There are a few basic parameters by which the cosmologists try to describe
our universe. In classical cosmology the important ones are
(i) Hubble parameter
(ii) Density parameter
(iii) Deceleration parameter.
This question is on the Deceleration parameter. How is it measured in
experimental searches. How could we know that it's value is negative
which imply that our universe is accelerating at present.
The notations can be found in
http://www.astro.umd.edu/~miller/teaching/astr422/lecture10.pdf
The actual measurement is the luminosity-distance relationship of Type Ia supernovae, which are considered to be "standard candles". Here is a decent explanation: http://cerncourier.com/cws/article/cern/37859. I recommend in particular that you look at Fig. 2 and the accompanying text.
OK, I can see the figure -2, attached below. Due to nuclear physics
properties, type 1a supernova has a fixed brightness. They have
plotted luminosity vs redshift. How will the graph look if acceleration
vanishes ? will it be a straight line.
This article also points out that there are two other independent
evidences for cosmic acceleration.
1) Analysis of CMB anisotropies
2)Sloan Digital Sky Survey & 2 degree field survey.
Therefore we see that there are at-least three independent
evidences in favor of cosmic acceleration.
In this curve
m-M= 5 log d_L + 25
M is the magnitude at 10 Kpc.
This quantity increases with redshift. However if
empty universe ie omega=0 case is subtracted
out from m-M, then we get delta(m-M), this is
also called magnitude residual, which is
plotted in the Y axis. Observational values of
delta (m-M) first increases and then decreases.
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