Spinning toroidal brane cosmology; a classical and quantum survey. (English) Zbl 1472.83119

Nejad, Salman Abarghouei; Dehghani, Mehdi; Monemzadeh, Majid

Nucl. Phys., B 950, Article ID 114871, 18 p. (2020).

Summary: We construct a cosmological model based on a free particle model which is constrained on an embedded toroidal brane, with a general rotation around a specific axis in the bulk space. Some related issues such as the rotation axis of the brane, the presence of gravitomagnetic background and its relation to the general angular velocity

•  nLab
•  Wikipedia
•  Wolfram MathWorld

of the brane, and its quantum mechanics and related issues such as minimal length and minimal momentum of the quantum model in the \(\mathbb{T}^3\) brane are studied. Also, some cosmological features such as the constraint which is imposed upon the toroidal universe by the isotropy and homogeneity conditions, the corresponding Hubble law

•  nLab
•  Wikipedia

, and accelerating expansion for the spinning toroidal model without considering a cosmological constant are also studied.

MSC:

83F05	Relativistic cosmology
83E30	String and superstring theories in gravitational theory
81T30	String and superstring theories; other extended objects (e.g., branes) in quantum field theory
83C60	Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism
83E05	Geometrodynamics and the holographic principle
83C22	Einstein-Maxwell equations

References:

[1]	Lachieze-Rey, M.; Luminet, J.-P., Cosmic topology, Phys. Rep., 254, 135, 1995
[2]	Ade, P. A.R., Planck 2013 results. XVI. Cosmological parameters, Astron. Astrophys., 571, A16, 2014
[3]	Ade, P. A.R., Planck 2015 results. XVI. Isotropy and statistics of the CMB, Astron. Astrophys., 594, A16, 2016
[4]	Zeldovich, Y. B.; Starobinsky, A. A., Quantum creation of a universe with nontrivial topology, Sov. Astron. Lett., 10, 15, 1984
[5]	Coule, D. H.; Martin, J., Quantum cosmology and open universes, Phys. Rev. D, 61, Article 063501 pp., 2000
[6]	Linde, A., Creation of a compact topologically nontrivial inflationary universe, J. Cosmol. Astropart. Phys., 0410, Article 004 pp., 2004
[7]	Riazuelo, A.; Uzan, J. P.; Lehoucq, R.; Weeks, J., Simulating cosmic microwave background maps in multi-connected spaces, Phys. Rev. D, 69, Article 103514 pp., 2004
[8]	Riazuelo, A.; Weeks, J.; Uzan, J. P.; Lehoucq, R.; Luminet, J. P., Cosmic microwave background anisotropies in multi-connected flat spaces, Phys. Rev. D, 69, Article 103518 pp., 2004
[9]	Saadeh, D.; Feeney, S. M.; Pontzen, A.; Peiris, H. V.; McEwen, J. D., How isotropic is the universe?, Phys. Rev. Lett., 117, Article 131302 pp., 2016
[10]	Cheng, C.; Zhao, W.; Huang, Q. G.; Santos, L., Preferred axis of CMB parity asymmetry in the masked maps, Phys. Lett. B, 757, 445, 2016
[11]	Hutsemekers, D., Evidence for very large-scale coherent orientations of quasar polarization vectors, Astron. Astrophys., 332, 410, 1998
[12]	Hutsemekers, D.; Lamy, L., Confirmation of the existence of coherent orientations of quasar polarization vectors on cosmological scales, Astron. Astrophys., 367, 381, 2001
[13]	Hutsemekers, D.; Cabanac, R.; Lamy, L.; Sluse, D., Mapping extreme-scale alignments of quasar polarization vectors, Astron. Astrophys., 441, 915, 2005
[14]	Pelgrims, V.; Hutsemekers, D., Polarization alignments of quasars from the JVAS/CLASS 8.4-GHz surveys, Mon. Not. R. Astron. Soc., 450, 4161, 2015
[15]	Antoniou, I.; Perivolaropoulos, L., Searching for a cosmological preferred axis: Union2 data analysis and comparison with other probes, J. Cosmol. Astropart. Phys., 1012, Article 012 pp., 2010
[16]	Cai, R. G.; Tou, Z. L., Direction dependence of the deceleration parameter, J. Cosmol. Astropart. Phys., 1202, Article 004 pp., 2012
[17]	Yang, X.; Wang, F. Y.; Chu, Z., Searching for a preferred direction with Union2.1 data, Mon. Not. R. Astron. Soc., 437, 1840, 2014
[18]	Chang, Z.; Lin, H. N., Comparison between hemisphere comparison method and dipole-fitting method in tracing the anisotropic expansion of the universe use the Union2 data set, Mon. Not. R. Astron. Soc., 446, 2952, 2015
[19]	Bengaly, C. A.P.; Bernui, A.; Alcaniz, J. S., Probing cosmological isotropy with Type IA supernovae, Astrophys. J., 808, 39, 2015
[20]	Javanmardi, B.; Porciani, C.; Kroupa, P.; Pflamm-Altenburg, J., Probing the isotropy of cosmic acceleration traced by Type Ia supernovae, Astrophys. J., 810, 47, 2015
[21]	Webb, J. K.; King, J. A.; Murphy, M. T.; Flambaum, V. V.; Carswell, R. F.; Bainbridge, M. B., Indications of a spatial variation of the fine structure constant, Phys. Rev. Lett., 107, Article 191101 pp., 2011
[22]	King, J. A.; Webb, J. K.; Murphy, M. T.; Flambaum, V. V.; Carswell, R. F.; Bainbridge, M. B.; Wilczynska, M. R.; Koch, F. E., Spatial variation in fine-structure constant, Mon. Not. R. Astron. Soc., 422, 3370, 2012
[23]	Mariano, A.; Perivolaropoulos, L., Is there correlation between fine structure and dark energy cosmic dipoles?, Phys. Rev. D, 86, Article 083517 pp., 2012
[24]	Longo, M. J., Detection of a dipole in the handedness of spiral galaxies with redshifts z ∼ 0.04, Phys. Lett. B, 699, 224, 2011
[25]	Longo, M. J., Evidence for a preferred handedness of spiral galaxies
[26]	Abarghouei Nejad, S.; Dehghani, M.; Monemzadeh, M., Lagrange multiplier and Wess-Zumino variable as large extra dimensions in the torus universe, J. High Energy Phys., 1801, Article 017 pp., 2018 · Zbl 1384.83019
[27]	Nakahara, M., Geometry, Topology and Physics, 2003, CRC Press · Zbl 1090.53001
[28]	Seiberg, N.; Witten, E., String theory and noncommutative geometry, J. High Energy Phys., 9909, Article 032 pp., 1999 · Zbl 0957.81085
[29]	Arkani-Hamed, N.; Dimopoulos, S.; Dvali, G. R., The hierarchy problem and new dimensions at a millimeter, Phys. Lett. B, 429, 263, 1998 · Zbl 1355.81103
[30]	Arkani-Hamed, N.; Dimopoulos, S.; Dvali, G. R., Phenomenology, astrophysics and cosmology of theories with sub-millimeter dimensions and TeV scale quantum gravity, Phys. Rev. D, 59, Article 086004 pp., 1999
[31]	Maartens, R.; Korama, K., Brane-world gravity, Living Rev. Relativ., 13, 5, 2010 · Zbl 1316.83038
[32]	Papantonapoulos, E., Brane cosmology, Lect. Notes Phys., 592, 458, 2002 · Zbl 1042.83035
[33]	Ashoorioon, A.; Mann, R. B., On the tensor/scalar ratio in inflation with UV cutoff, Nucl. Phys. B, 716, 261, 2005
[34]	Maggiore, M., A generalized uncertainty principle in quantum gravity, Phys. Lett. B, 304, 65, 1993
[35]	Maggiore, M., The algebraic structure of the generalized uncertainty principle, Phys. Lett. B, 319, 83, 1993
[36]	Maggiore, M., Quantum groups, gravity, and the generalized uncertainty principle, Phys. Rev. D, 49, 5182, 1994
[37]	Kempf, A.; Mangano, G.; Mann, R. B., Hilbert space representation of the minimal length uncertainty relation, Phys. Rev. D, 52, 1108, 1995
[38]	Ashoorioon, A.; Kempf, A.; Mann, R. B., Minimum length cutoff in inflation and uniqueness of the action, Phys. Rev. D, 71, Article 023503 pp., 2005
[39]	Das, S.; Mann, R. B., Planck scale effects on some low energy quantum phenomena, Phys. Lett. B, 704, 596, 2011
[40]	Aldrovandi, R.; Geraldo Pereira, J., An Introduction to Geometrical Physics, 2017, World Scientific Publishing Co. Pte. Ltd. · Zbl 1355.00013
[41]	Mashhoon, B., Gravitoelectromagnetism: a brief review
[42]	Ida, D., Brane-world cosmology, J. High Energy Phys., 09, Article 014 pp., 2000 · Zbl 0990.83537
[43]	Das, P.; Pramanik, S.; Ghosh, S., Particle on a torus knot: constrained dynamics and semi-classical quantization in a magnetic field, Ann. Phys., 374, 67, 2016 · Zbl 1377.70040
[44]	Amelino-Camelia, G., On the fate of Lorentz symmetry in relative-locality momentum spaces, Phys. Rev. D, 85, Article 084034 pp., 2012
[45]	Ghosh, S.; Pal, P., Deformed special relativity and deformed symmetries in a canonical framework, Phys. Rev. D, 75, Article 105021 pp., 2005
[46]	Pramanik, S.; Ghosh, S.; Pal, P., Electrodynamics of a generalized charged particle in doubly special relativity framework, Ann. Phys., 346, 113, 2014 · Zbl 1342.78019
[47]	Cianfrani, F.; Kowalski-Glikman, J.; Pranzetti, D.; Rosati, G., Symmetries of quantum spacetime in three dimensions, Phys. Rev. D, 94, Article 084044 pp., 2016
[48]	Arzano, M.; Kowalski-Glikman, J., Non-commutative fields and the short-scale structure of spacetime, Phys. Lett. B, 771, 222, 2017 · Zbl 1372.81145
[49]	Ruegg, H.; Tolstoy, V. N., Representation theory of quantized Poincaré algebra. Tensor operators and their applications to one-particle systems, Lett. Math. Phys., 32, 85, 1994 · Zbl 0826.16038
[50]	Lukierski, J.; Ruegg, H.; Tolstoy, V. N.; Nowicki, A., Twisted classical Poincare algebras, J. Phys. A, 27, 2389, 1994 · Zbl 0834.17027
[51]	Amelino-Camelia, G.; Freidel, L.; Kowalski-Glikman, J.; Smolin, L., Relative locality: a deepening of the relativity principle, Gen. Relativ. Gravit., 43, 2547, 2011 · Zbl 1228.83040
[52]	Amelino-Camelia, G.; Freidel, L.; Kowalski-Glikman, J.; Smolin, L., Relative locality: a deepening of the relativity principle, Int. J. Mod. Phys. D, 20, 2867, 2011 · Zbl 1263.83064
[53]	Amelino-Camelia, G.; Smolin, L.; Starodubtsev, A., Quantum symmetry, the cosmological constant and Planck scale phenomenology, Class. Quantum Gravity, 21, 3095, 2004 · Zbl 1061.83025
[54]	Perlmutter, S., A supernova at z = 0.458 and implications for measuring the cosmological deceleration, Astrophys. J., 440, L41, 1995
[55]	Monemzadeh, M.; Dehghani, M.; Abarghouei Nejad, S., Gauging the relativistic particle model on the noncommutative plane, Int. J. Theor. Phys., 56, 1793, 2017 · Zbl 1366.81272
[56]	Horada, K.; Mukaida, H., Gauge invariance and systems with second-class constraints, Z. Phys. C, 48, 151, 1990
[57]	Deriglazov, A. A.; Kuzentsova, Z., Conversion of second class constraints by deformation of Lagrangian local symmetries, Phys. Lett. B, 646, 47, 2007 · Zbl 1248.70021
[58]	Henneaux, M.; Teiltelboim, C., Quantization of Gauge System, 1992, University Press · Zbl 0838.53053
[59]	Steinhardt, P. J.; Turok, N., A cyclic model of the universe, Science, 296, 1436, 2002 · Zbl 1226.83096
[60]	Ijjas, A.; Steinhardt, P. J., Bouncing cosmology made simple, Class. Quantum Gravity, 35, Article 135004 pp., 2018 · Zbl 1409.83236
[61]	Brandenberger, R.; Peter, P., Bouncing cosmologies: progress and problems, Found. Phys., 47, 797, 2017 · Zbl 1372.83002
[62]	Aghanim, N., Planck 2018 results. VI. Cosmological parameters
[63]	Sotiriou, T. P.; Faraoni, V., f(R) theories of gravity, Rev. Mod. Phys., 82, 451, 2010 · Zbl 1205.83006