A class of scalar-tensor theories (STT) including a non-metricity that unifies metric, Palatini and hybrid metric-Palatini gravitational actions with non-minimal interaction is proposed and investigated from the point of view of their consistency with generalized conformal transformations. It is shown that every such theory can be represented on-shell by a purely metric STT possessing the same solutions for a metric and a scalar field. A set of generalized invariants is also proposed. This extends the formalism previously introduced in \cite{kozak2019}. We then apply the formalism to Starobinsky model, write down the Friedmann equations for three possible cases: metric, Palatini and hybrid metric-Palatini, and compare some inflationary observables.

中文翻译：

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新类别的混合度量帕拉蒂尼标量张量引力理论

提出了一类标量张量理论 (STT)，包括将度量、Palatini 和混合度量-Palatini 引力作用与非最小相互作用统一起来的非度量性，并从它们与广义保形变换的一致性的角度进行研究。结果表明，每个这样的理论都可以在壳上表示为纯度量 STT，该 STT 对度量和标量场具有相同的解。还提出了一组广义不变量。这扩展了之前在 \cite{kozak2019} 中引入的形式主义。然后我们将形式主义应用到 Starobinsky 模型，写下三种可能情况的弗里德曼方程：度量、帕拉蒂尼和混合度量帕拉蒂尼，并比较一些膨胀的可观测值。