Since Bravely Default: Flying Fairy isn’t a Final Fantasy title so producer Tomoya Asano didn’t have to use Ramuh, Shiva, and Ifrit.
Bravely Default has five new summons:
Prometheus’ Fire makes a fire breathing train appear. In Greek mythology, Prometheus is the deity that gave fire to humans.
Ziusudra’s Sin summons a woman-like figure that floods the screen with water. Ziusaudra is from the Sumerian flood myth.
Hraesvelgr transforms from an airplane into a bird-like creature that hits all enemies with a wind attack. Hraesvelgr sits at the edge of the heavens and makes the wind blow when he flaps his wings, according to Norse mythology.
Girtablilu is a giant scorpion that makes the earth shake when it slams both of its claws into the ground. Girtablilu are servants of the sun god Shamash in the Epic of Gilgamesh.
Deus Ex is a giant machine that builds up electric energy and shoots lightning. Square Enix seems to have taken inspiration from the phrase "deus ex machina" for this summon. I wonder if this was a missed opportunity to make a chibi Adam Jensen since Deus Ex: Human Revolution is simply called Deus Ex in Japan.