Why do we expect Type Ia Supernovae to be brighter in a decelerating Universe than what has been observed? This seminal review paper in the PNAS by Robert P. Kirshner (https://www.pnas.org/content/96/8/4224) says the following:


  If the universe had been decelerating—–in the way it would if it contained the closure density of matter, that is, if Ωm = 1—then the light emitted at redshift z = 0.5 by a SN Ia would not have traveled as far, compared with a situation where the universe had been coasting at a constant rate—characteristic of an empty universe, where Ωm = 0. For a universe with Ωm = 1, the flux from the distant supernova therefore would be ≈25% brighter. But the distant supernovae are not brighter than expected in a coasting universe, they are dimmer. For this to happen, the universe must be accelerating while the light from the supernova is in transit to our observatories.


I didn't understand this.

Why do we expect Type Ia Supernovae at a particular distance to be more or less brighter based on the matter density of the Universe?

In other words, why should the brightness of anything at a particular distance  depend on whether the Universe was accelerating or not?
Observed brightness (or magnitude) depends on the distance between the source and the observer. The further the distance, the fainter we will observe given the same source.

If the distance r1 is measured between the source and the observer given the accelerating universe, then the distance r2 measured given the decelerating universe would be r2 &lt; r1. Therefore, this answers your second question. For the first question, the answer is directly followed the current model that predicts less matter density given faster expansion of The Universe.