How will the luminosity of the current very near supernova Ia "PTF 11kly" develop in the next weeks and why? Currently there is a unique chance for amateur astronomers to observe a very near type Ia supernova, named PTF 11kly.
As standard candles are very important to measure distances in the universe, can you give a brief overview of how the luminosity of "PTF 11kly" will probably develop according to current star models?
Where do our current models lack accuracy? Is this single supernova so special, that it can fill some gaps in our knowledge?
 A: The biggest thing about this supernova is how CLOSE it is.  A mere 21 million light years away (as opposed to being a billion light years away).  The folks at John Hopkins think that studying a ype Ia supernova is valuable for several reasons.

SNe Ia are also very bright compared to other standard candles, which means they can be seen at high redshifts and so are important to cosmology. This is due to the following: the expansion of the universe is inferred from the observation of a correlation between recession velocity and distance -- the farther away an object is, the faster it is moving away from us. Velocity relates to redshift, and so the ability to determine distances out to high redshifts allows us to measure the rate of expansion. This rate is given by Hubble's constant in the local universe where the expansion is a linear relationship: v=H_0*d. However, this relation can in general be much more complex, as it depends on the densities of the various components of the universe. For example, matter tends to slow down the expansion, and if the universe is curved that will also affect the expansion rate. We have observed that the expansion is accelerating, and since we don't know of anything that can cause this acceleration, we call it Dark Energy.

They conclude with

Type Ia Supernovae are not only an odd astrophysical phenomenon, they're also an important tool for studying cosmology. The JHU-led mission ADEPT hopes to study the nature of the Dark Energy using both a BAO study and high redshift SNe Ia observations. In order for this to happen, we need to determine whether ADEPT will be able to delineate between different cosmological models, and to do this realistically requires complex simulations, of which the list in Section 4 is only a basic outline. The true conclusion will not be until NASA decides ADEPT's fate at the end of 2008, so stay tuned.

Now that's from 2008, so this is a wonderful opportunity to get an "up close" look at what a Type Ia will tell them.
Caltech also talks about using a Type Ia as a Standard Candle, as well as getting a better understanding of Dark Energy and the Hubble Constant.
A: A Type Ia supernova is different from many others because of the extremely close similarity of the circumstances leading up to it. First you begin with a white-dwarf star which is composed of the Carbon and Oxygen remnant core of a former main sequence star under extreme pressures and held up by electron degeneracy pressure. A white-dwarf which happens to be near enough to a neighboring star may pull matter from that star. This matter will accumulate on the surface of the white-dwarf and increase its mass over time.
Eventually, if the mass of the white-dwarf reaches very near to the Chandrasekhar limit of about 1.4 solar masses the pressure and temperature of the star will start to rise to the point where Carbon and Oxygen fusion begins. This fusion process proceeds extremely rapidly. In a normal star the increase in temperature due to fusion reactions would result in expansion due to increased pressure, but a white-dwarf star is composed of electron degenerate matter which won't expand due to temperature in the same way. The fusion reaction has no means of regulating itself and thus rapidly progresses to the point of releasing enough energy to tear apart the star in only a few seconds. After the brightness from the initial explosion has diminished the supernova remnants will continue to shine for many days due to the radioactive decay of the Nickel-56 produced via fusion.
Most likely, due to the similarity in conditions leading up to the supernova (a Carbon/Oxygen electron degenerate core with almost exactly 1.4 solar masses of material around it) Type Ia's all have a very similar peak luminosity and relationship of luminosity to time.
However, they are not 100% identical. Variations in the composition of the white-dwarf (due to variations in the composition of the main sequence star that preceded it) will affect the supernova luminosity, but this variation can be accounted for by carefully observing the light-curve.
Because Type Ia supernova have very characteristic light-curves, because they are so bright and remain substantially bright over a period of days they can be used as "standard candles" across the entire Universe. SN 2011fe in M101 is the closest Type Ia supernova to have ever been observed with modern instruments. Being able to study the light-curve and spectra in enormous detail will help us improve our models of Type Ia supernova and perhaps lead to new insights or at least enhanced precision related to using them as standard candles.
