  After the prediction of many sub- and super-Chandrasekhar (at least a dozen
for the latter) limiting mass white dwarfs, hence apparently peculiar class of
white dwarfs, from the observations of luminosity of type Ia supernovae,
researchers have proposed various models to explain these two classes of white
dwarfs separately. We earlier showed that these two peculiar classes of white
dwarfs, along with the regular white dwarfs, can be explained by a single form
of the f(R) gravity, whose effect is significant only in the high-density
regime, and it almost vanishes in the low-density regime. However, since there
is no direct detection of such white dwarfs, it is difficult to single out one
specific theory from the zoo of modified theories of gravity. We discuss the
possibility of direct detection of such white dwarfs in gravitational wave
astronomy. It is well-known that in f(R) gravity, more than two polarization
modes are present. We estimate the amplitudes of all the relevant modes for the
peculiar as well as the regular white dwarfs. We further discuss the
possibility of their detections through future-based gravitational wave
detectors, such as LISA, ALIA, DECIGO, BBO, or Einstein Telescope, and thereby
put constraints or rule out various modified theories of gravity. This
exploration links the theory with possible observations through gravitational
wave in f(R) gravity.
