We consider the effective field theory formulation of torsional gravity in a cosmological framework to alter the background evolution. Then we use the latest H 0 measurement from the SH0ES Team, as well as observational Hubble data from cosmic chronometer and radial baryon acoustic oscillations, and we reconstruct the f(T) form in a model-independent way by applying Gaussian processes. Since the special square-root term does not affect the evolution at the background level, we finally summarize a family of functions that can produce the background evolution required by the data. Lastly, performing a fitting using polynomial functions and implementing the Bayesian information criterion, we find an analytic expression that may describe the cosmological evolution in great agreement with observations.

The non-singular bouncing cosmology is an alternative paradigm to inflation, wherein the background energy density vanishes at the bounce point, in the context of Einstein gravity. Therefore, the non-linear effects in the evolution of density fluctuations (δρ) may be strong in the bounce phase, which potentially provides a mechanism to enhance the abundance of primordial black holes (PBHs). This article presents a comprehensive illustration for PBH enhancement due to the bounce phase. To calculate the non-linear evolution of δρ, the Raychaudhuri equation is numerically solved here. Since the non-linear processes may lead to a non-Gaussian probability distribution function for δρ after the bounce point, the PBH abundance is calculated in a modified Press-Schechter formalism. In this case, the criterion of PBH formation is complicated, due to complicated non-linear evolutionary behavior of δρ during the bounce phase. Our results indicate that the bounce phase indeed has potential to enhance the PBH abundance sufficiently. Furthermore, the PBH abundance is applied to constrain the parameters of bounce phase, providing a complementary to the surveys of cosmic microwave background and large scale structure.