Planck-scale corrections to Friedmann equation

• Authors: Adel Awad , Ahmed Ali
• Languages of publication: EN

Abstracts

EN

Recently, Verlinde proposed that gravity is an emergent phenomenon which originates from an entropic force. In this work, we extend Verlinde’s proposal to accommodate generalized uncertainty principles (GUP), which are suggested by some approaches to quantum gravity such as string theory, black hole physics and doubly special relativity (DSR). Using Verlinde’s proposal and two known models of GUPs, we obtain modifications to Newton’s law of gravitation as well as the Friedmann equation. Our modification to the Friedmann equation includes higher powers of the Hubble parameter which is used to obtain a corresponding Raychaudhuri equation. Solving this equation, we obtain a leading Planck-scale correction to Friedmann-Robertson-Walker (FRW) solutions for the p = ωp equation of state.

Keywords

EN

quantum gravity; entropic force; thermodynamics; black holes

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2014
• Volume: 12
• Issue: 4
• Pages: 245-255

Dates

published

1 - 4 - 2014

online

23 - 4 - 2014

Contributors

author

Adel Awad

author

Ahmed Ali

References

• [1] D. Amati, M. Ciafaloni, G. Veneziano, Phys. Lett. B 216, 41 (1989) http://dx.doi.org/10.1016/0370-2693(89)91366-X[Crossref]
• [2] M. Maggiore, Phys. Lett. B 304, 65 (1993) http://dx.doi.org/10.1016/0370-2693(93)91401-8[Crossref]
• [3] M. Maggiore, Phys. Rev. D 49, 5182 (1994) http://dx.doi.org/10.1103/PhysRevD.49.5182[Crossref]
• [4] M. Maggiore, Phys. Lett. B 319, 83 (1993) http://dx.doi.org/10.1016/0370-2693(93)90785-G[Crossref]
• [5] L. J. Garay, Int. J. Mod. Phys. A 10, 145 (1995) http://dx.doi.org/10.1142/S0217751X95000085[Crossref]
• [6] S. Hossenfelder, M. Bleicher, S. Hofmann, J. Ruppert, S. Scherer, H. Stoecker, Phys. Lett. B 575, 85 (2003) http://dx.doi.org/10.1016/j.physletb.2003.09.040[Crossref]
• [7] C. Bambi, F. R. Urban, Class. Quant. Grav. 25, 095006 (2008) http://dx.doi.org/10.1088/0264-9381/25/9/095006[Crossref]
• [8] F. Scardigli, Phys. Lett. B 452, 39 (1999) http://dx.doi.org/10.1016/S0370-2693(99)00167-7[Crossref]
• [9] A. Kempf, G. Mangano, R. B. Mann, Phys. Rev. D52, 1108 (1995)
• [10] A. Kempf, J. Phys. A 30, 2093 (1997) http://dx.doi.org/10.1088/0305-4470/30/6/030[Crossref]
• [11] F. Brau, J. Phys. A 32, 7691 (1999) http://dx.doi.org/10.1088/0305-4470/32/44/308[Crossref]
• [12] A. F. Ali, S. Das, E. C. Vagenas, Phys. Lett. B 678, 497 (2009) http://dx.doi.org/10.1016/j.physletb.2009.06.061[Crossref]
• [13] S. Das, E. C. Vagenas, A. F. Ali, Phys. Lett. B 690, 407 (2010) http://dx.doi.org/10.1016/j.physletb.2010.05.052[Crossref]
• [14] G. Amelino-Camelia, Int. J. Mod. Phys. D 11, 35 (2002) http://dx.doi.org/10.1142/S0218271802001330[Crossref]
• [15] G. Amelino-Camelia, Phys. Lett. B 510, 255 (2001) http://dx.doi.org/10.1016/S0370-2693(01)00506-8[Crossref]
• [16] J. Kowalski-Glikman, S. Nowak, Phys. Lett. B 539, 126 (2002) http://dx.doi.org/10.1016/S0370-2693(02)02063-4[Crossref]
• [17] J. Magueijo, L. Smolin, Phys. Rev. D 67, 044017 (2003) http://dx.doi.org/10.1103/PhysRevD.67.044017[Crossref]
• [18] J. Magueijo, L. Smolin, Class. Quant. Grav. 21, 1725 (2004) http://dx.doi.org/10.1088/0264-9381/21/7/001[Crossref]
• [19] J. L. Cortes, J. Gamboa, Phys. Rev. D71, 065015 (2005)
• [20] S. Das, E. C. Vagenas, Phys. Rev. Lett. 101, 221301 (2008) http://dx.doi.org/10.1103/PhysRevLett.101.221301[Crossref]
• [21] S. Das, E. C. Vagenas, Can. J. Phys. 87, 233 (2009) http://dx.doi.org/10.1139/P08-105[Crossref]
• [22] A. F. Ali, S. Das, E. C. Vagenas, Phys. Rev. D 84, 044013 (2011) http://dx.doi.org/10.1103/PhysRevD.84.044013[Crossref]
• [23] W. Chemissany, S. Das, A. F. Ali, E. C. Vagenas, JCAP 1112, 017 (2011) http://dx.doi.org/10.1088/1475-7516/2011/12/017[Crossref]
• [24] M. Sprenger, M. Bleicher, P. Nicolini, Class. Quant. Grav. 28, 235019 (2011) http://dx.doi.org/10.1088/0264-9381/28/23/235019[Crossref]
• [25] A. F. Ali, JHEP 1209, 067 (2012) http://dx.doi.org/10.1007/JHEP09(2012)067[Crossref]
• [26] A. F. Ali, H. Nafie, M. Shalaby, Europhys. Lett. 100, 20004 (2012) http://dx.doi.org/10.1209/0295-5075/100/20004[Crossref]
• [27] A. Tawfik, H. Magdy, A. F. Ali, Gen. Rel. Grav. 45, 1227 (2013) http://dx.doi.org/10.1007/s10714-013-1522-0[Crossref]
• [28] A. Tawfik, H. Magdy, A. F. Ali, arXiv:1205.5998 [physics.gen-ph]
• [29] A. F. Ali, Class. Quant. Grav. 28, 065013 (2011) http://dx.doi.org/10.1088/0264-9381/28/6/065013[Crossref]
• [30] B. Majumder, S. Sen, Phys. Lett. B 717, 291 (2012) http://dx.doi.org/10.1016/j.physletb.2012.09.035[Crossref]
• [31] K. Nozari, S. Saghafi, JHEP 1211, 005 (2012) http://dx.doi.org/10.1007/JHEP11(2012)005[Crossref]
• [32] B. Majumder, Phys. Lett. B 709, 133 (2012) http://dx.doi.org/10.1016/j.physletb.2012.02.022[Crossref]
• [33] K. Nozari, A. Etemadi, Phys. Rev. D 85, 104029 (2012) http://dx.doi.org/10.1103/PhysRevD.85.104029[Crossref]
• [34] I. Pikovski et al., Nature Phys. 8, 393 (2012) http://dx.doi.org/10.1038/nphys2262[Crossref]
• [35] F. Marin et al., Nature Phys. 9, 71 (2013) http://dx.doi.org/10.1038/nphys2503[Crossref]
• [36] J. D. Bekenstein, Phys. Rev. D 86, 124040 (2012) http://dx.doi.org/10.1103/PhysRevD.86.124040[Crossref]
• [37] J. D. Bekenstein, arXiv:1301.4322 [gr-qc]
• [38] E. P. Verlinde, JHEP 1104, 029 (2011) http://dx.doi.org/10.1007/JHEP04(2011)029[Crossref]
• [39] A. F. Ali, A. Tawfik, Adv. High Energy Phys. 2013, 126528 (2013)
• [40] J. D. Bekenstein, Phys. Rev. D 7, 2333 (1973) http://dx.doi.org/10.1103/PhysRevD.7.2333[Crossref]
• [41] J. M. Bardeen, B. Carter, S. W. Hawking, Commun. Math. Phys. 31, 161 (1973) http://dx.doi.org/10.1007/BF01645742[Crossref]
• [42] S. W. Hawking, Commun. Math. Phys. 43, 199 (1975) [Erratum-ibid. 46, 206 (1976)] http://dx.doi.org/10.1007/BF02345020[Crossref]
• [43] R. -G. Cai, L. -M. Cao, N. Ohta, Phys. Rev. D 81, 061501 (2010) http://dx.doi.org/10.1103/PhysRevD.81.061501[Crossref]
• [44] G. t’Hooft, gr-qc/9310026
• [45] P. Nicolini, Phys. Rev. D 82, 044030 (2010) http://dx.doi.org/10.1103/PhysRevD.82.044030[Crossref]
• [46] C. Bastos, O. Bertolami, N. C. Dias, J. N. Prata, Class. Quant. Grav. 28, 125007 (2011) http://dx.doi.org/10.1088/0264-9381/28/12/125007[Crossref]
• [47] K. Nozari, S. Akhshabi, Phys. Lett. B 700, 91 (2011) http://dx.doi.org/10.1016/j.physletb.2011.04.056[Crossref]
• [48] S. H. Mehdipour, A. Keshavarz, A. Keshavarz, Europhys. Lett. 91, 10002 (2012) http://dx.doi.org/10.1209/0295-5075/98/10002[Crossref]
• [49] A. Sheykhi, Phys. Rev. D 81, 104011 (2010) http://dx.doi.org/10.1103/PhysRevD.81.104011[Crossref]
• [50] S. H. Hendi, A. Sheykhi, Phys. Rev. D 83, 084012 (2011) http://dx.doi.org/10.1103/PhysRevD.83.084012[Crossref]
• [51] B. Majumder, Adv. High Energy Phys. 2013, 296836 (2013)
• [52] M. Aghaei Abchouyeh, B. Mirza, Z. Sherkatghanad, Gen. Rel. Grav. 46, 1617 (2014) http://dx.doi.org/10.1007/s10714-013-1617-7[Crossref]
• [53] A. Sheykhi, M. H. Dehghani, S. E. Hosseini, Phys. Lett. B 726, 23 (2013) http://dx.doi.org/10.1016/j.physletb.2013.08.035[Crossref]
• [54] N. Komatsu, S. Kimura, Phys. Rev. D 88, 083534 (2013) http://dx.doi.org/10.1103/PhysRevD.88.083534[Crossref]
• [55] M. Eune, W. Kim, Phys. Rev. D 88, 067303 (2013) http://dx.doi.org/10.1103/PhysRevD.88.067303[Crossref]
• [56] M. Cavaglia, S. Das, R. Maartens, Class. Quant. Grav. 20, L205 (2003) http://dx.doi.org/10.1088/0264-9381/20/15/101[Crossref]
• [57] M. Cavaglia, S. Das, Class. Quant. Grav. 21, 4511 (2004) http://dx.doi.org/10.1088/0264-9381/21/19/001[Crossref]
• [58] A. J. M. Medved, E. C. Vagenas, Phys. Rev. D70, 124021 (2004)
• [59] F. Scardigli, Nuovo Cim. B 110, 1029 (1995) http://dx.doi.org/10.1007/BF02726152[Crossref]
• [60] R. J. Adler, P. Chen, D. I. Santiago, Gen. Rel. Grav. 33, 2101 (2001) http://dx.doi.org/10.1023/A:1015281430411[Crossref]
• [61] A. J. M. Medved, E. C. Vagenas, Phys. Rev. D 70, 124021 (2004) http://dx.doi.org/10.1103/PhysRevD.70.124021[Crossref]
• [62] B. Majumder, Phys. Lett. B 703, 402 (2011) http://dx.doi.org/10.1016/j.physletb.2011.08.026[Crossref]
• [63] G. Amelino-Camelia, M. Arzano, A. Procaccini, Phys. Rev. D 70, 107501 (2004) http://dx.doi.org/10.1103/PhysRevD.70.107501[Crossref]
• [64] E. M. Lifshitz, L. P. Pitaevskii, V. B. Berestetskii, Landau-Lifshitz Course of Theoretical Physics, Volume 4: Quantum Electrodynamics, (Reed Educational and Professional Publishing, Butterworth-Heinemann in Oxford, UK, 1982)
• [65] D. Christodoulou, Phys. Lett. 25, 1596 (1970) http://dx.doi.org/10.1103/PhysRevLett.25.1596[Crossref]
• [66] D. Christodoulou, R. Ruffini, Phys. Rev. D 4, 3352 (1971) http://dx.doi.org/10.1103/PhysRevD.4.3552[Crossref]
• [67] C. Adami, quant-ph/0405005
• [68] K. A. Bronnikov, S. A. Kononogov, V. N. Melnikov, Gen. Rel. Grav. 38, 1215 (2006) http://dx.doi.org/10.1007/s10714-006-0300-7[Crossref]
• [69] R. -G. Cai, S. P. Kim, JHEP 0502, 050 (2005) http://dx.doi.org/10.1088/1126-6708/2005/02/050[Crossref]
• [70] A. Awad, Phys. Rev. D 87, 103001 (2013) http://dx.doi.org/10.1103/PhysRevD.87.103001[Crossref]
• [71] L. Randall, R. Sundrum, Phys. Rev. Lett. 83, 4690 (1999) http://dx.doi.org/10.1103/PhysRevLett.83.4690[Crossref]
• [72] P. Callin, F. Ravndal, Phys. Rev. D 70, 104009 (2004) http://dx.doi.org/10.1103/PhysRevD.70.104009[Crossref]
• [73] S. -Q. Yang et al., Phys. Rev. Lett. 108, 081101 (2012) http://dx.doi.org/10.1103/PhysRevLett.108.081101[Crossref]
• [74] C. D. Hoyle et al., Phys. Rev. D 70, 042004 (2004) http://dx.doi.org/10.1103/PhysRevD.70.042004[Crossref]
• [75] F. Buisseret, V. Mathieu, B. Silvestre-Brac, Class. Quant. Grav. 24, 855 (2007) http://dx.doi.org/10.1088/0264-9381/24/4/006[Crossref]
• [76] G. L. Murphy, Phys. Rev. D 8, 4231 (1973) http://dx.doi.org/10.1103/PhysRevD.8.4231[Crossref]
• [77] P. A. R. Ade et al., arXiv:1303.5082 [astro-ph.CO]
• [78] S. del Campo, JCAP 12, 005 (2012) http://dx.doi.org/10.1088/1475-7516/2012/12/005[Crossref]
• [79] U. H. Danielsson, Phys. Rev. D 66, 023511 (2002) http://dx.doi.org/10.1103/PhysRevD.66.023511[Crossref]

Identifiers

DOI

10.2478/s11534-014-0441-3