We apply the bottom-up reconstruction technique in the context of bouncing cosmology in F(R) gravity, where the starting point is a suitable ansatz of observable quantity (like spectral index or tensor to scalar ratio) rather than a priori form of Hubble parameter. In inflationary scenario, the slow roll conditions are assumed to hold true, and thus the observational indices have general expressions in terms of the slow-roll parameters, as for example the tensor to scalar ratio in F(R) inflation can be expressed as $r=48{ϵ}_F^2$ with ${ϵ}_F=-\frac{1}{H_F^2}\frac{d{H}_F}{d{t}_F}$ and $H_F$, $t_F$ are the Hubble parameter, cosmic time respectively. However, in the bouncing cosmology (say in F(R) gravity theory), the slow-roll conditions are not satisfied, in general, and thus the observable quantities do not have any general expressions that will hold true irrespective of the form of F(R). Thus, in order to apply the bottom-up reconstruction procedure in F(R) bouncing model, we use the conformal correspondence between F(R) and scalar-tensor model where the conformal factor in the present context is chosen in a way such that it leads to an inflationary scenario in the scalar-tensor frame. Due to the reason that the scalar and tensor perturbations remain invariant under conformal transformation, the observable viability of the scalar-tensor inflationary model confirms the viability of the conformally connected F(R) bouncing model. Motivated by these arguments, here we construct a viable non-singular bounce in F(R) gravity directly from the observable indices of the corresponding scalar-tensor inflationary model.

我们在F（R）重力弹跳宇宙学的背景下应用了自下而上的重建技术，其中起点是可观察量的合适ansatz（例如光谱指数或张量与标量比），而不是Hubble参数的先验形式。在通货膨胀的情况下，假定慢滚动条件成立，因此观测指标具有关于慢滚动参数的一般表达式，例如F（R）通胀中的张量与标量比可以表示为$\mathrm{[R}=48{ϵ}_F^2$ 与 ${ϵ}_F=-\frac{\mathrm{1个}}{H_F^2}\frac{d{H}_F}{d{Ť}_F}$ 和 $H_F$， ${Ť}_F$是哈勃参数，分别是宇宙时间。但是，在弹跳宇宙学中（如F（R）引力论中所述），通常不满足慢速滚动条件，因此，无论F的形式如何，可观察到的量均不具有将成立的任何通用表达式。 （R）。因此，为了在F（R）弹跳模型中应用自下而上的重建过程，我们使用F（R）和标量张量模型之间的保形对应关系，其中在本文中选择保形因子，使得它导致标量张量框架中出现通货膨胀情况。由于标量和张量摄动在保形变换下保持不变的原因，标量-张量膨胀模型的可观察到的生存能力证实了保形连接的F（R）弹跳模型的生存能力。