Generation of exact solutions of Fridman equations leading to Cardy–Verlinde formula by Darboux transformation
It is considered a possibility of generation of exact solutions for Friedman equations by Darboux transformation, for which Cardy — Verlinde formula is valid. Two modifications of Darboux transformation are offered, which let generate such solutions. Exact solutions are obtained, for which Cardy — Verlinde formula is valid at least near some singularities.
1. Verlinde E. On the Holographic Principle in the Radiation Dominated Universe. URL: (2010) [arXiv:hep-th/0008140].
2. Brevik I., Nojiri S., Odintsov S. D. et al. Cardy—Verlinde formula in FRW Universe with inhomogeneous generalized fluid and dynamical entropy bounds near the future singularity // Eur. Phys. J. 2010. Vol. C69. P. 563—574.
3. Brevik I., Nojiri S., Odintsov S. D. et al. Entropy and Universality of Cardy—Verlinde formula in Dark Energy Universe // Phys. Rev. 2004. D70:043520.
4. Brevik I., Odintsov S. D. On the Cardy—Verlinde Entropy Formula in Viscous Cosmology // Ibid. 2002. D 65, 067302.
5. James E. L., Nojiri S., Odintsov S. D. et al. The Ads/CFT Correspondence and Logariphmic Corrections to raneworld Cosmology and the Cardy—Verlinde Formula // Phys. Lett. 2002. B544. Р. 337—345.
6. Wang B., Abdalla A., Su R.—K. Relating Friedmann equation to Cardy formula in universes with cosmological constant // Ibid. 2001. P. 394—398.