标题： 统一爱因斯坦引力和帕拉蒂尼引力 显示英文标题

标题： Unifying Einstein and Palatini gravities

摘要： 我们考虑一类新的$f(\R)$引力理论，其中联络与共形缩放的度规$\hat g_{\mu\nu}=C(\R)g_{\mu\nu}$相关，而缩放因子仅依赖于数量曲率$\R$。 我们将它们称为 C-理论，并证明爱因斯坦引力和 Palatini 引力可以作为特殊极限情况得到。 此外，即使在$f(\R)=\R$的情况下，C-理论也包含完全不同的物理上独立的引力理论。 通过非线性$f(\R)$， C-理论在爱因斯坦引力和 Palatini 引力之间插值和外推，并可能避免它们的一些概念性和观测性问题。 我们进一步表明，C-理论具有标量-张量形式，在某些特殊情况下可简化为简单的 Brans-Dicke 型引力。 如果物质场与联络耦合，则 C-理论中的守恒定律会发生修改。 关于平坦空间的扰动稳定性由拉格朗日函数的一个简单条件决定。 显示英文摘要

摘要： We consider a novel class of $f(\R)$ gravity theories where the connection is related to the conformally scaled metric $\hat g_{\mu\nu}=C(\R)g_{\mu\nu}$ with a scaling that depends on the scalar curvature $\R$ only. We call them C-theories and show that the Einstein and Palatini gravities can be obtained as special limits. In addition, C-theories include completely new physically distinct gravity theories even when $f(\R)=\R$. With nonlinear $f(\R)$, C-theories interpolate and extrapolate the Einstein and Palatini cases and may avoid some of their conceptual and observational problems. We further show that C-theories have a scalar-tensor formulation, which in some special cases reduces to simple Brans-Dicke-type gravity. If matter fields couple to the connection, the conservation laws in C-theories are modified. The stability of perturbations about flat space is determined by a simple condition on the lagrangian.