Dirac-Born-Infeld-Einstein Theory with Weyl Invariance
Affiliation(s)
Japan Women’s College of Physical Education, Setagaya, Tokyo 157-8565, Japan. Yamaguchi Junior College, Hofu-shi, Yamaguchi 747-1232, Japan. Yamaguchi University, Yamaguchi-shi, Yamaguchi 753-8512, Japan.
Japan Women’s College of Physical Education, Setagaya, Tokyo 157-8565, Japan. Yamaguchi Junior College, Hofu-shi, Yamaguchi 747-1232, Japan. Yamaguchi University, Yamaguchi-shi, Yamaguchi 753-8512, Japan.
ABSTRACT
Weyl invariant gravity has been investigated as the fundamental theory of the vector inflation. Accordingly, we consider a Weyl invariant extension of Dirac-Born-Infeld type gravity. We find that an appropriate choice of the metric removes the scalar degree of freedom which is at the first sight required by the local scale invariance of the action, and then a vector field acquires mass. Then non-minimal couplings of the vector field and curvatures are induced. We find that the Dirac-Born-Infeld type gravity is a suitable theory to the vector inflation scenario.
Weyl invariant gravity has been investigated as the fundamental theory of the vector inflation. Accordingly, we consider a Weyl invariant extension of Dirac-Born-Infeld type gravity. We find that an appropriate choice of the metric removes the scalar degree of freedom which is at the first sight required by the local scale invariance of the action, and then a vector field acquires mass. Then non-minimal couplings of the vector field and curvatures are induced. We find that the Dirac-Born-Infeld type gravity is a suitable theory to the vector inflation scenario.
Cite this paper
T. Maki, N. Kan and K. Shiraishi, "Dirac-Born-Infeld-Einstein Theory with Weyl Invariance," Journal of Modern Physics, Vol. 3 No. 9, 2012, pp. 1081-1087. doi: 10.4236/jmp.2012.39142.
T. Maki, N. Kan and K. Shiraishi, "Dirac-Born-Infeld-Einstein Theory with Weyl Invariance," Journal of Modern Physics, Vol. 3 No. 9, 2012, pp. 1081-1087. doi: 10.4236/jmp.2012.39142.
References
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Mitra, “One Loop Calculation of Cosmological Constant in a Scale Invariant Theory,” Modern Physics Letters A, Vol. 24, No. 26, 2009, pp. 2069-2079. doi:10.1142/S0217732309031351 [32] P. Jain and S. Mitra, “Standard Model with Cosmologically Broken Quantum Scale Invariance,” Modern Physics Letters A, Vol. 25, No. 3, 2010, pp. 167-177. doi:10.1142/S0217732310032317 [33] P. Jain, S. Mitra and N. K. Singh, “Cosmological Implications of a Scale Invariant Standard Model,” Journal of Cosmology and Astroparticle Physics, No. 3, 2008. [34] P. K. Aluri, P. Jain and N. K. Singh, “Dark Energy and Dark Matter in General Relativity with Local Scale In- variance,” Modern Physics Letters A, Vol. 24, No. 20, 2009, pp. 1583-1595. doi:10.1142/S0217732309030060 [35] P. K. Aluri, P. Jain, S. Mitra, S. Panda and N. K. Singh, “Constraints on the Cosmological Constant due to Scale Invariance,” Modern Physics Letters A, Vol. 25, No. 16, 2010, pp. 1349-1364. doi:10.1142/S0217732310032561 [36] P. Jain, S. Mitra, S. Panda and N. K. Singh, “Scale Invariance as a Solution to the Cosmological Constant Problem,” arXiv:1010.3483 [hep-ph]. [37] P. Jain, P. Karmakar, S. Mitra, S. Panda and N. K. Singh, “Cosmological Perturbation Analysis in a Scale Invariant Model of Gravity,” Classical and Quantum Gravity, Vol. 28, No. 21, 2011, Article ID: 215010. doi:10.1088/0264-9381/28/21/215010 [38] E. Scholz, “Cosmological Spacetimes Balanced by a Scale Covariant Scalar Field,” Foundations of Physics, Vol. 39, No. 1, 2009, pp. 45-72. doi:10.1007/s10701-008-9261-x [39] E. Scholz, “Weyl Geometric Gravity and ‘Breaking’ of Electroweak Symmetry,” Annalen der Physik, Vol. 523, No. 7, 2011, pp. 507-530. doi:10.1002/andp.201100032 [40] S. Deser and G. W. Gibbons, “Born-Infeld-Einstein Actions?” Classical and Quantum Gravity, Vol. 15, No. 5, 1998, pp. L35-L39. doi:10.1088/0264-9381/15/5/001 [41] M. N. R. Wohlfarth, “Gravity a la Born-Infeld,” Classical and Quantum Gravity, Vol. 21, No. 8, 2004, pp. 1927-1940. doi:10.1088/0264-9381/21/8/001 [42] D. N. Vollick, “Palatini Approach to Born-Infeld-Einstein Theory and a Geometric Description of Electrodynamics,” Physical Review D, Vol. 69, No. 6, 2004, Article ID: 064030. doi:10.1103/PhysRevD.69.064030 [43] D. N. Vollick, “Born-Infeld-Einstein Theory with Matter,” Physical Review D, Vol. 72, No. 8, 2005, Article ID: 084026. doi:10.1103/PhysRevD.72.084026 [44] D. N. Vollick, “Black Hole and Cosmological Space-Times in Born-Infeld-Einstein Theory,” gr-qc/0601136. [45] J. A. Nieto, “Born-Infeld Gravity in Any Dimension,” Physical Review D, Vol. 70, No. 4, 2004, Article ID: 044042. doi:10.1103/PhysRevD.70.044042 [46] D. Comelli and A. Dolgov, “Determinant-Gravity: Cosmological Implications,” Journal of High Energy Physics, No. 11, 2004. [47] D. Comelli, “Born-Infeld Gravity,” International Journal of Modern Physics A, Vol. 20, No. 11, 2005, pp. 2331-2335. doi:10.1142/S0217751X05024584 [48] D. Comelli, “Born-Infeld Type Gravity,” Physical Review D, Vol. 72, No. 6, 2005, Article ID: 064018. doi:10.1103/PhysRevD.72.064018 [49] E. Rojas, “Higher Order Curvature Terms in Born-Infeld Type Brane Theories,” International Journal of Modern Physics D, Vol. 20, No. 1, 2011, pp. 59-75. doi:10.1142/S0218271811018615 [50] I. Gullu, T. C. Sisman and B. Tekin, “Unitarity Analysis of General Born-Infeld Gravity Theories,” Physical Review D, Vol. 82, No. 12, 2010, Article ID: 124023. doi:10.1103/PhysRevD.82.124023 [51] A. D. Linde, “Chaotic Inflation,” Physics Letters B, Vol. 129, No. 3-4, 1983, pp. 177-181. doi:10.1016/0370-2693(83)90837-7 [52] E. Silverstein and D. Tong, “Scalar Speed Limits and Cosmology: Acceleration from D-cceleration,” Physical Review D, Vol. 70, No. 10, 2004, Article ID: 103505. doi:10.1103/PhysRevD.70.103505 [53] M. Alishahiha, E. Silverstein and D. Tong, “DBI in the Sky,” Physical Review D, Vol. 70, No. 12, 2004, Article ID: 123505. [54] I. Gullu, T. C. Sisman and B. Tekin, “Born-Infeld Extension of New Massive Gravity,” Classical and Quantum Gravity, Vol. 27, No. 16, 2010, Article ID: 162001. doi:10.1088/0264-9381/27/16/162001 [55] I. Gullu, T. C. Sisman and B. Tekin, “c-Functions in the Born-Infeld Extended New Massive Gravity,” Physical Review D, Vol. 82, No. 2, 2010, Article ID: 024032. doi:10.1103/PhysRevD.82.024032 [56] A. Ghodsi and D. M. Yekta, “Black Holes in Born-Infeld Extended New Massive Gravity,” Physical Review D, Vol. 83, No. 10, 2011, Article ID: 104004. doi:10.1103/PhysRevD.83.104004 [57] D. P. Jatkar and A. Sinha, “New Massive Gravity and AdS4 Counterterms,” Physical Review Letters, Vol. 106, No. 17, 2011, Article ID: 171601. doi:10.1103/PhysRevLett.106.171601 [58] E. A. Bergshoeff, O. Hohm and P. K. Townsend, “Massive Gravity in Three Dimensions,” Physical Review Letters, Vol. 102, No. 20, 2009, Article ID: 201301. doi:10.1103/PhysRevLett.102.201301 [59] E. A. Bergshoeff, O. Hohm and P. K. Townsend, “More on Massive 3D Gravity,” Physical Review D, Vol. 79, No. 12, 2009, Article ID: 124042. doi:10.1103/PhysRevD.79.124042 [60] S. Dengiz and B. Tekin, “Higgs Mechanism for New Massive Gravity and Weyl Invariant Extensions of Higher Derivative Theories,” Physical Review D, Vol. 84, No. 2, 2011, Article ID: 024033. doi:10.1103/PhysRevD.84.024033 [61] T. Moon, J. Lee and P. Oh, “Conformal Invariance in Einstein-Cartan-Weyl Space,” Modern Physics Letters A, Vol. 25, No. 37, 2010, pp. 3129-3143. doi:10.1142/S0217732310034201 [62] T. Moon, P. Oh and J. Sohn, “Anisotropic Weyl Symmetry and Cosmology,” Journal of Cosmology and Astroparticle Physics, 2010, arXiv: 1002.2549v3.
[1] L. H. Ford, “Inflation Driven by a Vector Field,” Physical Review D, Vol. 40, No. 4, 1989, pp. 967-972. [2] A. B. Burd and J. E. Lidsey, “An Analysis of Inflationary Models Driven by Vector Fields,” Nuclear Physics B, Vol. 351, No. 3, 1991, pp. 679-694. doi:10.1016/S0550-3213(05)80039-2 [3] A. Golovnev, V. Mukhanov and V. Vanchurin, “Vector Inflation,” Journal of Cosmology and Astroparticle Physics, No. 6, 2008. [4] A. Golovnev and V. Vanchurin, “Cosmological Perturbations from Vector Inflation,” Physical Review D, Vol. 79, No. 10, 2009, Article ID: 103524. doi:10.1103/PhysRevD.79.103524 [5] T. Maki, Y. Naramoto and K. Shiraishi, “On the Cosmology of Weyl’s Gauge Invariant Gravity,” Acta Physica Polonica B, Vol. 41, No. 6, 2010, pp. 1195-1201. [6] H. Weyl, “Electron and Gravitation,” Zeitschrift für Physik, Vol. 56, 1929, pp. 330-352. doi:10.1007/BF01339504 [7] S. Deser, “Scale Invariance and Gravitational Coupling,” Annals of Physics, Vol. 59, No. 1, 1970, pp. 248-253. doi:10.1016/0003-4916(70)90402-1 [8] D. K. Sen and K. A. Dunn, “A Scalar-Tensor Theory of Gravitation in a Modified Riemannian Manifold,” Journal of Mathematical Physics, Vol. 12, No. 4, 1971, pp. 578-586. doi:10.1063/1.1665623 [9] P. A. M. Dirac, “Long Range Forces and Broken Symmetries,” Proceedings of the Royal Society A, Vol. 333, No. 4, 1973, pp. 403-418. [10] P. G. O. Freund, “Local Scale Invariance and Gravitation,” Annals of Physics, Vol. 84, No. 1-2, 1974, pp. 440-454. doi:10.1016/0003-4916(74)90310-8 [11] R. Utiyama, “On Weyl’s Gauge Field,” Progress of Theoretical Physics, Vol. 50, No. 6, 1973, pp. 2080-2090. doi:10.1143/PTP.50.2080 [12] R. Utiyama, “On Weyl’s Gauge Field 2,” Progress of Theoretical Physics, Vol. 53, No. 2, 1975, pp. 565-574. doi:10.1143/PTP.53.565 [13] K. Hayashi, M. Kasuya and T. Shirafuji, “Elementary Particles and Weyl’s Gauge Field,” Progress of Theoretical Physics, Vol. 57, No. 2, 1977, pp. 431-440. doi:10.1143/PTP.57.431 [14] K. Hayashi and T. Kugo, “Everything about Weyl’s Gauge Field,” Progress of Theoretical Physics, Vol. 61, No. 1, 1979, pp. 334-346. doi:10.1143/PTP.61.334 [15] D. Ranganathan, “A Geometric Interpretation for the Dirac Field in Curved Space,” Journal of Mathematical Physics, Vol. 28, No. 10, 1987, pp. 2437-2439. doi:10.1063/1.527732 [16] H. Cheng, “The Possible Existence of Weyl’s Vector Meson,” Physical Review Letters, Vol. 61, No. 19, 1988, pp. 2182-2184. doi:10.1103/PhysRevLett.61.2182 [17] H. Cheng, “Dark Matter and Scale Invariance,” 2004. [18] W. F. Kao, “Inflationary Solution in Weyl Invariant Theory,” Physics Letters A, Vol. 149, No. 2-3, 1990, pp. 76-78. doi:10.1016/0375-9601(90)90528-V [19] W. F. Kao, “Scale Invariance and Inflation,” Physics Letters A, Vol. 154, No. 1-2, 1991, pp. 1-4. [20] W. F. Kao, “Higher Derivative Weyl Gravity,” Physical Review D, Vol. 61, No. 4, 2000, Article ID: 047501. doi:10.1103/PhysRevD.61.047501 [21] W. F. Kao, S.-Y. Lin and T.-K. Chyi, “Weyl Invariant Black Hole,” Physical Review D, Vol. 53, No. 4, 1996, pp. 1955-1962. doi:10.1103/PhysRevD.53.1955 [22] D. Hochberg and G. Plunien, “Theory of Matter in Weyl Space-Time,” Physical Review D, Vol. 43, No. 10, 1991, pp. 3358-3367. doi:10.1103/PhysRevD.43.3358 [23] W. R. Wood and G. Papini, “Breaking Weyl Invariance in the Interior of a Bubble,” Physical Review D, Vol. 45, No. 10, 1992, pp. 3617-3627. doi:10.1103/PhysRevD.45.3617 [24] M. Pawlowski, “Gauge Theory of Phase and Scale,” Turkish Journal of Physics, Vol. 23, No. 5, 1999, pp. 895-902. [25] H. Nishino and S. Rajpoot, “Broken Scale Invariance in the Standard Model,” hep-th/0403039. [26] H. Nishino and S. Rajpoot, “Standard Model and SU(5) GUT with Local Scale Invariance and the Weylon,” arXiv: 0805.0613 [hep-th]. [27] H. Nishino and S. Rajpoot, “Implication of Compensator Field and Local Scale Invariance in the Standard Model,” Physical Review D, Vol. 79, No. 12, 2009, Article ID: 125025. doi:10.1103/PhysRevD.79.125025 [28] H. Nishino and S. Rajpoot, “Weyl’s Scale Invariance for the Standard Model, Renormalizability and the Zero Cos- mological Constant,” Classical and Quantum Gravity, Vol. 28, No. 14, 2011, Article ID: 145014. doi:10.1088/0264-9381/28/14/145014 [29] H. Wei and R.-G. Cai, “Cheng-Weyl Vector Field and Its Cosmological Application,” Journal of Cosmology and Astroparticle Physics, No. 9, 2007. [30] P. Jain and S. Mitra, “Cosmological Symmetry Breaking, Pseudo-Scale Invariance, Dark Energy and the Standard Model,” Modern Physics Letters A, Vol. 22, No. 22, 2007, pp. 1651-1661. doi:10.1142/S0217732307023754 [31] P. Jain and S. Mitra, “One Loop Calculation of Cosmological Constant in a Scale Invariant Theory,” Modern Physics Letters A, Vol. 24, No. 26, 2009, pp. 2069-2079. doi:10.1142/S0217732309031351 [32] P. Jain and S. Mitra, “Standard Model with Cosmologically Broken Quantum Scale Invariance,” Modern Physics Letters A, Vol. 25, No. 3, 2010, pp. 167-177. doi:10.1142/S0217732310032317 [33] P. Jain, S. Mitra and N. K. Singh, “Cosmological Implications of a Scale Invariant Standard Model,” Journal of Cosmology and Astroparticle Physics, No. 3, 2008. [34] P. K. Aluri, P. Jain and N. K. Singh, “Dark Energy and Dark Matter in General Relativity with Local Scale In- variance,” Modern Physics Letters A, Vol. 24, No. 20, 2009, pp. 1583-1595. doi:10.1142/S0217732309030060 [35] P. K. Aluri, P. Jain, S. Mitra, S. Panda and N. K. Singh, “Constraints on the Cosmological Constant due to Scale Invariance,” Modern Physics Letters A, Vol. 25, No. 16, 2010, pp. 1349-1364. doi:10.1142/S0217732310032561 [36] P. Jain, S. Mitra, S. Panda and N. K. Singh, “Scale Invariance as a Solution to the Cosmological Constant Problem,” arXiv:1010.3483 [hep-ph]. [37] P. Jain, P. Karmakar, S. Mitra, S. Panda and N. K. Singh, “Cosmological Perturbation Analysis in a Scale Invariant Model of Gravity,” Classical and Quantum Gravity, Vol. 28, No. 21, 2011, Article ID: 215010. doi:10.1088/0264-9381/28/21/215010 [38] E. Scholz, “Cosmological Spacetimes Balanced by a Scale Covariant Scalar Field,” Foundations of Physics, Vol. 39, No. 1, 2009, pp. 45-72. doi:10.1007/s10701-008-9261-x [39] E. Scholz, “Weyl Geometric Gravity and ‘Breaking’ of Electroweak Symmetry,” Annalen der Physik, Vol. 523, No. 7, 2011, pp. 507-530. doi:10.1002/andp.201100032 [40] S. Deser and G. W. Gibbons, “Born-Infeld-Einstein Actions?” Classical and Quantum Gravity, Vol. 15, No. 5, 1998, pp. L35-L39. doi:10.1088/0264-9381/15/5/001 [41] M. N. R. Wohlfarth, “Gravity a la Born-Infeld,” Classical and Quantum Gravity, Vol. 21, No. 8, 2004, pp. 1927-1940. doi:10.1088/0264-9381/21/8/001 [42] D. N. Vollick, “Palatini Approach to Born-Infeld-Einstein Theory and a Geometric Description of Electrodynamics,” Physical Review D, Vol. 69, No. 6, 2004, Article ID: 064030. doi:10.1103/PhysRevD.69.064030 [43] D. N. Vollick, “Born-Infeld-Einstein Theory with Matter,” Physical Review D, Vol. 72, No. 8, 2005, Article ID: 084026. doi:10.1103/PhysRevD.72.084026 [44] D. N. Vollick, “Black Hole and Cosmological Space-Times in Born-Infeld-Einstein Theory,” gr-qc/0601136. [45] J. A. Nieto, “Born-Infeld Gravity in Any Dimension,” Physical Review D, Vol. 70, No. 4, 2004, Article ID: 044042. doi:10.1103/PhysRevD.70.044042 [46] D. Comelli and A. Dolgov, “Determinant-Gravity: Cosmological Implications,” Journal of High Energy Physics, No. 11, 2004. [47] D. Comelli, “Born-Infeld Gravity,” International Journal of Modern Physics A, Vol. 20, No. 11, 2005, pp. 2331-2335. doi:10.1142/S0217751X05024584 [48] D. Comelli, “Born-Infeld Type Gravity,” Physical Review D, Vol. 72, No. 6, 2005, Article ID: 064018. doi:10.1103/PhysRevD.72.064018 [49] E. Rojas, “Higher Order Curvature Terms in Born-Infeld Type Brane Theories,” International Journal of Modern Physics D, Vol. 20, No. 1, 2011, pp. 59-75. doi:10.1142/S0218271811018615 [50] I. Gullu, T. C. Sisman and B. Tekin, “Unitarity Analysis of General Born-Infeld Gravity Theories,” Physical Review D, Vol. 82, No. 12, 2010, Article ID: 124023. doi:10.1103/PhysRevD.82.124023 [51] A. D. Linde, “Chaotic Inflation,” Physics Letters B, Vol. 129, No. 3-4, 1983, pp. 177-181. doi:10.1016/0370-2693(83)90837-7 [52] E. Silverstein and D. Tong, “Scalar Speed Limits and Cosmology: Acceleration from D-cceleration,” Physical Review D, Vol. 70, No. 10, 2004, Article ID: 103505. doi:10.1103/PhysRevD.70.103505 [53] M. Alishahiha, E. Silverstein and D. Tong, “DBI in the Sky,” Physical Review D, Vol. 70, No. 12, 2004, Article ID: 123505. [54] I. Gullu, T. C. Sisman and B. Tekin, “Born-Infeld Extension of New Massive Gravity,” Classical and Quantum Gravity, Vol. 27, No. 16, 2010, Article ID: 162001. doi:10.1088/0264-9381/27/16/162001 [55] I. Gullu, T. C. Sisman and B. Tekin, “c-Functions in the Born-Infeld Extended New Massive Gravity,” Physical Review D, Vol. 82, No. 2, 2010, Article ID: 024032. doi:10.1103/PhysRevD.82.024032 [56] A. Ghodsi and D. M. Yekta, “Black Holes in Born-Infeld Extended New Massive Gravity,” Physical Review D, Vol. 83, No. 10, 2011, Article ID: 104004. doi:10.1103/PhysRevD.83.104004 [57] D. P. Jatkar and A. Sinha, “New Massive Gravity and AdS4 Counterterms,” Physical Review Letters, Vol. 106, No. 17, 2011, Article ID: 171601. doi:10.1103/PhysRevLett.106.171601 [58] E. A. Bergshoeff, O. Hohm and P. K. Townsend, “Massive Gravity in Three Dimensions,” Physical Review Letters, Vol. 102, No. 20, 2009, Article ID: 201301. doi:10.1103/PhysRevLett.102.201301 [59] E. A. Bergshoeff, O. Hohm and P. K. Townsend, “More on Massive 3D Gravity,” Physical Review D, Vol. 79, No. 12, 2009, Article ID: 124042. doi:10.1103/PhysRevD.79.124042 [60] S. Dengiz and B. Tekin, “Higgs Mechanism for New Massive Gravity and Weyl Invariant Extensions of Higher Derivative Theories,” Physical Review D, Vol. 84, No. 2, 2011, Article ID: 024033. doi:10.1103/PhysRevD.84.024033 [61] T. Moon, J. Lee and P. Oh, “Conformal Invariance in Einstein-Cartan-Weyl Space,” Modern Physics Letters A, Vol. 25, No. 37, 2010, pp. 3129-3143. doi:10.1142/S0217732310034201 [62] T. Moon, P. Oh and J. Sohn, “Anisotropic Weyl Symmetry and Cosmology,” Journal of Cosmology and Astroparticle Physics, 2010, arXiv: 1002.2549v3.