In this paper, we analyze the modified f(R) f ( R ) gravity models in Friedmann–Lemaître–Robertson–Walker (FLRW) background. The actions of bouncing cosmology are studied under consideration of different viable models in f(R) f ( R ) gravity theory that can resolve the difficulty of singularity in standard Big-Bang cosmology. Under different viable models in f(R) f ( R ) gravity theory, the cosmological constraints are plotted in provisions of cosmic-time, then investigated the bounce circumstance. In addition, the red-shift parameter is used to reconstruct the modified gravity, and compile the cosmological parameters that infer accelerated universe expansion. Finally, the situation stability is evaluated with a sound speed feature, which illustrates late-time stability.
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