Cosmological dimming

In an expanding Universe, the inverse-square law for propagation of radiation breaks down increasingly over long spacetime intervals, because the surface area encompassed by an expanding wavefront emitted at a particular time t0 is no longer simply the surface of a static sphere of radius c(t — t0). One consequence of this, seen in the relations from Chapter 1, is that the surface brightness of an extended source is not redshift-independent, as it would be in a static and Euclidean situation. Instead, the surface brightness scales as (1 + z)—4, a phenomenon known as Tolman dimming or the (1 + z)4 dimming. The loss in surface brightness becomes especially dramatic at redshifts z — 4 and above, where it exceeds a factor of 600. This gives us an unavoidable bias in favor of observing the most compact, high surface-brightness regions of galaxies at these redshifts. Using the observed ultraviolet structures of nearby galaxies and incorporating Tolman dimming, one can show that many nearby galaxies, even spirals with significant star formation, would be completely undetected in the Hubble Deep Field data for this reason. At high redshifts, we can only see galaxies which are truly exceptional by the standards of today's Universe.

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