论文标题
测量比例对称性和通胀：Weyl与Palatini重力
Gauging scale symmetry and inflation: Weyl versus Palatini gravity
论文作者
论文摘要
我们介绍了两种具有{\ it衡量}比例对称性的二次引力理论的通货膨胀的比较研究：1）原始的weyl二次引力和2）由类似的作用定义的理论，但在palatini方法中通过其Palatini对手替换Weyl Connection获得的palatini方法。这些理论具有该对称性的量规场（$w_μ$）引起的不同矢量非金属。这两种理论都有一种新型的自发性破裂，使测量量表对称性在没有物质的情况下，在此目的没有必要的标量场中，而是对此目的添加了临时性，而是几何起源和二次作用的一部分。 Einstein-Proca动作（$W_μ$），Planck量表和度量标准在$W_μ$获得质量（Stueckelberg机制）之后，在破碎的相位出现，然后将其脱离。在物质（$ ϕ_1 $）的存在下，非最终耦合，在两个理论中，标量势与耦合和田间缩放相似。对于小场值，电势是像希格斯一样的，而对于大型田间的通货膨胀是可能的。由于其$ r^2 $术语，这两个理论都具有小张量量表的比率（$ r \ sim 10^{ - 3} $），在palatini案例中较大。对于固定频谱索引$ n_s $，减少非最小耦合（$ξ_1$）增加了$ r $，而在Weyl Theory中，这是Starobinsky通货膨胀的限制。对于足够小的$ξ_1\ leq 10^{ - 3} $，与Palatini版本不同，Weyl Theory给出了与Starobinsky通货膨胀相似的依赖性$ r（n_s）$，同时还保护$ r $ $ r $免受更高的维操作员的校正。
We present a comparative study of inflation in two theories of quadratic gravity with {\it gauged} scale symmetry: 1) the original Weyl quadratic gravity and 2) the theory defined by a similar action but in the Palatini approach obtained by replacing the Weyl connection by its Palatini counterpart. These theories have different vectorial non-metricity induced by the gauge field ($w_μ$) of this symmetry. Both theories have a novel spontaneous breaking of gauged scale symmetry, in the absence of matter, where the necessary scalar field is not added ad-hoc to this purpose but is of geometric origin and part of the quadratic action. The Einstein-Proca action (of $w_μ$), Planck scale and metricity emerge in the broken phase after $w_μ$ acquires mass (Stueckelberg mechanism), then decouples. In the presence of matter ($ϕ_1$), non-minimally coupled, the scalar potential is similar in both theories up to couplings and field rescaling. For small field values the potential is Higgs-like while for large fields inflation is possible. Due to their $R^2$ term, both theories have a small tensor-to-scalar ratio ($r\sim 10^{-3}$), larger in Palatini case. For a fixed spectral index $n_s$, reducing the non-minimal coupling ($ξ_1$) increases $r$ which in Weyl theory is bounded from above by that of Starobinsky inflation. For a small enough $ξ_1\leq 10^{-3}$, unlike the Palatini version, Weyl theory gives a dependence $r(n_s)$ similar to that in Starobinsky inflation, while also protecting $r$ against higher dimensional operators corrections.
