Unimodular Mimetic $F(R)$ Inflation
  We propose the unimodular-mimetic $F(R)$ gravity theory, to resolve cosmological constant problem and dark matter problem in a unified geometric manner. We demonstrate that such a theory naturally admits accelerating universe evolution. Furthermore, we construct unimodular-mimetic $F(R)$ inflationary cosmological scenarios compatible with the Planck and BICEP2/Keck-Array observational data. We also address the graceful exit issue, which is guaranteed by the existence of unstable de Sitter vacua. 
S.D. Odintsov, V.K. Oikonomou
gr-qc astro-ph.CO hep-th