Leonardo Senatore (Stanford and SLAC)
What did we learn?
Wednesday, March 19, 14
How the universe begun
• it was very hot, and started with inflation
• To me, this is a milestone for mankind
Wednesday, March 19, 14
Congratulations
• My congratulations and my thanks
– to Cho-Lin Kuo and the BICEP2 Collaborations for the discovery of
Primordial B-modes
– to Linde and Guth for the formulation of Inflation
Wednesday, March 19, 14
What did we measured?
Wednesday, March 19, 14
Energy Scale of Inflation
• The standard story
2
H
hh2 i ⇠ 2
MPl
2
H
2
hh i ⇠ 2
MPlInflationary model
• For a slow roll
V( )⇠
)
2
MPl
H2
detection
)
)
V
hh i ⇠ 4
MPl
V ( ) ⇠ 1016 GeV
2
• Huge energy scale probed by cosmology
– the universe was very hot
– The energy scale is remarkably close to the Grand Unification Scale
• maybe further evidence of GUT and particle physics BSM implications
• Awesome!
Wednesday, March 19, 14
(1)
(1) (2)
(2)
(3)
How in detail did Inflation happened?
Wednesday, March 19, 14
5
•
•
•
10
A
Lesson
H
11
⇠ 10
MPl
Amplitude
of signal is not associated necessarily
with H
⇢
MPl
2
2
⇠ ✏ ; M . MPl ) hh i . ✏
⇠✏
⇥ hh ivacuu
–⇢total
there is possibly a larger signal that dominates the M
standard
oneH
Pl
HM
The2Gravity
Waves
ared⇢
nothnecessarily of quantum 2origin ⇢
2
2
H MPl hh i ⇠
) hh i ⇠
2
d
log
!
⇢
M
!⇠H a robust prediction oftotal
Scale invariance of the signal remains
Inflation Pl
dEh
M2
dEh
M2
⇠ 2
)
⇠ 2 ⇥ Nparticles
d!
MPl
d! Nparticles
MPl
n
n
n+1
n
n
3/2
˙
⇠
t ⇠ tn
2
2
˙
) m (t) ⇠ (t
Wednesday, March 19, 14
2
tn )
MPl
•
•
•
•
•
2
H
hh2 i ⇠ 2
MPl
2
VofHGravity
2
Energy hhScale
Waves
i ⇠2 4
2 2 2
V ( )2⇠ MH
)
Pl H
hh i ⇠ 2
MPlwaves:
Energy
of
gravity
) detection )
(2)
hh iM⇠ 2
Pl M
Pl
16
2
V ( ) ⇠ 10 GeV
V ( ) V⇠ MPl
H 2 )(3)h
V M 2 H 2 ) hh2 i ⇠
2
2
2 ( ) ⇠
V
2
4
⇠ MPl H
) hh 2i ⇠ 24 Pl
2V ( ) H
2
2 2
4 Pl
M
MPl!⇠H ⇠ MPl H hh i ⇠
)H detection ) (4)V
hh i ⇠ 2
) ⇢h ⇠ MPl (@h)
16 2
MPl
2)
16
detection
)
V
(
)
⇠
10
HGeV
) detection 2 ) HV ( ) ⇠ 10 GeV
2
hh i ⇠ 2
) ⇢(5)
hh i ⇠ 2
h ⇠
2
2
H
M
MPl 22
H
2
2 Pl
2
2
2
2
2
2
2
4
hh
i
⇠
)
⇢
⇠
M
(@h)
⇠
M
H
This is hh
minuscule
i⇠ 2
) ⇢h ⇠ MPl (@h) 2!⇠H ⇠ MPl H
⇠H
h hh i Pl
Pl
!⇠H
!
⇠
H
M
V
MPl
Pl
2
2
2
V ( ) ⇠ MPl H
) hh i ⇠ 4
For an !
harmonic
⇠ H oscillator with ! ⇠ H , vacuum energy
MPlis Evac ⇠ ! ⇠ H
16
E
⇠
!
⇠
H
)
detection
)
V
(
)
⇠
10
GeV
vac
So
⇢h ⇠ H 4 ) 2one quanta
) Minuscole!
H 2 per Hubble volume
2
2
2
hh i ⇠ 2
) ⇢h ⇠ MPl (@h) !⇠H ⇠ MPl
H 2 hh2 i ⇠ H 4
MPl
One graviton with ! ⇠ H per Hubble volume
• Consider our universe, which is accelerating. One quanta in the whole universe.
– Good luck with detecting it!
Wednesday, March 19, 14
Energy Scale of Gravity Waves
• In fact, we normally look at other sources
Wednesday, March 19, 14
Available Energy
• By definition, in Inflation there is a physical clock
˙ 2 ⇠ ḢM 2 ⇠ ✏H 2 M 2
Pl
Pl
2
H
˙ ⇠ ḢM 2 ⇠ ✏H 2 M 2
2
10
Pl
Pl
h( T /T ) i ⇠
⇠
10
2
2
⇢
HM
✏M
H
Pl power spectrum
• From
h( T /T )2 i ⇠
⇠ 10
hh2 ithe
⇠2 temperature
2
2
2
2
2
10 4
✏M4Pl
˙ ⇠
⇢total
)
ḢM M
⇠
✏H
M
⇠
10
H
H
Pl
Pl
Pl
2
2
2
10 4
4
˙
⇠
ḢM
⇠
✏H
M
⇠
10
H
H
Pl
Pl
˙22 ⇠ 10H H 4
H4
2
H
hh i ⇠ 2
hh2 i ⇠ 2
M
Pl
nt ⇠ 10%
MPl
Vuse the potential
52
V
2 energy (we2 cannot
So,
there
is
enough
2
2energy, just
2 its gradients)
H
'
10
H
V ( ) ⇠ MPl Hmin, vacuum
) hh i ⇠ 4 V ( ) ⇠ MPl H ) hh i ⇠ 4
MPl
MPl
3
hhpossibility:
i
1
lmin
50
16
Huge
16
)
detection
)
V
(
)
⇠
10
2) ⇠
2⇠
2 GeV
2
2
2GeV
p
) 2 detection
)
V
(
10
.
⇠
⇠
25%
⇢h ⇠ H MPl hh i = if = ⇢ ˙ 2 2⇠ ✏H MPl ) hh i ⇠ ✏
3/2
hh i
lmax
200 2
Nmodes
H
2
2
2
2
2
2
2
2
hh
i
⇠
)
⇢
⇠
M
(@h)
⇠
M
H
˙
h
Pl4
Pl H
2
2Pl ⇠ ✏H
2 MPl
2
2
2 2
!⇠H
⇠
ḢM
hh ki resolution
⇠ 2 ⇠)
kL ⇢h ⇠ MPl (@h) 2 !⇠H ⇠MMPlPl H hh i ⇠ H
Mthat
Pl usually this energy
Problem is
sitsHthere
and
nothing
!⇠
H does
2
10
h( TEFT
/T )(kiren
⇠ ) 2 ⇠ 10
P
(k
)
=
P
NL
ren
1
loop
!⇠H
⇠!⇠H
✏M
Pl Evac◆
✓
◆
✓
– not converted in Gravity Waves
2
⇠3
4 2
2
2
2
10 quanta
4
4
k
k
˙
⇢
⇠
H
) 10one
per Hubble
volume
Evac2 ⇠ ! ⇠ H
h✏H M
)
⇠
ḢM
⇠
⇠
H
H
Pl
Pl
h!k i ⇠4 ↵1
+2 ↵2
Hnow )
It⇢needs
converted
inflation
kimplement.
kH
⇠ Hto be )
one quantaHper Hubble
volume
Minuscole!
(
NL
)
2
10
•
•
•
•
•
10
h
2
⇠
⇤
Hinflation
and
not1 dilutedHaway
now
Z
Wednesday, March 19, 14
hh2 i ⇠
˙
2
2
MPl

2
2
2
V
(
Conversion and not-dilution
• A proof of principle
with Green, Horn, Silverstein PRD 2009
• Trapped Inflation
– Consider wiggly potential
V (φ)
– At each wiggle, coupling
V ⇠
X
2
(
n)
n2 n
n
3/2
˙
⇠
n
t
⇠
t
n
2
2
2
2
2
2
2
2
˙
⇢)
H(t)M⇠Pl hh
if = m⇢2˙(t)
2 ⇠ ✏H
2 MPl 2 )
h ⇠m
(t i t=
˙
n) )
⇠t ⇠
(t t tn )
X
n
2 2 2
X
2
2
2
˙V ⇠
⇠ ḢM
(
2 2
n ) ✏H
n
⇠
M
Pl
Pl
V ⇠
(
n)
2
n
t ⇠ nt
2
hh i ⇠ ✏
φ
(1)
(2)
2
˙
n
)
m
(t)
⇠
t
2for
(1) (t
– At t ⇠ tn 2, adiabaticity
is
broken
many
particles
are
produced
2
2
2
2
2
n
⇢h ⇠ H 2M2Pl hh˙ 2i =H
if =
MPl ) hh i ⇠ ✏
(3)
2 ⇢ ˙ 2 ⇠ ✏H10
)
m )(t)i⇠2⇠ (t3/2tn ) ⇠
2
2
2
22
2
2(2)
X
h(
T
/T
10
˙
t
⇠
t
˙
Hn MPlthh
i = if = ⇢ ˙ 2 ⇠ ✏H MPl 2) (4)
h
2 ⇠(t)
2 ⇠
22 ⇢h ⇠
X
)
(t
)
˙ 2 ⇠ ḢM
nm
n
2
⇠
✏H
M
✏M
2
2 Pl
n
Pl
V ⇠
(Pl
(3)
n)
22 V ⇠
2
n
(
)
2
2˙ 2 (t
2
2
˙
n
)
m
(t)
⇠
t
)
X
n
n
H 2 of 10 ⇠
⇠n ✏H
n22 conversion
2ḢM
2in
10nM
4 happens
4
– We
achieved
energy
,
and
this
continuously:
Pl
Pl
˙
h(⇢ T⇠/TH)2 M
i⇠
⇠
⇠=10
(5)
)
⇠
✏H
M
H
H
2 ḢM
2
22
2 2 ⇠ 102
X
2
Pl
Pl
hh
i
=
if
⇢
⇠
✏H
M
)
hh
i
⇠
✏
(4)
2
˙
h
Pl ✏M
Pl
2 n2 10
V
⇠
(
)
H
Pl
n
n+1
2
n
t ⇠2 ⇠t2naway,
V
⇠
(
)
n+1
2
2but 2gets
• ˙ 2n⇠ ˙ḢM
dilutes
replenished
by n⇠
h(
T
/T
)
i
⇠
2 H
2
2
10
4
✏H
M
(5)
)2
⇠PlḢMPl ⇠ Pl✏H MPl ⇠ 10 H ✏M 2 H 410n˙ 3/2
(6)
2
2
2
3/2
2
2
2
2
n
⇠
Pl⇠
hh
i
⇠
˙
˙
n
n
H
n
2
⇢
H
M
hh
i
=
if
)
m
(t)
⇠
(t
t
)
n
⇠
2
10
2 convert
n into Gravity
n
h
– We now
need
to
Waves
(continuously)
n
h(2 n+1
T /T
)H
i
⇠
⇠
10
(6)
Pl
2 2
2 2
2
2
10 4 2
2
˙
2
2 (7)H
Pl
✏M
hh i ⇠ M
X
)
⇠
ḢM
⇠
✏H
M
⇠
10
H
2 Pl 2
2
2
2
2 3/2
Pl
Pl
⇢ 2⇠ H M hh i = if = ⇢ ˙ 2 ⇠ ✏H M
2
n
Wednesday, March 19, 14
˙
2MPl
⇠
2
2
2
h
10
24
Pl
4
Pl
Conversion and not-dilution
• Conversion to Gravity Waves
• Imagine
n
decay to
n
• In this decay,
n+1
with Silverstein and Zaldarriaga 1109
V (φ)
(out of many)
n
3/2
n+1
˙
n
⇠
– gravitational
bremsstrahlung
is produced
n
3/2
n
n
⇠ ˙
t ⇠ tn
t ⇠ tn
⇢
HM
2
2
2
2
) m (t) )
⇠ ˙m
(t2hh
(t)it⇠n⇠)˙ 2 (t tn )22
⇢total MPl
X
X
2 2
2
2
2
10
V ⇠
( V ⇠n ) ˙( n⇠ 10n ) H 4n
n
n
φ
2nt ⇠
2 10%
2
2
2
2
⇢
⇠
H
M
hh
i
=
if
=
⇢
⇠
✏H
M
)
hh
i
2
˙2
2
2 h 2
2
2
Pl
Pl
⇢h can
⇠H
i
=
if
=
⇢
✏H
M
)
hh
i
⇠
˙52H⇠
– How large
this M
be?Pl hh
Pl
H
'
10
2 vacuum
˙ 2 ⇠ ḢM 2 ⇠ ✏H 2 Mmin,
Pl23
Pl
2
2
2
5
˙ ⇠ signal
hh
i
1
l
50
H
'
10
H
• Detectable
with
min
ḢMeven
⇠
✏H
M
2
min,
vacuum
Pl
Pl
⇠
⇠
25%
2 23 3/2H. p
10 ⇠
h( T /T
)hh
ihh⇠
⇠1N10modeslmin lmax50 200
i
2
i
2
– after some engineering
H
p
. 10
⇠
⇠
⇠ 25%
✏M
2
Pl
2
3/2
hh⇠
i 10
lmax
200
N⇠modes
h( T /T ) i ⇠
k
k
resolution
22
2
2L 2
10 4
4
˙
)✏MPl ⇠kresolution
ḢMPl ⇠
✏H
M
⇠
10
H
H
⇠ kL
Pl
P
(k
)
2 (k2ren ) 2= P1 loop
NL
EFT
ren
2
2 H
10
4
4
P (k ) = P
(k )
Wednesday, March 19, 14
•
•
105
Lesson
H
11
Bad: M ⇠ 10
Pl
– Amplitude
of signal is not associated necessarily
⇢
MPl
2 with H
2
⇠ ✏ ; M . MPl ) hh i . ✏
⇠✏
⇥ hh iv
⇢total
MPl
H
– Signal
not necessarily quantum
d⇢h
⇢ HM
2
2
2
2
But
H MPl hh i ⇠
) hh i ⇠
2
d log ! !⇠H a robust prediction ⇢total MPl
– Scale invariance of the signal remains
2
2
dE
M
dE
M
h
h
– Easier to produce
of magnitude
⇠ 2 observable
) tensor modes, by several
⇠ orders
⇥
N
particles
2
d!
MPl
d! Nparticles
MPl
– Possible non-Gaussian window
n
n
n+1
n
n
3/2
˙
⇠
t ⇠ tn
) m2 (t) ⇠ ˙ 2 (t
Wednesday, March 19, 14
tn )2
very similar to what happens to the vacuum state of an harmonic oscillator when one opens
he evolution of the wave function with time. As discussed, at early times
up very abruptly the width of the potential well.
he wave function follows adiabatically the wave function of the would be
This is an incredibly squeezed state with respect to the ground state of the harmonic
r with those time dependent mass and frequency
given by (103). However,
60
oscillator
with
frequency
!
⇠
e
H.
This
is no
more the vacuum state of the late time
• In usual vacuum fluctuations, Gaussianitystate
of the
fluctuations
rops below the Hubble rate, the natural time scale of the harmonic oscillator
harmonic oscillator. It has a huge occupation number, and it looks classical.
to keep up
with
Hubbleof
expansion.
The
state getsisfrozen
on the parameters
– as
vacuum
harmonic
oscillator
Gaussian
!(t) ⇠ H. Bu substituting k/a ! H, a ! k/H,the wave function at late
Non-Gaussian Window
|0iki /a⌧H =
(x)Y X
~ki ⌧Ha
e
3
1 ki
V H2
2
~
ki
V (x)
~
k
|
~ki i
Rapid Expansion
(107)
(x)
V (x)
in field space. Its width is given by
h
~k
2
H2
H
x
x
3 3 ~
0
~
= ~k,~kfluctuations
' (2⇡)are(knot
+ kvacuum,
) 3 as not
V Gaussian
!1
(108)
•~k0 iHere
0V
3
k
k
Figure 9: Formation of a squeezed state by the rapid expansion of the universe.
28
Let us check that indeed that wave function is semiclassical. The typical condition to check
if a wavefunction is well described by a semiclassical approximation is to check if the -length
• This motivates analysis of non-Gaussianity of B-modes
– Yes, they can!
29
hh3 i
1
lmin
50
.p
⇠
⇠
⇠ 25%
2
3/2
hh i
lmax
200
Nmodes
kresolution ⇠ kL
PNL (kren ) = P1 loop EFT (kren )
✓
◆2
✓
◆⇠3
Wednesday, March 19, 14
k
k
n
n
⇠
Scale Invariance
t⇠t
2 is scale invariant
2
2
˙
the
signal
) m (t) ⇠ (t tn )
X
2 2
V ⇠
(
n)
n
n
• Everything happens
in the same way at every e-fold
–
n
• It is very hard to obtain scale invariance without being in de Sitter
2
2
2
2
2
⇢hwe⇠
Hit? MPl hh i = if = ⇢ ˙ 2 ⇠ ✏H MPl )
• Could
make
2
2
– Theorem:
scalar:2 if there
is
a
single
scalar field, this is impossible
˙ 2 ⇠ forḢM
⇠
✏H
M
Pl
Pl
with Baumann and Zaldarriaga
• but more than one field can 2
JCAP 2010
H
2 waves: only inflation can 10
– Theorem:
for
gravity
make them scale invariant
h( T /T ) i ⇠
⇠
10
2
✏MPl
with Perko, Silverstein and Zaldarriaga
in progress
2
2 n ⇠ 10% 2
2
10 4
˙
• This)
motivates analysis
of tilt at t⇠ ✏H M
⇠ ḢM
Pl
Pl ⇠ 10 H
5
H
'
10
Hmin, vacuum
2
H
3
2
Wednesday, March 19, 14
How did Inflation begun?
Wednesday, March 19, 14
Seeing the beginning of Inflation
• Very mild tension with Planck
with Bousso and Harlow
1210
– Maybe scalar fluctuations are smaller at large angles
– Naturally associated with a steepening of Inflationary potential
– Can be associated with us originating from a bubble
• Interesting to check in the data if this is possible
– Both large angle CMB
– and Large Scale Structures
Wednesday, March 19, 14
Conclusions
• Inflation and Gravitational Waves have been discovered
– Just beautiful
• Now, after celebrating,
– we want to know how Inflation happened and how it started
• this is not ungratefulness
• As normal, any discovery allows the possibility of addressing new questions
– in a never ending story
Wednesday, March 19, 14