This paper investigates the possibility of reconstruction of the generic function in Formula: see text gravitational theory by considering some well-known cosmological bouncing models, namely, exponential evaluation, oscillatory, power law and matter bounce model, where Formula: see text and Formula: see text are Ricci scalar and trace of energy–momentum tensor, respectively. Due to the complexity of dynamical field equations, we propose some ansatz forms of function Formula: see text in perspective models and examine which type of Lagrangian is capable of reproducing bouncing solution via analytical expression. It is seen that for some cases of exponential, oscillatory and matter bounce models, it is possible to get analytical solution while in other cases, it is not possible to achieve exact (general) solutions so only complementary solutions can be discussed. However, for power-law model, all forms of generic function can be reconstructed analytically. Next we analyze the energy conditions and stability of these reconstructed cosmological bouncing models which have analytical forms. It is found that these models are stable for linear forms of Lagrangian only but the reconstructed solutions for power law are unstable for some nonlinear forms of Lagrangian. Further, we determine the observable quantities like spectral index (Formula: see text) and tensor-to-scalar ratio (Formula: see text) for the simplest reconstructed form of Formula: see text function. As a result, we directly confront the reconstructed linear form of Lagrangian in Formula: see text model with 2018 Planck observations. Furthermore, we analyze that Formula: see text gravity with dark energy epoch is consistent with Sne-Ia+BAO+H(z)+CMB data and show that bounce can unify with dark energy epochs in Formula: see text gravity.
Zubair et al. (Fri,) studied this question.