Observed Features of the Universe
• Universe is homogeneous and isotropic on lengths > 100 Mpc
• Universe expanding uniformly
• thermal background of radiation with T~3K
• chemical composition is roughly 75% H, 25% He, + trace
• ordinary matter is more abundant than ordinary antimatter
• nearly scale invariant spectrum of CMB fluctuations
• hierarchy of structure from 1 kpc to 1 Mpc scales
• universe is spatially flat
• ordinary matter is a minority (1/6x) of all matter
• matter is a minority (1/4x) of all energy
• expansion rate accelerating
Observed Features of the Universe
• Universe is homogeneous and isotropic on lengths > 100 Mpc
• Universe expanding uniformly
• thermal background of radiation with T~3K
• chemical composition is roughly 75% H, 25% He, + trace
• ordinary matter is more abundant than ordinary antimatter
• nearly scale invariant spectrum of CMB fluctuations
• hierarchy of structure from 1 kpc to 1 Mpc scales
• universe is spatially flat
• ordinary matter is a minority (1/6x) of all matter
• matter is a minority (1/4x) of all energy
• expansion rate accelerating
Why is the Universe homogeneous and isotropic?
Robs (t0) = radius of observable universe today
~ 1/H0 ~ t0
Robs (t) = size of same patch at time t
 ae
Robs (t e )  Robs (t o ) 
 ao
Rcausal (t e )  a(t e )
te
0

  to


dt
p
 te
a(t )
 ae

a
 o
te




t 
te

 
 1  p  0 1  p
1 p
Why is the Universe homogeneous and isotropic?
Robs (t0) = radius of observable universe today
~ 1/H0 ~ t0
Robs (t) = size of same patch at time t
Robs (t e )
 (1  p )
Rcausal (t e )
 ae

a
 o




 to

t
 e

 ~


(1  p )
 a e

 a
 o




Why is the Universe homogeneous and isotropic?
Robs (t0) = radius of observable universe today
~ 1/H0 ~ t0
Robs (t) = size of same patch at time t
Robs (t e )
~
Rcausal (t e )
 a e

 a
 o




>> 1
universe decelerating
HORIZON PROBLEM
Why is the Universe so FLAT?
8G
k
H 
 2
3
a
Recall:
1   tot 
2
k
a2H 2
1   tot
1   tot
1   tot

o
e

a e
2
a o
2
1
1
 2 2  2
a H
a
>> 1
universe decelerating
FLATNESS PROBLEM
Why so few monopoles?
 ~
gM
3
Rcausal
(te )
if monopoles
are stable:
 a e

~

3
Robs (t e )  a o
gM
 a e

~

3
Robs (t o )  a o
gM




3




3
MONOPOLE PROBLEM
HORIZON PROBLEM
Robs (t e )
~
Rcausal (t e )
(1  p )
 a e

 a
 o




a e
a
FLATNESS PROBLEM
1   tot
1   tot
o
e

a e 2
a o 2
a o
MONOPOLE PROBLEM
 mono
 a e

~ 3
Lobs (t o )  a e
gM




3
t
HORIZON PROBLEM
Robs (t e )
~
Rcausal (t e )
(1  p )
 a e

 a
 o




a e
a
FLATNESS PROBLEM
1   tot
1   tot
o
e

a e 2
a o 2
MONOPOLE PROBLEM
 mono
 a e

~ 3
Lobs (t o )  a e
gM




3
ainitial
a o
t
accelerated expansion
INFLATION
inflation = finite period of accelerated expansion
4G
a  
( 3 p)a
3
 p   
1
3
or
w 
p

  13
T








  12  2  V

 
p



p
 
 
 p 
w 
p


 12  2  V
 12  2  V
1  2
2
1  2
2







1 2
 2   V 
V
V
w < -1/3 means KE < V/2
  3 H    V '
V'

 1
V
Planck units
INFLATIONARY MENU
ENTRANCE
phase transition
“chaos”
stochastic
“tunneling from nothing”
defect driven
INFLATION
Slow roll
EXIT
scalar field decay
flat potentials
bubble nucleation
power-law potentials
de Sitter fluct’s
two or more fields
tensor (R + a R2 +…)
fermi condensate
KE driven
oscillation
extended
Density Perturbations
H nearly constant
Density Perturbations
inflation ends, H-1 grows
  0  
g 
(S )
 2
 
 B
 ;i
 B;i


2 ij  E;ij 
for scalar field, B and E = 0
Newtonian gauge:   
ds 2  a 2 ()[(1  2)d 2  (1  2)dx 2 ]
(T )
g 
0
 
0

0 

hij 
k
uk 

 k 
2
(
a
u k 
 

uk )
prime  d / d
dot  d / dt
uk  (k  U ) uk  0
2
U a
2
1 2
(2
k >>1:
 2V 
 k 
e
8 HV '


2 V '2
 2
ik
a 2k
uk ~
 V ")
ieik
k 3/ 2
k
uk 

 k 
2
(
a
u k 
 

uk )
prime  d / d
dot  d / dt
uk  (k  U ) uk  0
2
U a
1 V'
  2  
V 
2
1 2
(2
 2V 
8 HV '


2 V '2
 2
 V ")
2
 1
V"
 
 1
V
2
2


U

a
H
[6  2]
3H  V '
k
uk 

 
2
(
a
u k 
 

uk )
prime  d / d
dot  d / dt
uk  (k  U ) uk  0
2
U a
2
2
x
2
d uk
dx
2
1 2
(2
 2V 
8 HV '


 ( x   U ) uk  0
2
2
2 V '2
 2
 V ")
xk
2
x
2
d uk
dx
2
 ( x   U ) uk  0
2
2
n 
2
xk
1
4
large x  oscillating
uk ~
ieik
k 3/ 2
small x  growing
uk ~ x (C1 (k ) J n ( x)  C2 (k ) J n ( x))
uk ~ k
 n  12
with n 
1
2
 U
2
 C1   i C2
nearly scale
invariant !
2
x
2
d uk
dx
2
xk
 ( x   U ) uk  0
2
2
n 
2
1
4
large x  oscillating
uk ~
ieik
k 3/ 2
small x  growing
uk ~ x (C1 (k ) J n ( x)  C2 (k ) J n ( x))
uk ~ k
 n  12
~ k
 C1   i C2
( 6  2 )
More generally …
2
x
2
d uk
dx
2
 ( x   U ) uk  0
2
2
n 
2

xk
1
4
6(1 w)
( 2  3 w)
2
need this to
be small
w ~ -1: INFLATION
w >> 1: EKPYROTIC/CYCLIC
AMPLITUDE Strategies
1) Evolve u -equation
2) famous trick
k ~
2
3(1  w)a
2
 uk 


 H / a 


'
3) heuristic:
T
T
~
t / t
1/ t
3/ 2
1/ 2
t
 H
V
~
~ Ht ~ H
~
~
t
V'


2
3/ 2
The Cyclic Universe
w/Neil Turok
with many important contributions from:
Justin Khoury (Princeton), Burt Ovrut (Penn)
and Nathan Seiberg (IAS)
Consensus
(big bang + inflation)
big bang
Consensus
(big bang + inflation)
big bang
inflation
Consensus
Cyclic
(big bang + inflation)
PJS & Neil Turok
big bang
“bang”
inflation
radiation
radiation
matter
matter
dark energy
dark energy ??
???
Consensus
Cyclic
(big bang + inflation)
PJS & Neil Turok
big bang
“bang”
inflation
radiation
radiation
matter
matter
dark energy
dark energy ??
???
V
Y
Consensus
Cyclic
(big bang + inflation)
PJS & Neil Turok
big bang
“bang”
inflation
radiation
radiation
matter
matter
dark energy
dark energy ??
???
V
Y
Consensus
Cyclic
(big bang + inflation)
PJS & Neil Turok
big bang
“bang”
inflation
radiation
radiation
matter
matter
dark energy
dark energy ??
???
V
Y
Consensus
Cyclic
(big bang + inflation)
PJS & Neil Turok
big bang
“bang”
inflation
radiation
radiation
matter
matter
dark energy
dark energy ??
???
V
Y
Consensus
Cyclic
(big bang + inflation)
PJS & Neil Turok
big bang
“bang”
inflation
radiation
radiation
matter
matter
dark energy
dark energy ??
???
V “contraction”
Y
Consensus
Cyclic
PJS & Neil Turok
big bang
“bang”
inflation
radiation
radiation
matter
matter
dark energy
dark energy ??
“contraction”
???
“crunch”
the “bounce”
(big bang + inflation)
Consensus
Cyclic
PJS & Neil Turok
big bang
“bang”
inflation
radiation
radiation
matter
matter
dark energy
dark energy ??
“contraction”
???
“crunch”
Reproduces successful predictions
the “bounce”
(big bang + inflation)
Consensus
Cyclic
PJS & Neil Turok
big bang
“bang”
inflation
radiation
radiation
matter
matter
dark energy
dark energy ??
“contraction”
???
“crunch”
Fewer ingredients: no need for inflation
the “bounce”
(big bang + inflation)
Consensus
Cyclic
PJS & Neil Turok
big bang
“bang”
inflation
radiation
radiation
matter
matter
dark energy
dark energy ??
“contraction”
???
“crunch”
Dark energy given a purpose
the “bounce”
(big bang + inflation)
Consensus
Cyclic
PJS & Neil Turok
big bang
“bang”
inflation
radiation
radiation
matter
matter
dark energy
dark energy ??
“contraction”
???
“crunch”
Avoids infinities?
the “bounce”
(big bang + inflation)
Consensus
Cyclic
PJS & Neil Turok
big bang
“bang”
inflation
radiation
radiation
matter
matter
dark energy
dark energy ??
“contraction”
???
“crunch”
More complete theory of cosmic history
the “bounce”
(big bang + inflation)
The Cyclic Universe
“branes”
V
Y
Y
Field-theory
M-theory
The Cyclic Universe
THE BOUNCE
V
Y