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We investigate the inflationary realization in the context of unimodular$F(T)$ gravity, which is based on the $F(T)$ modification of teleparallelgravity, in which one imposes the unimodular condition through the use ofLagrange multipliers. We develop the general reconstruction procedure of the$F(T)$ form that can give rise to a given scale-factor evolution, and then weapply it in the inflationary regime. We extract the Hubble slow-roll parametersthat allow us to calculate various inflation-related observables, such as thescalar spectral index and its running, the tensor-to-scalar ratio, and thetensor spectral index. Then, we examine the particular cases of de Sitter andpower-law inflation, of Starobinsky inflation, as well as inflation in aspecific model of unimodular $F(T)$ gravity. As we show, in all cases thepredictions of our scenarios are in a very good agreement with Planckobservational data. Finally, inflation in unimodular $F(T)$ gravity has theadditional advantage that it always allows for a graceful exit for specificregions of the model parameters.

Inflationary cosmology in unimodular $F(T)$ gravity