  The present thesis is focused on the study of FLRW cosmology in modified
gravities and with scalar fields. The mystery of dark energy has made that the
last decade, many efforts in theoretical physics have been focused on the
explanation of the current acceleration of the Universe expansion. On the other
hand, an early accelerated epoch, known as inflation, is also required in the
standard cosmological model in order to fit the observational data. Here, we
study the possibility to explain both effects under the same mechanism, by
means of scalar fields or modified gravity. In this sense, F(R) and
Gauss-Bonnet gravities are studied. This analysis is also extended to
Ho\v{r}ava-Lifshitz gravity, a theory that seems to be power counting
renormalizable, in spite of it contains other serious problems that are also
discussed in the thesis.
