Cosmic Evolution in Fractional Action Cosmology

Subscription Access

Authors

  • Victor K. Shchigolev Department of Theoretical Physics, Ulyanovsk State University, Ulyanovsk 432000, Russia Author

DOI:

https://doi.org/10.5890/DNC.2013.04.002

Abstract

For the fractional action cosmological model, derived earlier by the author from the variational principle for a fractional action functional, the exact solutions are obtained. The case of a quasi - vacuum state of matter that fills the universe is considered. Moreover, on the basis of specific ansatz proposed in this paper for the cosmological term, the class of exact solutions of the model equations is obtained. Examples for some given laws of the cosmological term evolution are provided. Besides, a formula for the effective equation of state is derived, and the deceleration parameter of the obtained models is studied.

References

[1] Shchigolev, V.K. (2011), Cosmological models with fractional derivaties and fractional action functional, Communications in Theoretical Physics, 56, 389-396.

[2] Shchigolev, V.K., Cosmic Evolution in Fractional Action Cosmology, arXiv: 1208.3454v2.

[3] Uchaikin, V.V. (2008), Fractional Derivatives Method, Artishok, Ulyanovsk (in Russian).

[4] Calcagni, G. (2010), Quantum field theory, gravity and cosmology in a fractal universe, Journal of High Energy Physics, 3, 1-38.

[5] Calcagni, G. (2010), Fractal universe and quantum gravity, Physical Review Letters, 104, 251301.

[6] Karami, K., Jamil, M., Ghaffari, S., Fahimi, K., Holographic, new agegraphic and ghost dark energy models in fractal cosmology, arXiv:1201.6233.

[7] Lemets, O.A., Yerokhin, D.A., Interacting dark energy models in fractal cosmology, arXiv:1202.3457.

[8] Debnath, U., Jamil, M., Chattopadhyay, S. (2010), Fractional action cosmology: emergent, logamediate, intermediate, power law scenarios of the universe and generalized second law of thermodynamics, International Journal of Theoretical Physics, 51, 812-837.

[9] Jamil, M., Rashid, M.A., et al. (2012), Fractional action cosmology with power law weight function, Journal of Physics: Conference Series, 354, 012008.

[10] Sahni, V., Saini, T. D., Starobinsky, A., Alam, U. (2003), Statefinder - a new geometrical diagnostic of dark energy, JETP Letters, 77, 201-206.

[11] Overduin, J.M., Cooperstock, F.I. (1998), Evolution of the scale factor with a variable cosmological term, Physical Review D, 58, 043506.

[12] Sahni, V., Starobinsky, A. (2000), The Case for a positive cosmological Λ-term, International Journal of Modern Physics D, 9, 373-443.

[13] Riess, A.G., et al. (1998), Observational evidence fromsupernovae for an accelerating universe and a cosmological constant, Astronomical Journal, 116, 1009-1038.

[14] Perlmutter, S., et al. (1999),Measurements of Omega and Lambda from 42 high-redshift supernovae, Astrophysical Journal, 517, 565-586.

[15] Novello, M., Bergliaffa, S.E.P. (2008), Bouncing cosmologies, Physics Reports, 463, 127-213.

Article Metrics

Citations 20 Crossref
PublishedApril 2013

Usage tracking begins September 1, 2026.

History Published

Issue

Section

Research Articles

How to Cite

Shchigolev, V. K. (2026). Cosmic Evolution in Fractional Action Cosmology. Discontinuity, Nonlinearity, and Complexity, 2(2), 115-123. https://doi.org/10.5890/DNC.2013.04.002