Unimodular $F(R)$ Gravity
  We extend the formalism of the Einstein-Hilbert unimodular gravity in the
context of modified $F(R)$ gravity. After appropriately modifying the
Friedmann-Robertson-Walker metric in a way that it becomes compatible to the
unimodular condition of having a constant metric determinant, we derive the
equations of motion of the unimodular $F(R)$ gravity by using the metric
formalism of modified gravity with Lagrange multiplier constraint. The
resulting equations are studied in frames of reconstruction method, which
enables us to realize various cosmological scenarios, which was impossible to
realize in the standard Einstein-Hilbert unimodular gravity. Several unimodular
$F(R)$ inflationary scenarios are presented, and in some cases, concordance
with Planck and BICEP2 observational data can be achieved.
