标题： 研究$f(R)$熔胀：背景演化和约束 显示英文标题

标题： Investigating $f(R)$-Inflation: background evolution and constraints

摘要： 在本工作中，我们研究在乔丹框架中度规-$f(R)$改变的引力理论框架内生成暴胀机制的可能性。 我们探讨标量场是否可以在乔丹框架中非最小地耦合到引力并起到原始暴胀子的作用。 特别关注于构建一个在乔丹框架中表现出标量场慢滚阶段并允许宇宙演化具有准德西特解的动力学情景。 为了与标准宇宙学模型保持一致，我们在暴胀阶段结束时施加与$\Lambda$冷暗物质模型的匹配条件。 此外，为了解决暴胀后物质缺失的问题，我们考虑一种辐射型粒子产生过程，该过程保持能量密度近似恒定。 我们将理论模型与背景观测数据进行对比，具体包括经SH0ES校准的Pantheon+和经BBN校准的DESI。 我们评估其可行性，并讨论其对缓解哈勃常数矛盾的含义。 显示英文摘要

摘要： In this work, we investigate the possibility of generating an inflationary mechanism within the framework of a metric-$f(R)$ modified gravity theory, formulated in the Jordan frame. We explore whether the scalar field, non-minimally coupled to gravity and emerging in the Jordan frame, can play the role of the primordial inflaton. Particular attention is devoted to constructing a dynamical scenario in the Jordan frame that exhibits a slow-rolling phase for the scalar field and admits a quasi-de Sitter solution for cosmic evolution. To ensure consistency with the standard cosmological model, we impose a matching condition with the $\Lambda$CDM model at the end of the inflationary phase. Furthermore, to address the problem of the absence of matter after inflation, we consider a radiation-type particle creation process that maintains an approximately constant energy density. We test our theoretical model against background observational data, specifically Pantheon+ calibrated with SH0ES and DESI calibrated with BBN. We asses its viability and discuss implications for alleviating the Hubble constant tension.