  The Kepler and TESS missions delivered high-precision, long-duration
photometric time series for hundreds of main-sequence stars with
gravito-inertial (g) pulsation modes. This high precision allows us to evaluate
increasingly detailed theoretical stellar models. Recent theoretical work
extended the traditional approximation of rotation (TAR), a framework to
evaluate the effect of the Coriolis acceleration on g-modes, to include the
effects of the centrifugal acceleration in the approximation of slightly
deformed stars, which so far had mostly been neglected in asteroseismology.
This extension of the TAR was conceived by rederiving the TAR in a
centrifugally deformed, spheroidal coordinate system. We explore the effect of
the centrifugal acceleration on g modes and assess its detectability in
space-based photometry. We implement the new framework to calculate the
centrifugal deformation of precomputed 1D spherical stellar structure models
and compute the corresponding g-mode frequencies, assuming uniform rotation.
The framework is evaluated for a grid of stellar structure models covering a
relevant parameter space for observed g-mode pulsators. The centrifugal
acceleration modifies the effect of the Coriolis acceleration on g modes,
narrowing the equatorial band in which they are trapped. Furthermore, the
centrifugal acceleration causes the pulsation periods and period spacings of
the most common g modes (prograde dipole modes and r modes) to increase with
values similar to the observational uncertainties in Kepler and TESS data. The
effect of the centrifugal acceleration on g~modes is formally detectable in
modern space photometry. Implementation of the new theoretical framework in
stellar structure and pulsation codes will allow for more precise asteroseismic
modelling of centrifugally deformed stars, to assess its effect on mode
excitation, -trapping and -damping.
