Mimetic Einstein-Cartan-Sciama-Kibble (ECSK) gravity
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Springer
Received: July 28, 2020 Accepted: September 23, 2020 Published: October 23, 2020
Fernando Izaurieta,a Perla Medina,a,b,c Nelson Merino,d Patricio Salgadod and Omar Valdiviad,e,1 a
Departamento de F´ısica, Universidad de Concepci´ on, Casilla 160-C, Concepci´ on, Chile b Universidad Austral de Chile (UACh), Campus Isla Teja, Ed. Emilio Pugin, Valdivia, Chile c Centro de Estudios Cient´ıficos (CECs), Avenida Arturo Prat 514, Valdivia, Chile d Instituto de Ciencias Exactas y Naturales (ICEN), Facultad de Ciencias, Universidad Arturo Prat, Iquique, Chile e Institute of Space Sciences (IEEC-CSIC), C. Can Magrans s/n, 08193 Cerdanyola del Valles (Barcelona), Spain
E-mail: [email protected], [email protected], [email protected], [email protected], [email protected] Abstract: In this paper, we formulate the Mimetic theory of gravity in first-order formalism for differential forms, i.e., the mimetic version of Einstein-Cartan-Sciama-Kibble (ECSK) gravity. We consider different possibilities on how torsion is affected by Weyl transformations and discuss how this translates into the interpolation between two different Weyl transformations of the spin connection, parameterized with a zero-form parameter λ. We prove that regardless of the type of transformation one chooses, in this setting torsion remains as a non-propagating field. We also discuss the conservation of the mimetic stress-energy tensor and show that the trace of the total stress-energy tensor is not null but depends on both, the value of λ and spacetime torsion. Keywords: Classical Theories of Gravity, Cosmology of Theories beyond the SM ArXiv ePrint: 2007.07226
1
Corresponding author.
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)150
JHEP10(2020)150
Mimetic Einstein-Cartan-Sciama-Kibble (ECSK) gravity
Contents 1
2 Review of mimetic gravity
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3 ECSK gravity and first order formalism
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4 Conformal Riemann-Cartan structure
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5 Mimetic ECSK gravity 5.1 Mimetic field equations 5.2 Conservation laws
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6 The trace of the stress-energy tensor, torsion and λ
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7 Summary & comments
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Introduction
General Relativity (GR) is a classical field theory describing the gravitational interaction through the Einstein field equations. Remarkably, it has proven success in a wide range of phenomena [1], including black-holes as realistic astrophysical objects [2] and the existence of gravitational waves [3–5]. Another significant development of GR lies in the context of cosmology, where extending Einstein’s field equations, by the inclusion of an early inflationary stage and a cold dark matter contribution, is in good agreement with observational data [6]. This fact is somehow dramatic since we know very little about the nature of dark matter, apart from the fact that it does not appear to interact with the electromagnetic field. For this reason, the problem of identifying dark matter candidates attracts attention from both cosmology and particle physics. There are several dark matter candidates
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