Existentialism: Sora No Woto touches several points of Existentialism, most notably Angst, Despair and the Absurd. An overarching theme of the show is how people give meaning to their lives, from religion to sticking up for their True Companions or their country, or clinging to delusions like Madam Jacquotte, in the face of an aloof, uncaring universe, contrasted to the pointlessness of it ("If the world is going to die, what are we fighting for?"). The episodes where this is more blatant are episode seven and the last DVD episode (in particular Rio's final voice-over). Filicia Heideman in particular is a textbook case of The Anti-Nihilist.
Filicia in episode seven: There can't possibly be any meaning in this world. But isn't that wonderful in its own right? Because if there isn't any, we can find our own.
Rio's answer to the question posited in episode seven (What are we fighting for?):
Let's go, to our dreams and more. Even if the world is to die, everything until that moment is our future.