Re: Does WMAP disprove a time-varying cosmological constant?

In article <e03g3r$mis$2@xxxxxxxxx>,
Phillip Helbig---remove CLOTHES to reply <helbig@xxxxxxxxxxxxxxxxxxxxxxxx> wrote:
In article <1143270883.477476.53800@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
frank_k_sheldon@xxxxxxxxxxx writes:

But if the cosmological constant depends on time,
(and thus is not constant), this should have measureable effects.
I'm no expert, but then maybe the fact that long ago it had a different
value should be noticed in distant stars.

Can this connection be tested? Has it been tested by WMAP?

In principle, yes, it can be tested. Of course, one has to work out the
power spectrum for the CMB in such a model and compare it to WMAP. The
latter is rather straightforward, the former might not be: depending on
the theory involved, it might require much more than just fitting the
Friedmann equations with a variable lambda.

Some classes of models with time-varying cosmological "constants" have
been worked out in detail. The buzzword these days for this idea is
"the dark energy equation of state." A true cosmological constant is
equivalent to filling the Universe with a perfect fluid with some
energy density rho and pressure P = - rho (in units where the speed of
light is one). A comological constant that slowly varies in time is
equivalent to a perfect fluid with a slightly different equation of
state (that is, relation between P and rho). The simplest possibility
is just

P = - w rho

for some constant w. There's a lot of information out there about the
observational constraints on w in these models. The most recent WMAP papers,
particularly the one by Spergel et al., should get you started:

http://lambda.gsfc.nasa.gov/product/map/dr2/map_bibliography.cfm

Of course, there's no particular reason to believe that that simple
equation of state is right; it's just an
"everything-is-linear-to-first-order" approximation. People also
study slightly more sophisticated models in which the equation of
state is parametrized by two free parameters instead of just w, but
the data aren't yet good enough to strongly constrain things in a huge
amount of detail. Further improvement in measurements of
high-redshift supernovae, along with better CMB data, are supposed to
eventually pin down this sort of thing.

-Ted

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