For Expanding Universe, with look back times to where Universe was noticeably different (density and expansion rate), Will see effects of expansion and D will be complex D will depend on 1+z,    and  m

Make observations of D versus 1+z Fit curves based on different amounts to   and  m Extract the best fit Never proves a model Demonstrates a model is consistent (or not) with observations

SNe are bright so can see far enough away to see effects of change in expansion rate of universe SNe Ia are “easy” to calibrate

Take case of where D is simple D = velocity/(Hubble “Constant”) ; D = V/H H is a measure of expansion rate, higher H higher expansion. H 0 = expansion rate now H 0 is what we measure out to z = about 0.1 for z in this range z = V/c where c = speed of light => z V If universe has been slowing down in expansion

Means higher H in past. For a given H 0 and  m we infer how fast the slow down => H 0  m H 0 and  m give D But suppose in last billion years expansion has speeded up? Then H 0 we see is higher than the value we should be using => we calculate D too low

=> calculate expected F too high, F = L/4  D 2 When we look, find SNe Ia fainter than expected if  m were 1  m low (0.2) is better, but Still not good because D versus 1+z is complex due to acceleration (   )

Positive means fainter SNe Ia fainter than expected velocity Sub from all and the result re- plotted below

Need to calibrate several effects seen SNe people have done a very thorough job One of “coolest” things is they see affect of “time dilation” (cf. Book pages ) Things moving faster appear to have slower moving clocks If we take 1+z to be a relative velocity with respect to us, we get the right answer for the SN light versus time! Special relativity works; the model all hangs together

More sample light curves Fig.1: UBVRI and Bolometric Light Curves of SN 1994D, from Vacca & Leibundgut (1996). Solid lines are the best fits of the model to the data; residuals are plotted below each panel. Dashed lines are the commonly used templates for Type Ia light curves.

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