本文在乔丹框架下研究 f(R)-引力中原初宇宙的经典与量子特征，证明比安基 IX 模型在奇点附近可避免混沌行为，并对比安基 I 模型进行量子化，发现奇点仍存在。
摘要：
我们分析了在 f(R)-引力的乔丹框架表述中所看到的原初宇宙的一些相关特征，尤其是当非最小耦合标量场的势项可以忽略时。我们首先在乔丹框架中构建哈密顿图像，使用 3-度规行列式作为基本变量，并指出其共轭动量仅线性地出现在标量约束中。然后，我们构建了描述一般非均匀宇宙学模型动力学的基本形式，并将其专门化以描述比安基宇宙在经典和量子层面的行为。作为一个基本问题，我们证明，当附加标量模式的势项在初始奇点附近足够小可以忽略时，比安基 IX 宇宙学不再受到标准爱因斯坦动力学真空中典型的混沌行为的影响。事实上，稳定的 Kasner 稳定性区域的存在及其吸引特性得到了恰当刻画。最后，我们研究了比安基 I 模型的规范量子化，使用非最小耦合标量场作为时间变量，并表明对于相应的 Wheeler-DeWitt 方程，守恒流的存在得到了概述。我们还演化了一个局域波包在各向同性宇宙中的行为，证明在这个修正后的量子动力学中奇点仍然存在。
英文摘要：
We analyze some relevant features of the primordial Universe as viewed in the Jordan frame formulation of the f(R)-gravity, especially when the potential term of the non-minimally coupled scalar field is negligible. We start formulating the Hamiltonian picture in the Jordan frame, using the 3-metric determinant as a basic variable and we outline that its conjugated momentum appears linearly only in the scalar constraint. Then, we construct the basic formalism to characterize the dynamics of a generic inhomogeneous cosmological model and specialize it in order to describe behaviors of the Bianchi Universes, both on a classical and a quantum regime. As a fundamental issue, we demonstrate that, when the potential term of the additional scalar mode is negligible near enough to the initial singularity, the Bianchi IX cosmology is no longer affected by the chaotic behavior, typical in vacuum of the standard Einsteinian dynamics. In fact, the presence of stable Kasner stability region and its actractive character are properly characterized. Finally, we investigate the canonical quantization of the Bianchi I model, using as time variable the non-minimally coupled scalar field and showing that the existence of a conserved current is outlined for the corresponding Wheeler-DeWitt equation. The behavior of a localized wave-packet for the isotropic Universe is also evolved, demonstrating that the singularity is still present in this revised quantum dynamics.
Investigating $f(R)$-Inflation: background evolution and constraints
Sapienza University of Rome（罗马第一大学）；INFN - Sezione di Roma（意大利国家核物理研究所罗马分部）；Tor Vergata University of Rome（罗马托尔维加塔大学）；INAF - Osservatorio Astronomico di Roma（意大利国家天体物理研究所罗马天文台）；ENEA - C.R. Frascati（意大利国家新能源与可再生能源机构弗拉斯卡蒂研究中心）
