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\section{Introduction}  %Rotation in stars  Stars Though prevalent, stellar rotation and the resulting internal rotational profile, together with the mechanisms that contribute to angular momentum transport, remain poorly probed.   %Stars  are gravitationally bound, rotating spheroids of plasma, with rotation potentially playing an important role in their evolution and observable properties \cite{Maeder:2009}. %\cite{Maeder:2009}.  Despite this, we know little about their internal rotation profile and the mechanisms that contribute to angular momentum transport. Different classes of mechanisms have been discussed in the literature, proposed,  in particular hydrodynamical instabilities and circulations induced by rotation \citep[See][for a review]{Maeder:2000}, magnetic torques \citep{Gough:1998,Spruit:1999,Spruit:2002,Spada:2010} and internal  gravity waves \citep[See e.g.,][]{Charbonnel:2005}. In the absence of strong mass loss, the bulk of the redistribution of angular momentum is expected to occur in a star when shearing is generated  during episodes of expansion or contraction. At the end of the main sequence most stars, after exhausting hydrogen in their cores, ignite hydrogen in a shell. Above this shell the star begins to expand, while the core contracts. In the absence of a strong coupling between core and envelope, conservation of angular momentum implies that the core has to spin up considerably while the envelope spins down. This would lead to very rapidly rotating stellar cores and a shear layer between core and envelope. Evolutionary calculations that include angular momentum transport from rotational instabilities and circulations,also  predict rapidly rotating stellar cores after core-hydrogen exhaustion at the end of stellar evolution  \citep[e.g.,][]{Heger_Langer_Woosley_2000,larends_Yoon_Heger_Herwig_2008,Eggenberger:2012,Marques:2013}. This is at odds with the observed rotation rate of white dwarfs (WD) and neutron stars (NS), which instead can be somewhat recovered including angular momentum transport due to magnetic torques in radiative regions \citep[Tayler-Spruit dynamo (TS)][]{Spruit:2002,Heger:2005,larends_Yoon_Heger_Herwig_2008}. In the era of space asteroseismology, KEPLER the Kepler satellite  allowed for the measurement of the core rotation in many red giant stars using the splitting of mixed modes \citep{Beck:2012,Deheuvels:2012,Mosser:2012}. Mixed modes are oscillations that have an acoustic component (p-mode) in the envelope and are g-modes (restoring force is gravity) in the stellar  coreof the star  \citep[See e.g.,][]{Beck:2011}. Similarly to the case of compact remnants, models solely including angular momentum transport $j-$transport  due to rotational mixing and circulations can not reproduce the observed rotation rates \citep{Eggenberger:2012,Marques:2013,Ceillier:2013}, and predict rotation rates 2 to 3 orders of magnitude above the observations. While the adopted treatment of angular momentum transport is approximated and rely on a number of assumptions, \citet{Marques:2013} have shown that even pushing to the limit of the allowed parameter space one can not reproduce the observed values. They claim that ``the seismology of red-giant stars emphasize that an additional mechanism, is needed to achieve a slower core rotation of red-giant stars''. It is clear that the next step is testing if models including transport of angular momentum due to TS magnetic fields can explain the asteroseismic observations.  We recall that, while the physics of the Tayler instability is solid, the existence of the Tayler-Spruit dynamo loop is currently debated on both analytical and numerical grounds \citep{Braithwaite:2006,Zahn:2007}. However observations of the spin rates of compact objects (WD and NS) are in much better agreement with models including this angular momentum transport mechanism \citep{Heger:2005,larends_Yoon_Heger_Herwig_2008}, which has also been discussed in the context of the rigid rotation of the solar core \citep{Eggenberger:2005}, but see also \citet{Denissenkov:2010}.  We compare our results with KEPLER Kepler  asteroseismic observations of mixed modes in red giants. In particular we have been trying to reproduce, using models including different physics of angular momentum transport, the splittings observed in the red giant star KIC 8366239. We further compare predicted core rotation rates with observations of stars during core He-burning and in the WD stage. We show that it is difficult, even in the presence of magnetic torques due to TS magnetic fields, to fully account for the evolution of the core rotation rate from the end of the main sequence to the WD stage. We also show that a constant diffusivity, as discussed in \citet{Eggenberger:2012}, can not explain the full core angular momentum evolution past core H exhaustion.