统一爱因斯坦和帕拉提尼引力
Unifying Einstein and Palatini gravities
摘要：
我们考虑一类新的$f(\R)$引力理论，其中的连接与共形标度度量$\hat g_{μν}=C(\R)g_{μν}$的缩放，仅取决于标量曲率$\R$。我们称之为C-理论，并表明，爱因斯坦和Palatini引力可以得到特殊的限制。此外，C理论包括全新的物理上不同的引力理论，即使当$f(\R)=\R$。有了非线性$f(\R)$，C-理论就可以内插和外推爱因斯坦和帕拉蒂尼的情形，并可能避免它们的一些概念和观测问题。我们进一步证明了C-理论有一个标量张量公式，在某些特殊情况下，它可以简化为简单的Brans-Dicke型引力。如果物质场耦合到这种联系，那么C-理论中的守恒律就被修正了。关于平坦空间的扰动的稳定性由拉格朗日量上的一个简单条件确定。
英文摘要：
We consider a novel class of $f(\R)$ gravity theories where the connection is related to the conformally scaled metric $\hat g_{μν}=C(\R)g_{μν}$ 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.
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