Abstract:
We propose a cosmological scenario in which the universe undergoes through a non-singular bounce,
and after the bounce, it decelerates having a matter-like dominated evolution during some regime
of the deceleration era, and finally at the present epoch it evolves through an accelerating stage.
Our aim is to study such evolution in the context of Chern–Simons corrected F(R) gravity theory
and confront the model with various observational data. Using the reconstruction technique, and in
addition by employing suitable boundary conditions, we determine the form of F(R) for the entire
possible range of the cosmic time. The form of F(R) seems to unify a non-singular bounce with
a dark energy epoch, in particular, from a non-singular bounce to a deceleration epoch and from
a deceleration epoch to a late time acceleration era. It is important to mention that the bouncing
scenario in the present context is an asymmetric bounce, in particular, the Hubble radius monotonically
increases and asymptotically diverges at the late contracting era, while it seems to decrease with time
at the present epoch. The decreasing behaviour of the Hubble radius ensures a late time acceleration
era of the universe. Moreover, due to the aforesaid evolution of the Hubble radius, the primordial
perturbation modes generate at the deep contracting era far away from the bounce when all the
perturbation modes lie within the horizon. Correspondingly we calculate the scalar and tensor power
spectra, and accordingly, we evaluate the primordial observable quantities like the spectral index of
the scalar curvature perturbation, the tensor-to-scalar ratio, and as a result, they are found to be in
agreement with the latest Planck 2018 constraints. In this regard, the Chern–Simons term seems to
have considerable effects on the tensor perturbation evolution, however keeping intact the scalar part
of the perturbation with that of in the case of a vacuum F(R) model, and as a result, the Chern–Simons
term proves to play an important role in making the observable quantities consistent with the Planck
results. Furthermore the theoretical expectation of the effective equation of state parameter of the
dark energy epoch is confronted with the Planck+SNe+BAO data.
