标题： 关于$f(\mathcal{R})$引力中宇宙减速-加速转变红移的宇宙学界限 显示英文标题

标题： Cosmographic bounds on the cosmological deceleration-acceleration transition redshift in $f(\mathcal{R})$ gravity

摘要： 我们考察了一类$f(\mathcal{R})$引力宇宙学模型的观测可行性。特别关注来自宇宙减速-加速转变红移近期观测确定的限制。利用这些模型中里奇标量是红移$z$的函数这一事实，即$\mathcal {R=R}(z)$，并且$f(z)$也是这样，我们借助宇宙学描述法将更高阶$z$处评估的一个$f(z)$检验函数与晚期宇宙学界限联系起来。 首先，我们考虑一种模型无关的方法来构建数值上的$f(z)$，要求在$z=0$处对应的宇宙学模型退化为标准的$\Lambda$CDM 模型。 然后，我们通过泰勒展开宇宙学系数的边界来推导出$f(z)$在晚时间观测约束。 在此过程中，我们用两个参数的对数修正来参数化可能偏离标准$\Lambda$CDM 模型的情况。 这两个参数的物理意义也通过牛顿近似进行了讨论。 其次，我们利用Ia型超新星视星等数据和哈勃参数测量值来提供宇宙学级数项的数值估计。 最后，我们利用这些估计来限制对数修正的两个参数。 我们发现模型中的减速参数在与观测一致的红移处改变符号。 显示英文摘要

摘要： We examine the observational viability of a class of $f(\mathcal{R})$ gravity cosmological models. Particular attention is devoted to constraints from the recent observational determination of the redshift of the cosmological deceleration-acceleration transition. Making use of the fact that the Ricci scalar is a function of redshift $z$ in these models, $\mathcal {R=R}(z)$, and so is $f(z)$, we use cosmography to relate a $f(z)$ test function evaluated at higher $z$ to late-time cosmographic bounds. First, we consider a model independent procedure to build up a numerical $f(z)$ by requiring that at $z=0$ the corresponding cosmological model reduces to standard $\Lambda$CDM. We then infer late-time observational constraints on $f(z)$ in terms of bounds on the Taylor expansion cosmographic coefficients. In doing so we parameterize possible departures from the standard $\Lambda$CDM model in terms of a two-parameter logarithmic correction. The physical meaning of the two parameters is also discussed in terms of the post Newtonian approximation. Second, we provide numerical estimates of the cosmographic series terms by using Type Ia supernova apparent magnitude data and Hubble parameter measurements. Finally, we use these estimates to bound the two parameters of the logarithmic correction. We find that the deceleration parameter in our model changes sign at a redshift consistent with what is observed.