论文标题
palatini二次重力：测量尺度对称性和通货膨胀的自发断裂
Palatini quadratic gravity: spontaneous breaking of gauged scale symmetry and inflation
论文作者
论文摘要
我们在palatini形式主义中研究二次重力$ r^2+r _ {[μν]}^2 $，其中连接和度量是独立的。此动作具有Weyl Gauge场的{\ it衡量}比对称性（也称为Weyl仪表对称性）$v_μ=（\tildeγ_μ-γ_μ）/2 $，带有$ \tildeγ_μ$（$ umpecivita）（$ \tildeγ_μ$）（$ \tildeγ__$）。由于$ r _ {[μν]}^2 $术语充当$v_μ$的仪表动力学术语，因此基础几何形状是非属性的。我们表明，在没有物质的情况下，该理论具有尺寸对称性和质量产生的优雅自发破裂，在此，在此目的中没有添加必要的标量字段（$ ϕ $），而是从$ r^2 $术语中“提取”。量规场通过吸收Stueckelberg Field（“ Dilaton”）的衍生项$ \partial_μ\ lnϕ $而变得巨大。在破碎的第一阶段中，发现与普朗克尺度$ M \ sim \ langleDangle \ rangle $和正宇宙常数成比例成正比的$v_μ$的爱因斯坦 - 普罗卡动作。在此规模$v_μ$ decouples以下，连接变为levi-civita，并恢复了指标和爱因斯坦重力。这些结果在存在具有palatini连接的非最低耦合标量场（类似于Higgs）的情况下仍然有效，并计算了电势。在这种情况下，该理论给出了成功的通货膨胀和张量表比率的特定预测，$ 0.007 \ leq r \ leq r \ leq 0.01 $对于当前频谱指数$ n_s $（$ 95 \％$ cl）和n = 60 efolds。 $ r $的该值比不同的非属性，比相似对称性的Weyl二次重力的通货膨胀大。这建立了非计量性和通货膨胀预测之间的联系，使我们能够通过未来的CMB实验来检验此类理论。
We study quadratic gravity $R^2+R_{[μν]}^2$ in the Palatini formalism where the connection and the metric are independent. This action has a {\it gauged} scale symmetry (also known as Weyl gauge symmetry) of Weyl gauge field $v_μ= (\tildeΓ_μ-Γ_μ)/2$, with $\tildeΓ_μ$ ($Γ_μ$) the trace of the Palatini (Levi-Civita) connection, respectively. The underlying geometry is non-metric due to the $R_{[μν]}^2$ term acting as a gauge kinetic term for $v_μ$. We show that this theory has an elegant spontaneous breaking of gauged scale symmetry and mass generation in the absence of matter, where the necessary scalar field ($ϕ$) is not added ad-hoc to this purpose but is "extracted" from the $R^2$ term. The gauge field becomes massive by absorbing the derivative term $\partial_μ\lnϕ$ of the Stueckelberg field ("dilaton"). In the broken phase one finds the Einstein-Proca action of $v_μ$ of mass proportional to the Planck scale $M\sim \langleϕ\rangle$, and a positive cosmological constant. Below this scale $v_μ$ decouples, the connection becomes Levi-Civita and metricity and Einstein gravity are recovered. These results remain valid in the presence of non-minimally coupled scalar field (Higgs-like) with Palatini connection and the potential is computed. In this case the theory gives successful inflation and a specific prediction for the tensor-to-scalar ratio $0.007\leq r \leq 0.01$ for current spectral index $n_s$ (at $95\%$CL) and N=60 efolds. This value of $r$ is mildly larger than in inflation in Weyl quadratic gravity of similar symmetry, due to different non-metricity. This establishes a connection between non-metricity and inflation predictions and enables us to test such theories by future CMB experiments.
