标题： 引力波在 Chern-Simons $f(R)$ 引力宇宙学中的手性 显示英文标题

标题： Chirality of Gravitational Waves in Chern-Simons $f(R)$ Gravity Cosmology

摘要： 在本文中，我们将考虑一个轴子Chern-Simons修正的$f(R)$引力理论框架，并研究生成的原初引力波的手征性。 特别地，我们将考虑两种主要的轴子模型，即经典的对齐轴子模型和动能轴子模型，这两种模型在暴胀拉格朗日量中存在$R^2$项的情况下，都提供了有趣的粒子现象学。 轴子在暴胀期间对背景演化没有显著影响，背景演化仅由$R^2$引力控制。 然而，由于Chern-Simons项的存在，张量扰动直接受到影响，我们的目标是揭示Chern-Simons项对引力波模式的影响程度，针对这两种轴子模型。 我们旨在产生原初张量模式行为的解析描述，因此我们解析求解了由$R^2$引力控制的近德西特原初演化的张量模式演化方程。 我们专注于超 horizon 和亚 horizon 模式的解析研究。 对于对齐模型，我们能够为亚 horizon 和超 horizon 模式提供解析解，在这种情况下我们发现了圆偏振函数的行为。 我们的结果表明，产生的张量谱具有强烈的手征性。 对于动能轴子模型，虽然仅获得了超 horizon 模式的解析解，为了掌握张量模式手征性的行为，我们研究了超 horizon 模式的手征性，但需要更全面的研究，尽管这在解析上是不可能的。 显示英文摘要

摘要： In this paper we shall consider an axionic Chern-Simons corrected $f(R)$ gravity theoretical framework, and we shall study the chirality of the generated primordial gravitational waves. Particularly, we shall consider two main axion models, the canonical misalignment axion model and the kinetic axion model, both of which provide an interesting particle phenomenology, in the presence of $R^2$ terms in the inflationary Lagrangian. The axion does not affect significantly the background evolution during the inflationary era, which is solely controlled by $R^2$ gravity. However, the due to the presence of the Chern-Simons term, the tensor perturbations are directly affected, and our aim is to reveal the extent of effects of the Chern-Simons term on the gravitational waves modes, for both the axion models. We aim to produce analytical descriptions of the primordial tensor modes behavior, and thus we solve analytically the evolution equations of the tensor modes, for a nearly de Sitter primordial evolution controlled by the $R^2$ gravity. We focus the analytical study on superhorizon and subhorizon modes. For the misalignment model, we were able to produce analytic solutions for both the subhorizon and superhorizon modes, in which case we found the behavior of the circular polarization function. Our results indicate that the produced tensor spectrum is strongly chiral. For the kinetic axion model though, analytic solutions are obtained only for the superhorizon modes. In order to have a grasp of the behavior of the chirality of the tensor modes, we studied the chirality of the superhorizon modes, however a more complete study is needed, which is impossible to do analytically though.