• 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. H0 = expansion rate now

• H0 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 H0 and m we infer how fast the slow down =>

• H0 <=> m

• H0 and m give D

• But suppose in last billion years expansion has speeded up?

• Then H0 we see is higher than the value we should be using => we calculate D too low

• => calculate expected F too high, F = L/4D2

• 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 174-177)

• 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

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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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