Albert Einstein had originally included an arbitrary term in his equations for General Relativity, called the "cosmological constant." This constant, put in by hand, was used to produce a stable solution for the scale parameter, R, of the universe. The solutions by Friedman and Lemaitre, which did not include the cosmological constant, produced unstable universes with scale parameters R(t) that depended on time.
Recent work trying to measure the distance to very distant objects, that is those with large red shifts, suggest that there may indeed be a need to include a term like the cosmological constant in the energy density of the universe. The WMAP results are strong evidence for the existence of a term like the cosmological constant. Solutions to the equations of General Relativity for the universe require as an input the total energy density from all sources( mass, fields, etc.) There are three broad categories of the energy density
1) energy density due to radiation , such as the
black
body radiation
2) energy density due to matter( baryonic, dark,
non-baryonic),
about 30% of critical density
3) energy density due to cosmological constant(
so-called
"dark energy") about 70% of critical density
Once we have determined the energy density the equations of GR produce a solution which tells us how the distance to an object is related to the Hubble constant H, to the components of the energy density, and to the red shift z ( which is actually a look back time).
distance = d(H, z, matter density, dark energy density)
Cosmologists try to fit the distance equation to experimental data in the hopes of extracting the separate components of the energy density from the fit. The most reliable large distance "candles" are super novae of class 1A, SNe 1A, whose luminosity light curve can be fitted to their true luminosity.
Super Novae 1A used as distance indicators:
Classical Energy Flux from a moving source
 |
Suppose a source of known luminosity, L moves away from an
observer
such that the distance D can be written as
D = v0t + at2/2. The measured flux F(t) the observer sees is given as F(t) = L/(4pD2(t)), p=3.14 F(t) = L/(4pt2(v0
+at/2)2).
|
 |
In the figure below from a paper (2000, Adam
G.
Riess (Space Telescope Science Institute))
is a plot of the magnitudes of SNe1A versus red shift.
Different fits are shown assuming different contributions to the
universe's
energy density. WM refers
to
matter density at 30% of critical mass density ( Critical mass density
is that value at which the Universe would coast to zero expansion rate
in infinite time.) and WL refers
to energy density contributed by the dark energy component. If we
believed
that the energy density were totally due to all forms of matter ( WM
= 1) then the supernovae at large distances would appear to be too bright
(smaller magnitudes).
There is not universal agreement among the
cosmologists
that these data plus the other data from the cosmic microwave
background
anisotropies, compel one to believe that there actually is dark energy.(However, the newest WMAP results
strongly point to the need for dark energy.)
The reasons that supernovae that occurred in the
distant
past may look dimmer than current ones include a possible change
in the chemical environment due to nucleosynthesis. Stellar dynamics
depend
on the mixture of elements present. Another reason for the dimness of
distant
supernovae may be due to dust in the galaxies or in space which has not
been adequately accounted for. It would be useful to obtain more data
on
distant supernova with z > 1. A value of z = 1 corresponds to about
6 billion
years for a Hubble constant of around 65km/s/Mpc.
Further discussion of the existence of "Dark Energy"
It is of interest to us in our historical survey
of
the development of our views on the Universe that the theorists have
given
the name of "quintessence" to the elementary particle field that is
responsible
for dark energy or the cosmological constant. Don't let the use of this
name confuse you into thinking they are arguing for the old fashioned
"celestial
matter" of the Aristotelians!
Complex Life, Gamma Ray Bursts and Dark Energy
Archival paper on Complex Life and Gamma Ray Bursts
discussion
of dark energy and negative pressure
_J. D. Cohn, living_with_lambda.pdf
Large Synoptic Survey Telescope
Is dark energy conclusion model dependent?
