
  26. Romero C., Fonseca-Neto J.B., Pucheu M.L., General relativity and Weyl geometry, Classical Quantum Gravity 29 (2012), 155015, 18 pages, arXiv:1201.1469.
  27. Salim J.M., Sautú S.L., Gravitational theory in Weyl integrable spacetime, Classical Quantum Gravity 13 (1996), 353-360.
  28. Weyl H., Gravitation und Elektrizität, Monatsbericht Kön.-Preuss. Akad. Wiss. Berlin (1918), 465-480.

Previous article  Next article   Contents of Volume 12 (2016)