Asymptotic behaviour of the Einstein-Yang-Mills-Higgs system in a Bianchi type I model
Main Article Content
Abstract
We study the Einstein-Yang-Mills-Higgs (EYMH) system with a positive cosmological constant in the Bianchi type I space-time with locally rotational symmetry (LRS). In particular, we consider the nonlinear interaction of the Higgs field with the Yang-Mills field coupled to an unknown gravitational field. For the considered model, from certain additional conditions (the temporal gauge and some symmetries), we derive the conservation laws for the field equations and we then deduce the exact formulation of equations in the geometric framework. Furthermore, using an iterative approch and some mathematical analysis tools, we study the above system of equations. We then establish a global existence result for the homogeneous solution and we analyse its asymptotic behaviour.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
References
R. Ayissi and N. Noutchegueme, Bianchi type I magnetzed cosmological models for the Einstein-Boltzmann equation with the cosmological constant, J. Math. Phys., Vol. 56 (1), 012501-012537 (2015).
A. B. Balakin, H. Dehnen and A. E. Zayats, Effective metrics in the non-minimal Einstein-Yang-Mills-Higgs theory. Ann. Phys., Vol. 323, 2183-2207 (2008).
J. D. Barrow and D. H. Sonoda, Asymptotic stability of Bianchi type universes, Phys. Reports, Vol. 139(1), 1-49 (1986)
D. Christodoulou, Bounded variation solutions of the spherically symmetric Einstein-scalar-field equations, Comm. Pure. Appl. Math., Vol. 46, 1131-1220 (1993).
Y. Choquet-Bruhat and C. Dewitt-Morette. Analysis, Manifolds and Physics, Part II, Revised and Elarged Edition, North Holland, 2000.
D. Dongo, A. K. Nguelemo and N. Nouchegueme, The coupled Yang-Mills-
Boltzmann system in Bianchi type I space-time, Rep. Math. Phys., Vol. 86(2), 219-240 (2020).
M. Dossa and C. Tadmon, The characteristic initial value problem for the Einstein-
Yang-Mills-Higgs system in weighted Sobolev spaces, Appl. Math. Res. Express, Vol. 2010(2), 154-231 (2010).
A. Guth, Inflationary universe, Phys. Rev. D Vol. 23, 347 (1981).
M. Heusler, The scalar field as dynamical variable in inflation, Phys. Lett. B, Vol.
(1-2), 42-46 (1991), DOI: 10.1016/0370-2693(91)90550-A
[10] O. Hrycyna and M. Szydlowski, Dynamics of the Bianchi I model with non-minimally coupled scalar field near the singularity, AIP Conf. Proc. 1514, 191 (2013).
R. T. Jantzen, Cosmology of the Early Universe, World Scientific, Singapore, 1984.
E. W. Kolb and M. S. Turner, The early universe, Addison-Wesley, New York (1990).
H. Lee, Asymptotic behaviour of the relativistic Boltzmann equation in the Robert-sonWalker space-time, J. Differ. Equ., Vol. 255(11), 4267-4288 (2013).
I. Melo, Higgs potential and fundamental physics, Eur. J. Phyys., Vol. 38(6), DOI: 10.1088/1361-6404/aa8c3d, (2017).
N. Noutchegueme and A. Nangue, Einstein-Maxwell-Massive Scalar Field System in 3+1 formulation on Bianchi Spacetimes type I-VIII, Appl. Anal., vol. 93(5), 1036-1056 (2012).
A. D. Rendall, Accelerated cosmological expansion due to a scalar field whose potential has a positive lower bound, Class. Quantum Grav., Vol. 21(9), 2445-2454 (2004).
A. D. Rendall, Partial differential equation in general relativity, Oxford Graduate Texts in Mathematics, Oxford University Press, 2008.
N. Straumann, On the cosmological constant problems and the astronomical evidence for the homogeneous energy density with negative pressure, Part of Proceedings, 1 st Sminaire Poincar: l’Energie du Vide: Paris, France (2002), DOI: 10.1007/978-3-0348-8075-6−2
M. S. Volkov and D. V. Gal’tsov, Gravitating non-Abelian solitons and black holes with Yang-Mills fields, Phys. Rep., Vol. 319(1-2), 1-83 (1999).