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SUMMARY:Dynamics of linearized cosmological perturbations - Alan Rendall (
 AEI\, Potsdam)
DTSTART:20090309T160000Z
DTEND:20090309T170000Z
UID:TALK17040@talks.cam.ac.uk
CONTACT:Prof. Mihalis Dafermos
DESCRIPTION:In cosmology an important role is played by homogeneous and is
 otropic solutions of the Einstein-Euler equations and linearized perturbat
 ions of these. In this talk I present results of Paul Allen and myself on 
 the asymptotic behaviour of certain linearized solutions (so-called 'scala
 r perturbations') both in the approach to the initial singularity and at l
 ate times. The main equation of interest is a linear hyperbolic equation w
 hose coefficients depend only on time. Expansions for the solutions are ob
 tained in both asymptotic regimes. In both cases it is shown how general s
 olutions can be parametrized by certain functions which are coefficients i
 n the asymptotic expansion. The central technique in the proofs is that of
  energy estimates. An interesting feature of the results is a bifurcation 
 observed in the late-time asymptotics for an asymptotically polytropic equ
 ation of state\, occurring for the polytropic index corresponding to a rad
 iation fluid.
LOCATION:CMS\, MR13
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