Why may supernovae reveal the dark energy responsible for the accelerating expansion of the universe? More specifically why supernovae opposed to other cosmological species?
The presence of dark energy is inferred from the relationship between the distance of galaxies and their recession velocity. The FLRW metric allows us to calculate this relationship and the value of the cosmological constant is a parameter we can adjust to get the best fit.
The recession velocity is easy to measure because we get it from the red shift. However the distance is extremely difficult to measure accurately. However if we know the intrinsic brightness of distant objects we can calculate the distance because the apparent magnitude is related to the intrinsic brightness and the distance.
And this is where the type SN1a supernovae come in. We understand the physics of this type of supernova pretty well, and that means we can calculate the intrinsic brightness from the light curve. Once we know the intrinsic brightness we can calculate the distance and then we can draw the distance-recession velocity curve.
Other objects like galaxies cannot be used because they come in all shapes and sizes, so their intrinsic brightness cannot be calculated. Likewise the other types of supernovae are too variable to be a reliable candle.