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NOETHER-S SYMMETRY IN HORAVA-LIFSHITZ COSMOLOGY

M Arzimbetova

Abstract

Recently, Horava-Lifshitz proposed the theory of quantum gravity, which takes into account the degree of renormalizability in the ultraviolet. This was achieved by anisotropic scaling between space and time, and, therefore, it violates the Lorentz invariance in the ultraviolet range. The infrared limit of a theory reproduces the general theory of relativity for a particular choice of parameter, namely . Lorentz symmetry breaking is performed by preferred foliation of threedimensional space-like hypersurfaces, which, in turn, divide the coordinate into space and time. This makes it possible to record the action of Einstein Hilbert with higher spatial derivatives of the metric. It improves the ultraviolet behavior of the graviton propagator and displays the renormalizable power counting theory. Moreover, the action has only second-order time derivatives that prevent the presence of ghosts in the theory. In this paper, we consider Friedmann-Robertson-Walker flat space-time in the framework of the metric formalism of gravity. We created an effective Lagrangian in which the scale factor and the Ricci scalar play the role of independent dynamic variables. This Lagrangian is constructed in such a way that its variation is relative and gives the correct equations of motion as equations of action with the typical one. The type of function appearing in the modified action is then determined by the requirement that the Lagrangian admits the desired Noether symmetry. By Noether?s symmetry of this cosmological model of a minisuperspace, we understand that there is a vector field as an infinitesimal symmetry generator on the tangent space of the configuration space, such that the Lie derivative of the Lagrangian over this vector field vanishes. We will see that by presenting the Noether symmetry as a feature of the Lagrangian of the model under consideration, we can obtain the explicit form of the function. Since the existence of symmetry leads to constant motion, we can integrate the field equations, which then lead to the expansion of the power law of the Universe.

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DOI resolver: doi.org/10.5593/sgem2019/6.2/s28.084

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