We provide an $F(R)$ gravity description of a $\mathrm{\Lambda }\mathrm{CDM}$ bouncing model, without the need for matter fluids or for a cosmological constant. As we explicitly demonstrate, the two cosmological eras that constitute the $\mathrm{\Lambda }\mathrm{CDM}$ bouncing model can be generated by $F(R)$ gravity, which can lead to accelerating cosmologies. The resulting $F(R)$ gravity has the Einstein frame inflationary properties that have concordance with the latest Planck observational data. Both the $F(R)$ gravity stability properties are thoroughly investigated, and also, the gravitational particle production, a feature necessary for the viability of the $\mathrm{\Lambda }\mathrm{CDM}$ bounce scenario, is also addressed. As we will show, the $\mathrm{\Lambda }\mathrm{CDM}$ bounce model can be successfully described by pure $F(R)$ gravity, with appealing phenomenological attributes, which we extensively discuss.

• Received 20 January 2015

DOI:https://doi.org/10.1103/PhysRevD.91.064036