Kalahansa or Kalahamsa (Sanskrit) The swan in eternity; in the pre-cosmogonical aspect, Kalahansa becomes Brahman or Brahma (neuter), darkness or the unknowable; and second, the swan in time and space when by analogy Kalahansa becomes Brahma (masculine). Rather than Brahma being the Hansa-vahana (the one using the swan as vehicle), it is Brahma who is Kalahansa, while Purusha, the emanation from Brahma, as one of its aspects as a creative power, is the Hansa-vahana or swan-carrier.
"The 'Swan or goose' (Hansa) is the symbol of that male or temporary deity, as he, the emanation of the primordial Ray, is made to serve as a Vahan or vehicle for that divine Ray, which otherwise could not manifest itself in the Universe, being, antiphrastically, itself an emanation of 'Darkness' -- for our human intellect, at any rate" (SD 1:80).
"The 'First Cause' had no name in the beginnings. Later it was pictured in the fancy of the thinkers as an ever invisible, mysterious Bird that dropped an Egg into Chaos, which Egg becomes the Universe. Hence Brahm was called Kalahansa, 'the swan in (Space and) Time.' He became the 'Swan of Eternity,' who lays at the beginning of each mahamanvantara a 'Golden Egg.' It typifies the great Circle, or O, itself a symbol for the Universe and its spherical bodies" (SD 1:359).
[Kalahamsa, Goose, Swan]