Understand
Using the reconstruction technique with an auxiliary field, we investigate which $F(R)$ gravities can produce the matter bounce cosmological solutions.
- Owing to the specific functional form of the matter bounce Hubble parameter, the reconstruction technique leads, after some simplifications, to the same Hubble parameter as in the matter bounce scenario.
- Focusing the study to the large and small cosmic time $t$ limits, we were able to find which $F(R)$ gravities can generate the matter bounce Hubble parameter.
- In the case of small cosmic time limit, which corresponds to large curvature values, the $F(R)$ gravity is $F(R)\sim R+\alpha R^2$, which is an inflation generating gravity, and at small curvature, or equivalently, large cosmic time, the $F(R)$ gravity generating the corresponding limit of the matter bounce Hubble parameter, is $F(R)\sim \frac{1}{R}$, a gravity known to produce late-time acceleration.