标题： 模型无关的$F(R)$引力暴胀 显示英文标题

标题： Model Agnostic $F(R)$ Gravity Inflation

摘要： 在本工作中，我们构建了一个形式体系，可以揭示可行的$F(R)$暴胀理论类的一般特性。 我们假设慢滚时期发生，并且$F(R)$引力的德西特标量子质量$m^2(R)$在暴胀和晚期准德西特时期均为正或零，这是德西特时空稳定性的必要条件。 此外，我们要求德西特标量子质量也是里奇标量的单调递增函数，或者它有一个极值。 同时，$F(R)$引力函数需要依赖于宇宙学中的两个已知基本尺度，即宇宙学常数$\Lambda$和质量尺度$m_s^2=\frac{\kappa^2 \rho_m^{(0)}}{3}$，其中$\rho_m^{(0)}$表示当前时代冷暗物质的能量密度，即$F(R)=F(R,\Lambda,m_s^2)$。 利用这些一般假设，我们提供了可行的$F(R)$引力暴胀理论的主要特征，这些特征可以成功地同时描述暗能量时代。 统一描述暗能量和暴胀时代的这一独特特性源于德西特标量子质量$m^2(R)$的单调性要求。 这些可行的类别要么是$R^2$模型的变形，要么是$\alpha$-吸引子类型的理论。 对一般$F(R)$引力暴胀理论的可行性分析被简化为评估该理论的参数$x=\frac{R F_{RRR}}{F_{RR}}$和第一个慢滚指数，可以是数值的或近似的。 我们还区分了幂律$F(R)$引力与幂律演化。 显示英文摘要

摘要： In this work we construct a formalism that can reveal the general characteristics of classes of viable $F(R)$ inflationary theories. The assumptions we make is that the slow-roll era occurs, and that the de Sitter scalaron mass $m^2(R)$ of the $F(R)$ gravity is positive or zero, for both the inflationary and late-time quasi de Sitter eras, a necessary condition for the stability of the de Sitter spacetime. In addition, we require that the de Sitter scalaron mass is also a monotonically increasing function of the Ricci scalar, or it has an extremum. Also the $F(R)$ gravity function is required to depend on the two known fundamental scales in cosmology, the cosmological constant $\Lambda$ and the mass scale $m_s^2=\frac{\kappa^2 \rho_m^{(0)}}{3}$, with $\rho_m^{(0)}$ denoting the energy density of the cold dark matter at the present epoch, that is $F(R)=F(R,\Lambda,m_s^2)$. Using these general assumptions we provide the general features of viable classes of $F(R)$ gravity inflationary theories which remarkably can also simultaneously describe successfully the dark energy era. This unique feature of a unified description of the dark energy and inflationary eras stems from the requirement of the monotonicity of the de Sitter scalaron mass $m^2(R)$. These viable classes are either deformations of the $R^2$ model or $\alpha$-attractors type theories. The analysis of the viability of a general $F(R)$ gravity inflationary theory is reduced in evaluating the parameter $x=\frac{R F_{RRR}}{F_{RR}}$ and the first slow-roll index of the theory, either numerically or approximately. We also disentangle the power-law $F(R)$ gravities from power-law evolution.