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arXiv 1703.09686gr-qcmath-phmath.MP
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Horndeski理论中的非最小耦合、引力波和挠率

Nonminimal couplings, gravitational waves, and torsion in Horndeski's theory

José Barrientos, Fabrizio Cordonier-Tello, Fernando Izaurieta, Perla Medina, Daniela Narbona, Eduardo Rodríguez, Omar Valdivia

摘要:

Horndeski拉格朗日量汇集了引力与标量场之间所有可能的相互作用,从而产生四维时空中的二阶场方程。正如最初提出的那样,它只涉及没有挠率的现象学,挠率是几何的非黎曼特征。由于挠率可以潜在地影响有趣的现象,如引力波和早期宇宙膨胀,在本文中,我们允许挠率存在和传播的Horndeski框架内。为了实现这一目标,我们投下的Horndeski拉格朗日在嘉当的一阶形式主义,并引入波算子的设计行为协变的p型领域进行洛伦兹指数。我们发现,非最小耦合和二阶导数的标量场的拉格朗日量确实是通用的来源扭转。度规扰动耦合到背景扭转,出现新的扭转模。这些可以通过引力波检测到,但不能通过杨-米尔斯规范玻色子。

英文摘要:

The Horndeski Lagrangian brings together all possible interactions between gravity and a scalar field that yield second-order field equations in four-dimensional spacetime. As originally proposed, it only addresses phenomenology without torsion, which is a non-Riemannian feature of geometry. Since torsion can potentially affect interesting phenomena such as gravitational waves and early Universe inflation, in this paper we allow torsion to exist and propagate within the Horndeski framework. To achieve this goal, we cast the Horndeski Lagrangian in Cartan's first-order formalism, and introduce wave operators designed to act covariantly on p-form fields that carry Lorentz indices. We find that nonminimal couplings and second-order derivatives of the scalar field in the Lagrangian are indeed generic sources of torsion. Metric perturbations couple to the background torsion and new torsional modes appear. These may be detected via gravitational waves but not through Yang-Mills gauge bosons.

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