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CATEGORIES:Cosmology Lunch
SUMMARY:The Stability of the Euler-Einstein system with a
positive Cosmological Constant - Jared Speck (DPMM
S)
DTSTART;TZID=Europe/London:20100426T130000
DTEND;TZID=Europe/London:20100426T140000
UID:TALK24316AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/24316
DESCRIPTION:The Euler-Einstein system models the evolution of
a dynamic spacetime containing a perfect ﬂuid. In
this talk\, I will discuss the nonlinear stability
of the Friedmann-Lemaˆıtre-Robertson-Walker famil
y of background cosmological solutions to the Eule
r-Einstein system in 1 + 3 dimensions with a posit
ive cosmological constant Λ. The background soluti
ons describe an initially uniform quiet ﬂuid of po
sitive energy density evolving in a spacetime unde
rgoing accelerated expansion. The main result is a
proof that under the equation of state p = cs^2^
ρ\, 0 < cs^2^ < 1/3\, the \nbackground solutions
are globally future-stable under small perturbatio
ns. In particular\, the perturbed spacetimes\, whi
ch have the topological structure \n[0\, ∞) × T3 \
, are future causally geodesically complete. The r
esults I will present are extensions of previous j
oint work with Igor Rodnianski\, which covered the
case of an irrotational ﬂuid\, and of work by Han
s Ringstrom on the Einstein-non-linear-scalar-ﬁeld
system.\nMathematically\, the main result is a pr
oof of small-data global existence for a modiﬁed v
ersion of the Euler-Einstein equations that are eq
uivalent to the un-modiﬁed equations. The proof is
based on the vectorﬁeld method of Christodoulou a
nd Klainerman.\n\nIt is of special interest to not
e that the behavior of the ﬂuid in an exponentiall
y expanding spacetime differs drastically from the
case of ﬂat spacetime. More speciﬁcally\, Christo
doulou has recently shown that on the Minkowski sp
ace background\, data arbitrarily close to that of
an initially uniform quiet ﬂuid state can lead to
solutions that form shocks. In view of this fact\
, we remark that the proof of our result can be us
ed to show the following: exponentially expanding
spacetime backgrounds can prevent the formation of
shocks.
LOCATION:CMS\, Pav.B\, CTC Common Room (B1.19)
CONTACT:Tasos Avgoustidis
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