Accrording to modern cosmological theory, based on Einstein's General Relativity (our modern theory of gravity), the big bang did not occur somewhere in space; it occupied the whole of space. Indeed, it created space. Distant galaxies are not traveling at a high speed through space; instead, just like our own galaxy, they are moving relatively slowly with respect to any of their neighboring galaxies. It is the expansion of space, between the time when the stars in these distant galaxies emitted light and our telescopes receive it, that causes the wavelength of the light to lengthen (redshift). Space is itself infinitely elastic; it is not expanding into anything."
The lengthening, or redshifting, of light that Primack describes was first observed by Edwin Hubble in 1929. This phenomenon is often referred to, incorrectly, as a Doppler shift. A Doppler redshift results from the expansion of light emitted by a receding object. Cosmological redshifts result from the expansion of space (and the light moving through that space) between us and a distant galaxy or quasar. Space is expanding everywhere, so the more distant an object is, the more rapidly it appears to be moving away.