MEASURES OF THE MULTIVERSE Alex Vilenkin Tufts Institute of Cosmology Stanford, March 2008
Jan 15, 2016
MEASURES OF THE MULTIVERSE
Alex Vilenkin
Tufts Institute of Cosmology
Stanford, March 2008
Salute to Andrei !
The measure problemi+
Bubbles(pocket universes)
We want to find Pj – probability for a randomly picked observer to be in a bubble of type j.
The number of bubbles & the number of observers per bubble are infinite.
Need a cutoff. Results are strongly cutoff-dependent.
Measure proposals
Global time cutoff Garcia-Bellido, Linde & Linde (1994)Linde, Linde & Mezhlumian (1994)
Pocket-based Garriga, Schwartz-Perlov, A.V. & Winitzki (2005) Easther, Lim & Martin (2005)
Adjustable cutoff Linde (2007)
Causal-patch Bousso (2006), Susskind (2007)
We are in the process of working out the properties ofdifferent measures and their observational predictions.
THIS TALK:
Scale-factor cutoff measure
Predictions for .
Contrast with pocket-based measure
Based on work with Alan Guth,Andrea de Simone & Michael Salem.
,,Q
Work in progress…
t = const
steady-state evolution.
The distribution does not depend on the initial state(but depends on what we use as t).
t
Garcia-Bellido, Linde & Linde (1994)Linde, Linde & Mezhlumian (1994) Linde (2007)
Global time cutoff
t Possible choices of t :
(i) proper time along geodesics orthogonal to ;(ii) scale-factor time, .at
Volume in regions of any kind grows as
Linde & Mezhlumian (1996),Guth (2001), Tegmark (2004),Bousso, Freivogel & Yang (2007)
.~~ , max Plj MHeV
Observers who take less time to evolve are rewarded by a huge volume factor.
Observers who evolve faster than us by and measure are more numerous by
Gyr 1
)10exp() exp( 60
2.9KCMBT
Driven by fastest-expanding vacuum
Proper-time cutoff is ruled out.
Proper time cutoff leadsto “youngness paradox”
Scale-factor cutoff – a mild youngness bias
.3 , aV jGrowth of volume:
min)3( – decay rate of the slowest-decaying vacuum
The probability of living at T = 2.9K
is enhanced only by . 2.1/ 30 TT
Not ruled out and has interesting observational consequences.
Pocket-based measure
jjj wpP
jp – bubble abundance,
Garriga, Schwartz-Perlov, A.V. & Winitzki (2005)
Easther, Lim & Martin (2005)
– weight factor. Sample equal comoving volumes in all bubbles (all bubble spacetimes are identical at early times).
jw
3jj ZP
Slow-roll expansion inside the bubble
Note: large inflation inside bubbles is rewarded.
Similar Z-dependence for Linde’s adjustable cutoff.
Predictions for : Depend on the slow-roll expansion factor Z in the bubbles.
Pocket-based measure favors large inflation:
3jj ZP .1
Scale-factor cutoff does not:
1.-3 ,3 jj ZP
(unless large Z are strongly suppressed in the landscape)
Detectable negative curvature is feasible.
Freivogel, Kleban, Martinez & Susskind (2006)
Predictions for : Q
“Q catastrophe”Feldstein, Hall & Watari (2005)Garriga & A.V. (2006)
Depend on the shape of inflaton potential.
Pocket-based measure:
3)( ZQP – exponential Q-dependence
Scale-factor cutoff:
Mild Z-dependence no Q-catastrophe.
The exact form of P(Q) is model-dependent.
Distribution for : standard approach
A.V. (1995), Efstathiou (1995),Martel, Shapiro & Weinberg (1998).
Assume
)( )()( )()( selecprior fPP
constP prior )()( in the range of interest.
Assume )()(selecf asymptotic fraction of matter
clustered in large galaxies ( ).
Weinberg (1987), Linde (1987),
)(logd
dP
*
1012MM .
All constants other than are fixed.
Appropriate forpocket-based measure
0
Distribution for : scale-factor cutoff
Suppose observers do their measurements of at a fixedproper time after galactic halo collapse.
Gyr 5
(Allowing for chemical and biological evolution.)
)(P fraction of matter clustered in large galaxies 5 Gyr prior to the cutoff.
])/([ )( 1 aafadaP c
ac
Volume thermalized in scale factor interval da(reflects youngness bias).
Proper time corresponding to scalefactor change (ac /a).
3 ,)]2/3sinh([)( 3/21 HHa
Cutoff at .
Press-SchechterWarren et. al.
caa
)(logd
dP
*
Gyr 5
0
Once dominates, expansion accelerates, triggering scale-factor cutoff. Large values of are suppressed.
De Simone, Guth, Salem & A.V. (2008)
1012MM .
Varying M and
10 ,10 ,10 101112 MM .
Gyr 8 ,5 ,2
Including negative
ddP
ddP
*
*
(A) Count all halos formed more than 5 Gyr before the big crunch.
(B) Count all halos formed more than 5 Gyr before turnaround.
CONCLUSIONS
Scale-factor cutoff is a promising measure proposal.
Prediction for is a good fit to the data.
No Q-catastrophe.
Possibility of a detectable curvature.
No “Boltzmann brain” problem.(Assuming that the slowest-decaying vacuum does not support BBs)