A class of LQC-inspired models for homogeneous, anisotropic cosmology in higher dimensional early universe. (English) Zbl 1370.83126
Summary: The dynamics of a \((3 + 1)\) dimensional homogeneous anisotropic universe is modified by loop quantum cosmology and, consequently, it has generically a big bounce in the past instead of a big-bang singularity. This modified dynamics can be well described by effective equations of motion. We generalise these effective equations of motion empirically to \((d + 1)\) dimensions. The generalised equations involve two functions and may be considered as a class of LQC-inspired models for \((d + 1)\) dimensional early universe cosmology. As a special case, one can now obtain a universe which has neither a big bang singularity nor a big bounce but approaches asymptotically a ‘Hagedorn like’ phase in the past where its density and volume remain constant. In a few special cases, we also obtain explicit solutions.
MSC:
| 83F05 | Relativistic cosmology |
| 83C45 | Quantization of the gravitational field |
| 83E15 | Kaluza-Klein and other higher-dimensional theories |
| 85A40 | Astrophysical cosmology |
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
| 83C75 | Space-time singularities, cosmic censorship, etc. |
| 83D05 | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |
| 80A10 | Classical and relativistic thermodynamics |
Keywords:
loop quantum cosmology; higher dimensional cosmology; LQC inspired higher dimensional anisotropic cosmology; Hagedorn like phase; big-bang singularity; modified dynamicsReferences:
| [1] | Bojowald, M.: Absence of singularity in loop quantum cosmology. Phys. Rev. Lett. 86, 5227 (2001). doi:10.1103/PhysRevLett.86.5227. arXiv:gr-qc/0102069 · doi:10.1103/PhysRevLett.86.5227 |
| [2] | Bojowald, M.: The inverse scale factor in isotropic quantum geometry. Phys. Rev. D 64, 084018 (2001). doi:10.1103/PhysRevD.64.084018. arXiv:gr-qc/0105067 · doi:10.1103/PhysRevD.64.084018 |
| [3] | Bojowald, M.: Isotropic loop quantum cosmology. Class. Quantum Gravity 19, 2717 (2002). doi:10.1088/0264-9381/19/10/313. arXiv:gr-qc/0202077 · Zbl 1008.83037 · doi:10.1088/0264-9381/19/10/313 |
| [4] | Bojowald, M.: Homogeneous loop quantum cosmology. Class. Quantum Gravity 20, 2595 (2003). doi:10.1088/0264-9381/20/13/310. arXiv:gr-qc/0303073 · Zbl 1049.83008 · doi:10.1088/0264-9381/20/13/310 |
| [5] | Ashtekar, A., Bojowald, M., Lewandowski, J.: Mathematical structure of loop quantum cosmology. Adv. Theor. Math. Phys. 7(2), 233 (2003). doi:10.4310/ATMP.2003.v7.n2.a2. arXiv:gr-qc/0304074 · doi:10.4310/ATMP.2003.v7.n2.a2 |
| [6] | Ashtekar, A., Pawlowski, T., Singh, P.: Quantum nature of the big bang. Phys. Rev. Lett. 96, 141301 (2006). doi:10.1103/PhysRevLett.96.141301. arXiv:gr-qc/0602086 · Zbl 1153.83417 · doi:10.1103/PhysRevLett.96.141301 |
| [7] | Ashtekar, A., Pawlowski, T., Singh, P.: Quantum nature of the big bang: improved dynamics. Phys. Rev. D 74, 084003 (2006). doi:10.1103/PhysRevD.74.084003. arXiv:gr-qc/0607039 · Zbl 1197.83047 · doi:10.1103/PhysRevD.74.084003 |
| [8] | Ashtekar, A.: New variables for classical and quantum gravity. Phys. Rev. Lett. 57, 2244 (1986). doi:10.1103/PhysRevLett.57.2244 · doi:10.1103/PhysRevLett.57.2244 |
| [9] | Ashtekar, A.: New Hamiltonian formulation of general relativity. Phys. Rev. D 36, 1587 (1987). doi:10.1103/PhysRevD.36.1587 · doi:10.1103/PhysRevD.36.1587 |
| [10] | Ashtekar, A., Singh, P.: Loop quantum cosmology: a status report. Class. Quantum Gravity 28, 213001 (2011). doi:10.1088/0264-9381/28/21/213001. arXiv:1108.0893 [gr-qc] · Zbl 1230.83003 · doi:10.1088/0264-9381/28/21/213001 |
| [11] | Varadarajan, M.: On the resolution of the big bang singularity in isotropic loop quantum cosmology. Class. Quantum Gravity 26, 085006 (2009). doi:10.1088/0264-9381/26/8/085006. arXiv:0812.0272 [gr-qc] · Zbl 1161.83394 · doi:10.1088/0264-9381/26/8/085006 |
| [12] | Date, G.: Lectures on LQG/LQC. arXiv:1004.2952 [gr-qc] |
| [13] | Bodendorfer, N., Thiemann, T., Thurn, A.: New variables for classical and quantum gravity in all dimensions I. Hamiltonian analysis. Class. Quantum Gravity 30, 045001 (2013). doi:10.1088/0264-9381/30/4/045001. arXiv:1105.3703 [gr-qc] · Zbl 1266.83072 · doi:10.1088/0264-9381/30/4/045001 |
| [14] | Bodendorfer, N., Thiemann, T., Thurn, A.: New variables for classical and quantum gravity in all dimensions II. Lagrangian analysis. Class. Quantum Gravity 30, 045002 (2013). doi:10.1088/0264-9381/30/4/045002. arXiv:1105.3704 [gr-qc] · Zbl 1266.83073 · doi:10.1088/0264-9381/30/4/045002 |
| [15] | Bodendorfer, N., Thiemann, T., Thurn, A.: New variables for classical and quantum gravity in all dimensions III. Quantum theory. Class. Quantum Gravity 30, 045003 (2013). doi:10.1088/0264-9381/30/4/045003. arXiv:1105.3705 [gr-qc] · Zbl 1266.83074 · doi:10.1088/0264-9381/30/4/045003 |
| [16] | Rama, S.K., Saha, A.P.: Unpublished notes · Zbl 1166.83018 |
| [17] | Bhowmick, S., Rama, \[S.K.: 10 + 110+1\] to \[3 + 13+1\] in an early universe with mutually BPS intersecting branes. Phys. Rev. D 82, 083526 (2010). doi:10.1103/PhysRevD.82.083526. arXiv:1007.0205 [hep-th] · doi:10.1103/PhysRevD.82.083526 |
| [18] | Ashtekar, A., Wilson-Ewing, E.: Loop quantum cosmology of Bianchi I models. Phys. Rev. D 79, 083535 (2009). doi:10.1103/PhysRevD.79.083535. arXiv:0903.3397 [gr-qc] · doi:10.1103/PhysRevD.79.083535 |
| [19] | Linsefors, L., Barrau, A.: Modified Friedmann equation and survey of solutions in effective Bianchi-I loop quantum cosmology. Class. Quantum Gravity 31, 015018 (2014). doi:10.1088/0264-9381/31/1/015018. arXiv:1305.4516 [gr-qc] · Zbl 1287.83052 · doi:10.1088/0264-9381/31/1/015018 |
| [20] | Bowick, M.J., Wijewardhana, L.C.R.: Superstrings at high temperature. Phys. Rev. Lett. 54, 2485 (1985). doi:10.1103/PhysRevLett.54.2485 · doi:10.1103/PhysRevLett.54.2485 |
| [21] | Bowick, M.J., Wijewardhana, L.C.R.: Superstring gravity and the early universe. Gen. Relativ. Gravit. 18, 59 (1986). doi:10.1007/BF00843749 · doi:10.1007/BF00843749 |
| [22] | Brandenberger, R.H., Vafa, C.: Superstrings in the early universe. Nucl. Phys. B 316, 391 (1989). doi:10.1016/0550-3213(89)90037-0 · doi:10.1016/0550-3213(89)90037-0 |
| [23] | Tseytlin, A.A., Vafa, C.: Elements of string cosmology. Nucl. Phys. B 372, 443 (1992). doi:10.1016/0550-3213(92)90327-8. arXiv:hep-th/9109048 · doi:10.1016/0550-3213(92)90327-8 |
| [24] | Veneziano, G.: A model for the big bounce. JCAP 0403, 004 (2004). doi:10.1088/1475-7516/2004/03/004. arXiv:hep-th/0312182 · doi:10.1088/1475-7516/2004/03/004 |
| [25] | Nayeri, A., Brandenberger, R.H., Vafa, C.: Producing a scale-invariant spectrum of perturbations in a Hagedorn phase of string cosmology. Phys. Rev. Lett. 97, 021302 (2006). doi:10.1103/PhysRevLett.97.021302. arXiv:hep-th/0511140 · doi:10.1103/PhysRevLett.97.021302 |
| [26] | Rama, S.K.: A stringy correspondence principle in cosmology. Phys. Lett. B 638, 100 (2006). doi:10.1016/j.physletb.2006.05.047. arXiv:hep-th/0603216 · Zbl 1248.83172 · doi:10.1016/j.physletb.2006.05.047 |
| [27] | Rama, S.K.: A principle to determine the number \[(3 + 13+1)\] of large spacetime dimensions. Phys. Lett. B 645, 365 (2007). doi:10.1016/j.physletb.2006.11.077. arXiv:hep-th/0610071 · Zbl 1273.83196 · doi:10.1016/j.physletb.2006.11.077 |
| [28] | Chowdhury, B.D., Mathur, S.D.: Fractional brane state in the early universe. Class. Quantum Gravity 24, 2689 (2007). doi:10.1088/0264-9381/24/10/014. arXiv:hep-th/0611330 · Zbl 1117.83107 · doi:10.1088/0264-9381/24/10/014 |
| [29] | Rama, S.K.: Entropy of anisotropic universe and fractional branes. Gen. Relativ. Gravit. 39, 1773 (2007). doi:10.1007/s10714-007-0488-1. arXiv:hep-th/0702202 [HEP-TH] · Zbl 1150.83011 · doi:10.1007/s10714-007-0488-1 |
| [30] | Rama, S.K.: Consequences of U dualities for intersecting branes in the universe. Phys. Lett. B 656, 226 (2007). doi:10.1016/j.physletb.2007.09.069. arXiv:0707.1421 [hep-th] · Zbl 1246.83189 · doi:10.1016/j.physletb.2007.09.069 |
| [31] | Date, G.: Absence of the Kasner singularity in the effective dynamics from loop quantum cosmology. Phys. Rev. D 71, 127502 (2005). doi:10.1103/PhysRevD.71.127502. arXiv:gr-qc/0505002 · doi:10.1103/PhysRevD.71.127502 |
| [32] | Bodendorfer, N.: Black hole entropy from loop quantum gravity in higher dimensions. Phys. Lett. B 726, 887 (2013). doi:10.1016/j.physletb.2013.09.043. arXiv:1307.5029 [gr-qc] · Zbl 1331.83096 · doi:10.1016/j.physletb.2013.09.043 |
| [33] | Zhang, X.: Higher dimensional loop quantum cosmology. Eur. Phys. J. C 76(7), 395 (2016). doi:10.1140/epjc/s10052-016-4249-8. arXiv:1506.05597 [gr-qc] · doi:10.1140/epjc/s10052-016-4249-8 |
| [34] | Sotiriou, T.P.: Covariant effective action for loop quantum cosmology from order reduction. Phys. Rev. D 79, 044035 (2009). doi:10.1103/PhysRevD.79.044035. arXiv:0811.1799 [gr-qc] · doi:10.1103/PhysRevD.79.044035 |
| [35] | Date, G., Sengupta, S.: Effective actions from loop quantum cosmology: correspondence with higher curvature gravity. Class. Quantum Gravity 26, 105002 (2009). doi:10.1088/0264-9381/26/10/105002. arXiv:0811.4023 [gr-qc] · Zbl 1166.83018 · doi:10.1088/0264-9381/26/10/105002 |
| [36] | Helling, R.C.: Higher curvature counter terms cause the bounce in loop cosmology. arXiv:0912.3011 [gr-qc] |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
