Youm, Donam A note on the Cardy-Verlinde formula. (English) Zbl 1039.83513 Phys. Lett., B 531, No. 3-4, 276-280 (2002). Summary: We generalize the results of E. Verlinde [On the holographic principle in a radiation dominated universe, hep-th/0008140] to the case of the \((n+1)\)-dimensional closed FRW universe satisfying a general equation of state of the form \(p=w\rho\). We find that the entropy of the universe can no longer be expressed in a form similar to the Cardy formula, when \(w\neq1/n\). As a result, in general the entropy formula does not coincide with the Friedmann equation when the conjectured bound on the Casimir energy is saturated. Furthermore, the conjectured bound on the Casimir energy generally does not lead to the Hubble and the Bekenstein entropy bounds. Cited in 8 Documents MSC: 83F05 Cosmology Keywords:\((n+1)\)-dimensional closed FRW universe; entropy; Casimir energy bound PDF BibTeX XML Cite \textit{D. Youm}, Phys. Lett., B 531, No. 3--4, 276--280 (2002; Zbl 1039.83513) Full Text: DOI arXiv References: [1] Verlinde, E. [2] Cardy, J.L., Nucl. phys. B, 270, 186, (1986) [3] Wang, B.; Abdalla, E.; Su, R., Phys. lett. B, 503, 394, (2001) [4] Klemm, D.; Petkou, A.C.; Siopsis, G., Nucl. phys. B, 601, 380, (2001) [5] Cai, R.G., Phys. rev. D, 63, 124018, (2001) [6] Biswas, A.K.; Mukherji, S., Jhep, 0103, 046, (2001) [7] Birmingham, D.; Mokhtari, S., Phys. lett. B, 508, 365, (2001) [8] Klemm, D.; Petkou, A.C.; Siopsis, G.; Zanon, D., Nucl. phys. B, 620, 519, (2002) [9] Youm, D., Phys. lett. B, 515, 170, (2001) [10] Cai, R.; Myung, Y.S.; Ohta, N., Class. quantum grav., 18, 5429, (2001) [11] Nojiri, S.; Odintsov, S.D.; Ogushi, S., Int. J. mod. phys. A, 16, 5085, (2001) [12] Cai, R.G.; Zhang, Y.Z., Phys. rev. D, 64, 104015, (2001) [13] Nojiri, S.; Odintsov, S.D., Int. J. mod. phys. A, 16, 3273, (2001) [14] Nojiri, S.; Odintsov, S.D., Class. quantum grav., 18, 5227, (2001) · Zbl 0993.83044 [15] Youm, D., Mod. phys. lett. A, 16, 1327, (2001) [16] Wang, B.; Abdalla, E.; Su, R.K. [17] Nojiri, S.; Obregon, O.; Odintsov, S.D.; Quevedo, H.; Ryan, M.P., Mod. phys. lett. A, 16, 1181, (2001) [18] Danielsson, U.H. [19] Ogushi, S. [20] Petkou, A.C.; Siopsis, G. [21] Cai, R.G., Phys. lett. B, 525, 331, (2002) [22] Medved, A.J.M. [23] Medved, A.J.M. [24] Youm, D. [25] Halyo, E. [26] Myung, Y.S. [27] Medved, A.J. [28] Cai, R.G. [29] Jing, J. [30] Witten, E., Adv. theor. math. phys., 2, 505, (1998) [31] Savonije, I.; Verlinde, E., Phys. lett. B, 507, 305, (2001) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.