Noether symmetries of Einstein-aether scalar field cosmology
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Regular Article - Theoretical Physics
Noether symmetries of Einstein-aether scalar field cosmology Yusuf Kucukakca1,a , Amin Rezaei Akbarieh2,b 1 2
Department of Physics, Faculty of Science, Akdeniz University, 07058 Antalya, Turkey Department of Theoretical Physics and Astrophysics, Faculty of Physics, University of Tabriz, Tabriz 51666-16471, Iran
Received: 13 August 2020 / Accepted: 19 October 2020 © The Author(s) 2020
Abstract In this paper, we explore an Einstein-aether cosmological model by adding the scalar field in which it has an interaction with the aether field. For the cosmological implications of the model, we consider that the universe can be described by the spatially flat FRW metric together with the matter dominated universe. Applying Noether symmetry approach to the point-like Lagrangian we determine the explicit forms of unknown functions i.e. the potential and coupling function. We solve the analytical cosmological solutions of the field equations admitting the Noether symmetry, basically divided into two parts. Our results show that the obtained solutions lead to an accelerated expansion of the universe. We also discuss the tensor perturbations within the framework of this model in order to get information about the mass of gravitational waves.
1 Introduction Motivations for quantum gravitational theories has led to a growing focus in recent years that Lorentz symmetry may not be the main precise symmetry of nature. Lorentz symmetry can be violated by using a vector field in gravitational theories. This vector field creates a preferred direction in spacetime. That is why, recently, the study of Einstein-aether’s theory has received much attention. In fact, this theory is a modification of Einstein’s general theory of relativity, in which the space-time is described by the metric and a timelike vector field, which is called aether. This theory violates Lorentz symmetry since it has a preferred reference. In 2004, in [1], the theoretical and phenomenological aspects of this theory were examined. The existence of a dynamical timelike vector field can break the Lorentz symmetry. On the other hand, from particle physics, we know that breaking the symmetry can cause new phenomena. In this case, like the a e-mail:
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Higgs mechanism, the breaking of the Lorentz symmetry by this vector field can cause graviton to be massive. Various aspects of Einstein-aether’s theory have been studied in [2– 4]. These articles show that in this theory, by redefining the metric and the aether field, one of the coupling coefficients can be assumed to be zero, which makes it very easy to solve this model. In [5], the Noether’s conserved charge related to this model as well as the black hole mechanism in the framework of this model is studied. In this paper, although a general term for variation of energy and angular momentum has been obtained on the black hole horizon, no general term for black hole entropy has
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