Context : CoRoT and Kepler missions are now providing high-quality asteroseismic data for a large number of stars .
Among intermediate-mass and massive stars , fast rotators are common objects .
Taking the rotation effects into account is needed to correctly understand , identify , and interpret the observed oscillation frequencies of these stars .
A classical approach is to consider the rotation as a perturbation .

Aims : In this paper , we focus on gravity modes , such as those occurring in \gamma Doradus , slowly pulsating B ( SPB ) , or Be stars .
We aim to define the suitability of perturbative methods .

Methods : With the two-dimensional oscillation program ( TOP ) , we performed complete computations of gravity modes – including the Coriolis force , the centrifugal distortion , and compressible effects – in 2-D distorted polytropic models of stars .
We started with the modes \ell = 1 , n = 1 –14 , and \ell = 2 –3 , n = 1 –5 , 16–20 of a nonrotating star , and followed these modes by increasing the rotation rate up to 70 % of the break-up rotation rate .
We then derived perturbative coefficients and determined the domains of validity of the perturbative methods .

Results : Second-order perturbative methods are suited to computing low-order , low-degree mode frequencies up to rotation speeds \sim 100 \ > \mathrm { km s ^ { -1 } } for typical \gamma Dor stars or \sim 150 \ > \mathrm { km s ^ { -1 } } for B stars .
The domains of validity can be extended by a few tens of \ > \mathrm { km s ^ { -1 } } thanks to the third-order terms .
For higher order modes , the domains of validity are noticeably reduced .
Moreover , perturbative methods are inefficient for modes with frequencies lower than the Coriolis frequency 2 \Omega .
We interpret this failure as a consequence of a modification in the shape of the resonant cavity that is not taken into account in the perturbative approach .

Conclusions :