
CosmoCoffee

[1007.1417]
Unitary Evolution and Cosmological FineTuning

Authors:  Sean M. Carroll, Heywood Tam 
Abstract:  Inflationary cosmology attempts to provide a natural explanation for the
flatness and homogeneity of the observable universe. In the context of
reversible (unitary) evolution, this goal is difficult to satisfy, as
Liouville's theorem implies that no dynamical process can evolve a large number
of initial states into a small number of final states. We use the invariant
measure on solutions to Einstein's equation to quantify the problems of
cosmological finetuning. The most natural interpretation of the measure is the
flatness problem does not exist; almost all RobertsonWalker cosmologies are
spatially flat. The homogeneity of the early universe, however, does represent
a substantial finetuning; the horizon problem is real. When perturbations are
taken into account, inflation only occurs in a negligibly small fraction of
cosmological histories, less than $10^{6.6\times 10^7}$. We argue that while
inflation does not affect the number of initial conditions that evolve into a
late universe like our own, it nevertheless provides an appealing target for
true theories of initial conditions, by allowing for small patches of space
with subPlanckian curvature to grow into reasonable universes. 

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JeanLuc Lehners
Joined: 18 Feb 2010 Posts: 4 Affiliation: Princeton Center for Theoretical Science

Posted: July 14 2010 


Carroll and Tam have written a nice and very readable paper revisiting Penrose’s entropy problem as well as work related to Liouville’s theorem in the context of inflation. They look at the claim that inflation evolves from generic initial conditions. This often cited claim is radically at odds with Liouville’s theorem, which requires a given number of states of the universe to evolve into the same number of states at a later time. In other words, it is not possible for a large number of (highly curved and inhomogeneous) initial states to evolve into a small number of smooth and homogeneous “final” states. Thus it is not clear whether the main argument by which inflation is usually motivated actually holds up! (Of course inflation has the appealing byproduct that it can produce density perturbations along the way.)
The paper does not provide a resolution of the problem, but is interesting in that it highlights an often overlooked issue that is certainly in need of a solution, if we want to claim that inflation explains the initial conditions of the hot big bang cosmology. 

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