[hep-th/0611043] Sinks in the Landscape and the Invasion of
Posted: November 07 2006
This paper discusses various simple measures in eternal inflation, and whether or not they solve the Boltzmann Brain problem.
The problem is that a space with positive vacuum energy generates exponentially large volumes in the future in which fluctuations can give rise to Boltzmann Brains: thus most observers will be Boltzmann brains, in contradiction to our apparently very special memories associated with life on earth (nucleating a new bubble universe is much less likely than forming a brain). One simple solution is that the vacuum decays on the scale of a Hubble time, so the future volume remains on average finite (see e.g. hep-th/0610079). This is a short time of ~20 billion years. [Note that the anthropic reasoning here is pretty robust: there will be brains in essentially any choice of reference class you like, including an essentially identical copy of your current brain having the deluded belief that he lives on Earth]
This paper suggests instead that a 'standard' volume-weighted slicing measure of eternal inflation resolves the problem: most volume is generated in the highest energy vacuum, and most observers will therefore be formed shortly after its decay, i.e. near a thermalization surface and not a Boltzmann brain. What I don't see is how this is an acceptable solution: doesn't this weighting give the well-known 'youngness paradox' - that most observers will be in a very newly formed vacuum - in contradiction to observation that actually the universe is relatively old?
Perhaps another possibility is that there is some external clock associated with each vacuum. One logical possibility would be something like the ekpyrotic scenario (e.g. astro-ph/0605173): there is no Brain problem as long as the branes eventually re-collide and the entire expanded region is re-thermalized. Or perhaps downwards renormalization of the vacuum energy due to accumulation of super-Hubble quantum fluctuations (e.g. hep-ph/9602316) - though this seems to take too long.
Incidentally, the logical conclusion of the anthropic comments in the Discussion section is perhaps something like the proposal in math.ST/0608592 - though unfortunately it is unclear how this works in the infinite case.
The problem is that a space with positive vacuum energy generates exponentially large volumes in the future in which fluctuations can give rise to Boltzmann Brains: thus most observers will be Boltzmann brains, in contradiction to our apparently very special memories associated with life on earth (nucleating a new bubble universe is much less likely than forming a brain). One simple solution is that the vacuum decays on the scale of a Hubble time, so the future volume remains on average finite (see e.g. hep-th/0610079). This is a short time of ~20 billion years. [Note that the anthropic reasoning here is pretty robust: there will be brains in essentially any choice of reference class you like, including an essentially identical copy of your current brain having the deluded belief that he lives on Earth]
This paper suggests instead that a 'standard' volume-weighted slicing measure of eternal inflation resolves the problem: most volume is generated in the highest energy vacuum, and most observers will therefore be formed shortly after its decay, i.e. near a thermalization surface and not a Boltzmann brain. What I don't see is how this is an acceptable solution: doesn't this weighting give the well-known 'youngness paradox' - that most observers will be in a very newly formed vacuum - in contradiction to observation that actually the universe is relatively old?
Perhaps another possibility is that there is some external clock associated with each vacuum. One logical possibility would be something like the ekpyrotic scenario (e.g. astro-ph/0605173): there is no Brain problem as long as the branes eventually re-collide and the entire expanded region is re-thermalized. Or perhaps downwards renormalization of the vacuum energy due to accumulation of super-Hubble quantum fluctuations (e.g. hep-ph/9602316) - though this seems to take too long.
Incidentally, the logical conclusion of the anthropic comments in the Discussion section is perhaps something like the proposal in math.ST/0608592 - though unfortunately it is unclear how this works in the infinite case.