Arxiv is an online archive for all sorts of scientific or mathematical papers that pass standard academic review. A new paper on this site is:
http://arxiv.org/ftp/astro-ph/papers/0404/0404207.pdf

Supernovae Ia (SNe Ia) light curves have been used to prove the
universe is expanding. As standard candles, SNe Ia appear to indicate
the rate of expansion has increased in the past and is now decreasing.
This independent evaluation of SNe Ia light curves demonstrates a
Malmquist Type II bias exists in the body of supernova data. If this
bias is properly addressed, there is very little budget for time
dilation in the light curves of supernova.
...
For most of the 20th century astronomical observations such as
galactic evolution, heavy metal abundance, supernovae light curves and
the cosmic microwave background have fallen within the constraints of
the Einstein - de Sitter Big Bang model. In the last two decades these
relationships have become severely strained. The universe is too big
and too old; the magnitudes of supernovae are dimming too fast. There
are too many radio point sources. The far infrared continuum emissions
imply a dusty past that is completely at odds with multi-colored
supernovae and quasar spectrums. There is too little anisotropy in the
cosmic microwave background to support the observed galaxy
super-cluster structure. Heavy metal ratios equal to solar
concentrations have been quantified in the most redshifted objects we
observe. Something is wrong with this mature theory: It has failed in
too many predictions.


Here's a quick summary of these ideas (note, this part was written by me so it may contain errors, I'm not an astrophycist of course):

When a supernova occurs it takes place over a month. A lightcurve plots the luminosity of the explosion over that time.

Time dialation in light curves is an important observation that confirms expansion of the universe. The paper shows that the observational data might infact deny the time dilation of light curves.

This provides scientific evidence then that the universe may not be expanding. Here's why.

First, lets consider all the evidence for cosmic expansion. The two that are most interesting are:

1. Redshift in most galaxies, the further away the more shifted
2. Time dialition in light curves

Regarding the first bit of evidence, that the universe is expanding based on this observation alone is one of many interpretations of the evidence. For example, another interpretation is that over huge huge HUGE intergalactic distances photons start to loose energy. They just do.

E = hf

So if E gets smaller then f gets smaller too and the result is redshift. The result, if this were true, is that the photon would slow down after traversing these distances. c = fw, so f gets smaller so does c, and if v = d/t then we can say that assuming d does not get smaller than it is t that gets larger.

Basically there are two interpretation of #1 above:

a. The distance between a galaxy gets greater the further away they are
b. The time it takes for light to come from a galaxy gets greater the further away it is producing the illusion that the distance gets greater

So I think that evidence #1 on its own is hardly sufficient to judge either way. Thats ok, we just look for more data to support either position, thats science.

So we find lightcurves of supernova to be a standard candle in the universe and realize that if the supernova is moving away from us we will see some quantity of time dialation in the light curves. Evidence #2. Until now, we thought we did see the expected dialation, which is why expansion must be occuring. The paper shows that we don't, which casts considerable doubt on expansion, and when combined with the other failed predictions of the Big Bang model (given above) our confidence in this theory takes a serious blow.