REM - the Shape of Potentials for f(R) Theories in Cosmology and Tachyons

We investigated the reverse engineering method (REM) for constructing the potential of the scalar field in cosmological theories based on metric f(R) gravity and Friedman Robertson Walker (FRW) metric. Then transposing the new field and Friedman equations in an algebraic computing special library (in Maple + GrTennsorII platform) we graphically investigate the shape of the potentials in terms of the scalar field in at least two type of cosmology with exponential and linear scale factor expansion. Some perspectives and conclusions relating these results with tachyonic cosmology theories are noticed.