  Rotational splittings are currently measured for several main sequence stars
and a large number of red giants with the space mission Kepler. This will
provide stringent constraints on rotation profiles. Our aim is to obtain
seismic constraints on the internal transport and surface loss of angular
momentum of oscillating solar-like stars. To this end, we study the evolution
of rotational splittings from the pre-main sequence to the red-giant branch for
stochastically excited oscillation modes. We modified the evolutionary code
CESAM2K to take rotationally induced transport in radiative zones into account.
Linear rotational splittings were computed for a sequence of $1.3 M_{\odot}$
models. Rotation profiles were derived from our evolutionary models and
eigenfunctions from linear adiabatic oscillation calculations. We find that
transport by meridional circulation and shear turbulence yields far too high a
core rotation rate for red-giant models compared with recent seismic
observations. We discuss several uncertainties in the physical description of
stars that could have an impact on the rotation profiles. For instance, we find
that the Goldreich-Schubert-Fricke instability does not extract enough angular
momentum from the core to account for the discrepancy. In contrast, an increase
of the horizontal turbulent viscosity by 2 orders of magnitude is able to
significantly decrease the central rotation rate on the red-giant branch. Our
results indicate that it is possible that the prescription for the horizontal
turbulent viscosity largely underestimates its actual value or else a mechanism
not included in current stellar models of low mass stars is needed to slow down
the rotation in the radiative core of red-giant stars.
