Abstract
A D-dimensional gravitational model with a Gauss–Bonnet term and the cosmological constant Λ is considered. Assuming diagonal cosmological metrics, we find, for certain Λ > 0, new examples of solutions with an exponential time dependence of two scale factors, governed by two Hubble-like parameters H > 0 and h < 0, corresponding to submanifolds of dimensions m and l, respectively, with (m, l) = (4, 2), (5, 2), (5, 3), (6, 7), (7, 5), (7, 6) and D = 1 + m + l. Any of these solutions describes an exponential expansion of our 3-dimensional factor space with the Hubble parameter H and zero variation of the effective gravitational constant G. We also prove the stability of these solutions in the class of cosmological solutions with diagonal metrics.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Change history
17 November 2017
An erratum to this article has been published.
References
H. Ishihara, Phys. Lett. B 179, 217 (1986).
N. Deruelle, Nucl. Phys. B 327, 253 (1989).
E. Elizalde, A. N. Makarenko, V. V. Obukhov, K. E. Osetrin, and A. E. Filippov, Phys. Lett. B 644, 1 (2007).
A. Toporensky and P. Tretyakov, Grav. Cosmol. 13, 207 (2007).
I. V. Kirnos, A. N. Makarenko, S. A. Pavluchenko, and A. V. Toporensky, Gen. Rel. Grav. 42, 2633 (2010).
S. A. Pavluchenko and A. V. Toporensky, Mod. Phys. Lett. A 24, 513–521 (2009).
S. A. Pavluchenko, Phys. Rev. D 80, 107501 (2009).
D. Chirkov, S. Pavluchenko, and A. Toporensky, Mod. Phys. Lett. A 29, 1450093 (2014).
V. D. Ivashchuk, Grav. Cosmol. 16, 118 (2010).
V. D. Ivashchuk, Int. J. Geom. Meth. Mod. Phys. 7, 797 (2010).
V. D. Ivashchuk and A. A. Kobtsev, Eur. Phys. J. C 75, 177 (2015).
S. A. Pavluchenko, Phys. Rev. D 92, 104017 (2015).
K. K. Ernazarov, V. D. Ivashchuk, and A. A. Kobtsev, Grav. Cosmol. 22, 245 (2016).
V. D. Ivashchuk, “On stability of exponential cosmological solutions with non-static volume factor in the Einstein–Gauss–Bonnet model,” arXiv: 1607.01244; Eur. Phys. J. C 76, 431 (2016).
A. G. Riess et al., Astron. J. 116, 1009 (1998).
S. Perlmutter et al., Astrophys. J. 517, 565 (1999).
M. Kowalski, D. Rubin et al., “Improved cosmological constraints from new, old and combined supernova datasets,” arXiv: 0804.4142.
P. A. R. Ade et al. [Planck Collaboration], Astron. Astrophys. 571, A1 (2014).
M. Rainer and A. Zhuk, Gen. Rel. Grav. 32, 79–104 (2000); gr-qc/9808073.
V. D. Ivashchuk and V. N. Melnikov, Grav. Cosmol. 2(3), 211–220 (1996); hep-th/9612054.
K. A. Bronnikov, V. D. Ivashchuk, and V. N. Melnikov, Nuovo Cimento B 102, 209 (1998).
V. D. Ivashchuk and V. N. Melnikov, Grav. Cosmol. 20, 26 (2014).
E. V. Pitjeva, Astron. Vestnik 47, 419 (2013).
Author information
Authors and Affiliations
Corresponding author
Additional information
An erratum to this article is available at https://doi.org/10.1134/S0202289317040107.
Rights and permissions
About this article
Cite this article
Ivashchuk, V.D. On stable exponential solutions in Einstein–Gauss–Bonnet cosmology with zero variation of G . Gravit. Cosmol. 22, 329–332 (2016). https://doi.org/10.1134/S0202289316040095
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0202289316040095