Which type of star serves as a standard candle because its peak brightness is always the same?

The type Ia supernova. A white dwarf pulling matter from a companion detonates at close to a fixed mass, so it releases close to a fixed amount of energy - which means how bright it looks tells you how far away it is, out to billions of light years.

That is what found dark energy. Two independent teams in 1998 measured distant type Ia supernovae expecting to see the expansion of the universe slowing under gravity, and found them fainter than they should be - further away than expected. The expansion is accelerating, driven by something making up about 70 per cent of the universe that nobody can identify. Both teams checked for errors for months before publishing, because neither wanted the result.

The candles are not quite standard, either. Their peak brightness varies, and the technique only works because of an empirical correction discovered in the 1990s: brighter ones fade more slowly, so the shape of the light curve calibrates the peak. Cepheid variables do the same job at shorter range and are how the supernova scale is anchored - a ladder of methods, each calibrated against the one below it, and a persistent disagreement between the rungs about how fast the universe is expanding.