Holographic Bound in Quantum Field Energy Density and Cosmological Constant

Paolo  Castorina

doi:10.4236/jmp.2013.46110

Paolo Castorina^*

Abstract: The cosmological constant problem is reanalyzed by imposing the limitation of the number of degrees of freedom (d.o.f.) due to entropy bounds directly in the calculation of the energy density of a field theory. It is shown that if a quantum field theory has to be consistent with gravity and holography, i.e. with an upper limit of storing information in a given area, the ultraviolet momentum cut-off is not the Planck mass, Mp, as naively expected, but where Nu is the number of d.o.f. of the universe. The energy density evaluation turns out completely consistent with Bousso’s bound on the cosmological constant value. The scale , that in the “fat graviton” theory corresponds to the graviton size, originates by a self-similar rearrangement of the elementary d.o.f. at different scales that can be seen as an infrared-ultraviolet connection.

Keywords: Cosmological Constant; Holography; Quantum Fields

Cite this paper: P. Castorina, "Holographic Bound in Quantum Field Energy Density and Cosmological Constant," Journal of Modern Physics, Vol. 4 No. 6, 2013, pp. 807-811. doi: 10.4236/jmp.2013.46110.

References

[1] C. F. von Weizsaker, Komplemerterritat and I. Logik, Naturwissenschaflen, Vol. 42, 1955, pp. 521-529.

[2] J. A. Wheeler, “It for Bit,” In: L. Keldysh and V. Feinberg, Eds., Sakharov Memorial Lectures on Physics, Vol. 2, Nova Science, New York.

[3] R. Penrose, In: C. J. Isham, R. Penrose and D. Sciama, Eds., Quantum Gravity, an Oxford Symposium, Clarendon Press, Oxford, 1975.

[4] S. Doplicher, K.Fredenhagen and J. E. Roberts, Communications in Mathematical Physics, Vol. 172, 1995, pp. 187-220. doi:10.1007/BF02104515

[5] C. Rovelli, Classical and Quantum Gravity, Vol. 28, 2011, Article ID: 153002. arxive:1102.360

[6] C. Rovelli, “Zakopane Lectures on Loop Gravity,” arxive:1102.360.

[7] S. Muhki, Classical and Quantum Gravity, Vol. 28, 2011, Article ID: 153001.

[8] M. Blau and S. Theisen, General Relativity and Gravitation, Vol. 41, 2009, p. 743.

[9] J. D. Bekenstein, Physical Review D, Vol. 7, 1973, pp. 2333-2346. doi:10.1103/PhysRevD.7.2333

[10] J. D. Bekenstein, Physical Review D, Vol. 9, 1974, p. 3292.

[11] J. D. Bekenstein, Physical Review D, Vol. 23, 1981, p. 287. doi:10.1103/PhysRevD.9.3292

[12] R. Bousso, Journal of High Energy Physics, Vol. 9907, 1999, p. 4.

[13] R. Bousso, Physical Review Letters, Vol. 90, 2003, Article ID: 121302.

[14] R. Bousso, Review of Modern Physics, Vol. 74, 2002, p. 285. doi:10.1088/1126-6708/1999/07/004

[15] G. Hooft, “Dimensional Reduction in Quantum Gravity,” In: In: A. Alo, J. Ellis and S. Randjbar-Daemi, Eds, Salanfestschrift, World Scientific, Singapore, 1993, p. 284.

[16] L. Susskind, Journal of Mathematical Physics, Vol. 36, 1995, p. 6377. doi:10.1063/1.531249

[17] D. A. Lowe, J. Polchinsky, L. Susskind, L. Thorlacius and J. Uglum, Physical Review D, Vol. 52, 1995, pp. 6997-7010. doi:10.1103/PhysRevD.52.6997

[18] E. Witten, Advances in Theoretical and Mathematical Physics, Vol. 2, 1998, p. 253.

[19] J. M. Maldacena, “Gravity, Particle Physics and Their Unification,” arxive: hep-ph/0002092

[20] T. Jacobson, Physical Review Letters, Vol. 75, 1995, pp. 1260-1263. doi:10.1103/PhysRevLett.75.1260

[21] T. Padmanabhan, Classical and Quantum Gravity, Vol. 19, 2002, p. 5387.

[22] T. Padmanabhan, “Thermodynamiacl Aspect of gravity. New insights,” arxive 0911.5004.

[23] E. P. Verlinde, Journal of High Energy Physics, Vol. 1104, 2011, p. 29.

[24] T. Banks, hep-th/0007146; hep-th/0306074.

[25] S. Weinberg, Physical Review Letters, Vol. 59, 1987, pp. 2607-2610. doi:10.1103/PhysRevLett.59.2607

[26] A. Cohen, D. Kaplan and A. Nelson, Physical Review Letters, Vol. 82, 1999, pp. 4971-4974. doi:10.1103/PhysRevLett.82.4971

[27] S. D. H. Hsu, Physical Letters B, Vol. 594, 2004, pp. 13-16. doi:10.1016/j.physletb.2004.05.020

[28] R. A. Knop, et al., The Astrophysical Journal, Vol. 598, 2003, p. 102. doi:10.1086/378560

[29] P. Astier, et al., Astronomy & Astrophysics, Vol. 447, 2006, p. 31. doi:10.1051/0004-6361:20054185

[30] A. Kogut, et al., The Astrophysical Journal, Vol. 665, 2007, p. 355. doi:10.1086/519754

[31] M. Tegmark, et al., Physical Review D, Vol. 74, 2006, Article ID: 123507. doi:10.1103/PhysRevD.74.123507

[32] P. Erdos and R. L.Graham, Journal of Combinatorial Theory, Series A, Vol. 19, 1975, pp. 119-123. doi:10.1016/0097-3165(75)90099-0

[33] F. Chung and R. L. Graham, Journal of Combinatorial Theory, Series A, Vol. 116, 2009, pp. 1167-1175. doi:10.1016/j.jcta.2009.02.005

[34] R. Sundrum, Physical Review D, Vol. 69, 2004, Article ID: 044014. doi:10.1103/PhysRevD.69.044014

[35] R. Sundrum, Nuclear Physics B, Vol. 690, 2004, pp. 302-330. doi:10.1016/j.nuclphysb.2004.05.011

[36] T. Gornitz, International Journal of Theoretical Physics, Vol. 27, 1988, pp. 527-542. doi:10.1007/BF00668835

[37] M. Douglas and N. Nekrasov, Reviews of Modern Physics, 73, 2001, pp. 977-1029. doi:10.1103/RevModPhys.73.977

[38] R. J. Szabo, Physics Reports, Vol. 378, 2003, pp. 207-299. doi:10.1016/S0370-1573(03)00059-0

[39] S. S. Gubser and S. L. Sondhi, Nuclear Physics B, Vol. 605, 2001, pp. 395-424. doi:10.1016/S0550-3213(01)00108-0

[40] P. Castorina and D. Zappala, Physical Review D, Vol. 68, 2003, Article ID: 065008. doi:10.1103/PhysRevD.68.065008

[41] R. Jaffe, Physical Review D, Vol. 72, 2005, Article ID: 021301. doi:10.1103/PhysRevD.72.021301

[42] C. Beck and M. C. Mackey, International Journal of Modern Physics D, Vol. 17, 2008, p. 71. doi:10.1142/S0218271808011870

[43] V. Branchina, M. Di Liberto and I. Lodato, Journal of Cosmology and Astroparticle Physics, 0908:011.2009.

[44] P. Jetzer and N. Strauman, Physical Letters B, Vol. 639, 2006, p. 57. doi:10.1016/j.physletb.2006.06.020

[45] S.-Q. Yang, et al., Physical Review Letters, Vol. 108 2012, Article ID: 081111.

[46] S. M. Carroll, Living Reviews in Relativity, Vol. 3, 2001, p. 1.

[47] S. Nobbenhuis, Foundations of Physics, Vol. 36, 2006, p. 613.