Transcript Issues in Inflationary and Cyclic Cosmology

Great explanatory power:
horizon – flatness – monopoles – entropy
Great predictive power:
?
?
?
Wtotal = 1
nearly scale-invariant perturbations
slightly red tilt
adiabatic
gaussian
gravitational waves
consistency relations
“the classic(al) perspective”
dominantly a classical process…
an ordering process…
in which quantum physics plays
a small but important perturbative role
“the (true) quantum perspective”
Inflation is dominantly a quantum process…
in which (classical) inflation amplifies
rare quantum fluctuations…
resulting in a peculiar kind of disorder
Eternal Inflation
Vilenkin, 1983
PJS, 1983
“I would argue that once one accepts eternal
inflation as a logical possibility, then there is no
contest in comparing an eternally inflating version of
inflation with any theory that is not eternal....”
Alan Guth, 2000
•
Powerfully predictive?
Linde, Linde, Mezhlumian, PRD 50, 2456 (1994)
• If Eternal to the Past, then maybe we can
uniquely determine the probabilities.
SINGULARITY PROBLEM
cf. Borde and Vilenkin, PRL 72, 3305 (1994); PRD 56, 717 (1997)
•
Maybe can find measure that does
not depend on initial conditions
Global
vs.
Local Measures?
•
Immune from initial conditions?
• Important properties insensitive to initial
conditions?
Garriga, Guth and Vilenkin, hep-th/0612242
Aguirre, Johnson and Shomer, arxiv:0704.3473
Chang, Kleban, Levi, arxiv:07012.2261
Aguirre, Johnson, arxiv:0712.3038
“Persistence of Memory Effect”
tinitial
• Important properties insensitive to initial
conditions?
YELLOW: anisotropic!
t=0
• Perhaps we know the Iniitial Condiions??
Entropy Problem:
requires entropically disfavored initial state?
Penrose
“the (true) quantum perspective”
• Singularity problem
theory incomplete ?
• Unpredictability problem
threatens flatness and
scale invariance?
• Persistence of memory
threatens isotropy?
• Entropy problem
advantage  problem
“the (true) quantum perspective”
• Singularity problem
• Unpredictability problem
• Persistence of memory
1) Inflation is fast
energy density large or
Hsmoothing > Hnormal >> Htoday
• Entropy problem
2) Quantum physics is random
“the (true) quantum perspective”
• Singularity problem
• Unpredictability problem
• Persistence of memory
• Entropy problem
But suppose
Hsmoothing << Hnormal
How do we go from small H to large H ?
H =  4  G (   p)
Hsmoothing contracting
implies must resolve singularity problem
Ekpyrotic model
Cyclic model
“ekpyrotic
contraction”
“ekpyrotic
contraction”
bounce
bounce
radiation
radiation
..
.
matter
dark energy
ekpyrotic phase: ultra-slow contraction
with w >>1
Erickson, Wesley, PJS. Turok
Erickson, Gratton, PJS, Turok
H =
2
0

8G m
3
a
3


0

8G r
3
a
4

0
2
a
6
8G
3 a 3 (1w )
 ... 
k
a2
 inflaton
w >> 1
N.B. Do not need finely tuned initial conditions
or inflation or dark energy …
ekpyrotic phase: ultra-slow contraction
with w >>1
Erickson, Wesley, PJS. Turok
Erickson, Gratton, PJS, Turok
H =
2
0

8G m
3
a
3


0

8G r
3
a
4

0
2
a
6
8G
3 a 3 (1w )
 ... 
k
a2
 inflaton
w >> 1
… and avoid chaotic mixmaster behavior …
ekpyrotic phase: ultra-slow contraction
with w >>1
Erickson, Wesley, PJS. Turok
Erickson, Gratton, PJS, Turok
H =
2
0

8G m
3
a
3


0

8G r
3
a
4

0
2
a
6
8G
3 a 3 (1w )
 ... 
k
a2
 inflaton
w >> 1
… and Hsmoothing << Hnormal and contracting
ekpyrotic phase: ultra-slow contraction
with w >>1
Erickson, Wesley, PJS. Turok
Erickson, Gratton, PJS, Turok
H =
2
0

8G m
3
a
3


0

8G r
3
a
4

0
2
a
6
8G
3 a 3 (1w )
 ... 
k
a2
 inflaton
w >> 1
… and scale-invariant perturbations of scalar fields.
How to get w >> 1 ?
V
“branes”
Field-theory

 2  V ( )

w=

1
2

  V ( )
1
2
1
2

Curiously, precision tests can distinguish
the two key qualitative differences
between inflation and ekpyrotic/cyclic models
• Hsmoothing is exponentially different
gravitational waves
• w is orders of magnitude different
local non-gaussianity
“local” non-gaussianity generated when modes
are outside the horizon (“local” NG)
z=zL+
2
f
z
L
5 NL
3
Maldacena
Komatsu & Spergel
“intrinsic” NG contribution (positive fNL)
3
depending on e = (1 + w)
2
or steepness of potential
int
f NL ~
e ek e conv ~
wek wconv