标量场与度规-仿射几何的非最小耦合
Scalar field with nonminimal couplings to metric-affine geometry
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中文总结 AI 辅助
研究标量场与度规-仿射引力的非最小耦合，推导场方程并消去联络，得到等效度规理论，分析各扇区动能函数变化，展示导数与混合耦合重塑势能，并给出宇宙学方程。
中文摘要 AI 辅助
我们研究了在仿射曲率中线性、且包含所有独立的宇称偶和宇称奇、由挠率和非度规性二次项（包括混合收缩）组成的作用量中，标量场与度规-仿射引力的非最小耦合。我们还引入了类似Nieh-Yan的导数耦合，即标量场导数与四个挠率和非度规性矢量之间的耦合。我们推导了联络、度规和标量场方程，并且由于联络方程是代数方程，在一般的非退化分支上消去独立的联络，得到等价的度规标量-张量理论，其中非黎曼相互作用编码在一个有效动能函数中。我们对几个扇区进行了分类，发现纯二次非度规性扇区和纯二次挠率扇区分别使爱因斯坦框架动能函数相对于最简单的度规-仿射标量-张量模型保持不变，而它们的同时存在、导数耦合以及一般的混合挠率-非度规性相互作用可以修改该函数。在导数耦合扇区中，射影一致性对耦合施加了一个关系。然后我们考虑多项式耦合函数，并研究由此产生的正则场重定义和爱因斯坦框架势。特别地，我们说明了导数耦合和混合挠率-非度规性耦合如何在正则场空间中重塑二次和四次势，并表明对于适当的导数耦合和非最小耦合选择，约当框架二次势在正则归一化后可以映射为自然暴胀势。最后，我们分别施加宇宙学原理，确定二次耦合的约化组合和标量场超动量，并在最简单的扇区中获得相应的修正宇宙学方程。
英文摘要
We study a scalar field nonminimally coupled to metric-affine gravity within actions linear in the affine curvature and containing all independent parity-even and parity-odd terms quadratic in torsion and nonmetricity, including mixed contractions. We also include Nieh-Yan-like derivative couplings between the scalar-field derivative and the four torsion and nonmetricity vectors. We derive the connection, metric, and scalar-field equations and, since the connection equation is algebraic, eliminate the independent connection on the generic nondegenerate branch to obtain an equivalent metric scalar-tensor theory in which the non-Riemannian interactions are encoded in an effective kinetic function. We classify several sectors and find that the pure quadratic nonmetricity and pure quadratic torsion sectors separately leave the Einstein-frame kinetic function unchanged relative to the simplest metric-affine scalar-tensor model, whereas their simultaneous presence, the derivative couplings, and generic mixed torsion-nonmetricity interactions can modify it. In the derivative-coupling sector, projective consistency imposes a relation among the couplings. We then consider polynomial coupling functions and study the resulting canonical field redefinition and Einstein-frame potentials. In particular, we illustrate how derivative and mixed torsion--nonmetricity couplings reshape quadratic and quartic potentials in canonical-field space, and show that a quadratic Jordan-frame potential can be mapped, for a suitable choice of derivative and nonminimal couplings, into a natural-inflation potential after canonical normalization. Finally, we separately impose the cosmological principle, determine the reduced combinations of quadratic couplings and the scalar field hypermomentum, and obtain the corresponding modified cosmological equations in the simplest sectors.
发表机构
- University of Tartu（塔尔图大学）
- Scuola Superiore Meridionale di Napoli (SSM)（那不勒斯南方高等学院）
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