A Dark energy question (based on Blandford's talk at SSI)

I was just browsing through transparencies of this year's SLAC summer
school transprancies on Cosmology which are online at
http://www-conf.slac.stanford.edu/ssi/2003
anyhow I was through Blandford's talk on transparency 4
which is at http://www-conf.slac.stanford.edu/ss...rd/p1pg04.html
I find that for a darl energy/dark atter dominated universe
j= a'''a^2/(a')^3 = constant

I had never seen this before. can anyone provide a reference where
this has
been derived or discussed? also is this true for any dark energy eqn
of state?
Thanks

(Melroy) writes:

I was just browsing through transparencies of this year's SLAC summer
school transprancies on Cosmology which are online at
http://www-conf.slac.stanford.edu/ssi/2003
anyhow I was through Blandford's talk on transparency 4
which is at http://www-conf.slac.stanford.edu/ss...rd/p1pg04.html
I find that for a darl energy/dark atter dominated universe
j= a'''a^2/(a')^3 = constant

I had never seen this before. can anyone provide a reference where this
has been derived or discussed? also is this true for any dark energy eqn
of state?

It can be trivially shown to be true for any universe that is
asymptotically de Sitter (exponentially expanding) --- simply
plug in an exponential scale-factor and do the math.

Whether this is true for any "dark energy" equiation of state will depend
on whether the "dark energy" contribution plus the initial expansion rate
is large enough to get the Universe over the Lemaitre hump so that it does
not recollapse, and on whether the "dark energy" stress tensor asymptotically
approaches a positive constant times the metric in the limit that the
"ordinary matter" and "dark matter" become infinitely dilute --- i.e.,
whether it asymototically behaves like an "ordinary" cosmological constant.

However, even more perverse cosmologies are possible: For example,
if the ratio w = P/\rho of the dark energy's pressure to its energy density
is less than -1 (in theorist's units where c = 1), then the Universe
expands to infinite dilution in a finite time, in a so-called "Big Rip"
or "Crack of Doom" --- see http://www.arXiv.org/abs/astro-ph/0302506.
"Dark energy" with this property is called "Phantom Energy" for some reaon
(perhaps as a nod to "The Phantom Menace").


-- Gordon D. Pusch

perl -e '$_ = \n"; s/NO\.//; s/SPAM\.//; print;'

(Melroy) writes:

I was just browsing through transparencies of this year's SLAC summer
school transprancies on Cosmology which are online at
http://www-conf.slac.stanford.edu/ssi/2003
anyhow I was through Blandford's talk on transparency 4
which is at http://www-conf.slac.stanford.edu/ss...rd/p1pg04.html
I find that for a darl energy/dark atter dominated universe
j= a'''a^2/(a')^3 = constant

I had never seen this before. can anyone provide a reference where this
has been derived or discussed? also is this true for any dark energy eqn
of state?

It can be trivially shown to be true for any universe that is
asymptotically de Sitter (exponentially expanding) --- simply
plug in an exponential scale-factor and do the math.

Whether this is true for any "dark energy" equiation of state will depend
on whether the "dark energy" contribution plus the initial expansion rate
is large enough to get the Universe over the Lemaitre hump so that it does
not recollapse, and on whether the "dark energy" stress tensor asymptotically
approaches a positive constant times the metric in the limit that the
"ordinary matter" and "dark matter" become infinitely dilute --- i.e.,
whether it asymototically behaves like an "ordinary" cosmological constant.

However, even more perverse cosmologies are possible: For example,
if the ratio w = P/\rho of the dark energy's pressure to its energy density
is less than -1 (in theorist's units where c = 1), then the Universe
expands to infinite dilution in a finite time, in a so-called "Big Rip"
or "Crack of Doom" --- see http://www.arXiv.org/abs/astro-ph/0302506.
"Dark energy" with this property is called "Phantom Energy" for some reaon
(perhaps as a nod to "The Phantom Menace").


-- Gordon D. Pusch

perl -e '$_ = \n"; s/NO\.//; s/SPAM\.//; print;'