Towards chaotic inflation in SUSY GUTs
The rebirth of D-term inflation
arxiv[hep-ph] 1406.6300, 1410.xxxx
Valerie Domcke
SISSA, INFN Trieste
in collaboration with
W. Buchmüller, K. Schmitz
and T. Yanagida
inflation
ΛGUT
MPP
M
Motivation
Data:
r ∼ 0.1 (?)
→
1/4
V0
∼ 1016 GeV ∼ ΛGUT
Coincidence!
Amazing!
∆ϕ & few MP
SUSY GUTs
→ How can we link the scale of inflation to a scale of particle physics?
Theory: supersymmetric D-term hybrid inflation
consistent in supergravity
no cosmic string problem
new regime with very different predictions
D-term inflation: data and theory
— Valerie Domcke — SISSA — 02.10.2014 — Page 2
Outline
small- and large-field models of inflation
the chaotic regime of D-term hybrid inflation
dynamical generation of a Fayet-Illiopoulos term
conclusion and outlook
D-term inflation: data and theory
— Valerie Domcke — SISSA — 02.10.2014 — Page 3
Some observations about slow-roll inflation
The basics:
V (ϕ)
D-term inflation: data and theory
— Valerie Domcke — SISSA — 02.10.2014 — Page 4
Some observations about slow-roll inflation
The basics:
N∗ ' 50
=
V (ϕ)
As =
ϕend
ϕ∗
1
2
V0
V
2
V∗
24π 2 ∗ ,
,
η=
V 00
V
ns = 1 − 6∗ + 2η∗ , r = 16∗
∆ϕ & 5 MP
D-term inflation: data and theory
N
50
p
r
0.1
[Lyth ’96]
— Valerie Domcke — SISSA — 02.10.2014 — Page 4
Some observations about slow-roll inflation
The basics:
N∗ ' 50
=
V (ϕ)
As =
ϕend
1
2
V0
V
2
V∗
24π 2 ∗ ,
,
VR HΦL
V ∼ λΛ4
Φ @MP D
N
50
p
r
0.1
[Lyth ’96]
Large-field models:
Small-field models:
0
V 00
V
ns = 1 − 6∗ + 2η∗ , r = 16∗
∆ϕ & 5 MP
ϕ∗
η=
r < 10−3
V ∼ m2 ϕ2
r ∼ 0.1
Can large-field models be connected to grand unification?
D-term inflation: data and theory
— Valerie Domcke — SISSA — 02.10.2014 — Page 4
D-term hybrid inflation in a nutshell
A supersimple model:
[Binetruy, Dvali ’96; Halyo ’96] [Kawasaki, Yamaguchi, Yanagida ’00]
U (1) gauge symmetry with Fayet-Iliopoulos term ξ
W = λφS+ S− ,
K = 21 (φ + φ̄)2 + S+ S̄+ + S− S̄−
ξ: vacuum energy
φ: inflaton ϕ,
tree-level flat
S± : waterfall field,
|S+ | destabilize at
ϕc =
gp
2ξ
λ
ϕ
s
D-term inflation: data and theory
— Valerie Domcke — SISSA — 02.10.2014 — Page 5
D-term hybrid inflation in a nutshell
A supersimple model:
[Binetruy, Dvali ’96; Halyo ’96] [Kawasaki, Yamaguchi, Yanagida ’00]
U (1) gauge symmetry with Fayet-Iliopoulos term ξ
W = λφS+ S− ,
K = 21 (φ + φ̄)2 + S+ S̄+ + S− S̄−
φ: inflaton ϕ,
tree-level flat
S± : waterfall field,
|S+ | destabilize at
gp
ϕc =
2ξ
λ
0.5
4
Scalar potential VHjL @L GUT
D
ξ: vacuum energy
0.4
new: ϕ2
ln ϕ
0.3
0.2
jc
0.1
0.0
Inflaton field j @M P D
λ g: D-term hybrid inflation. λ g: new regime
D-term inflation: data and theory
— Valerie Domcke — SISSA — 02.10.2014 — Page 5
Quantum mechanics: tachyonic growth
Close to the critical point:
ϕ(t) ' ϕc + ϕ̇c t
→
V (s; t) '
1 2 2 1 3 2
g ξ − D ts + O(t2 , s4 )
2
2
→ tachyonic growth of sk for small k: [Asaka, Buchmüller, Covi ’01]
9 2
2 −2Ht
3
s¨k + k e
− H − D t sk = 0
4
s0
< s2 HtL >1 2  s0
100
10-2
spinodal time
hs2 (t)i = svacuum
without backreaction
10-1
smin
10-3
loc
tsp
HestimateL
tdec
1
2
Time t @1  Hc D
3
4
decoherence time
|sk (t)πsk (t)| ~
ṡ/H > H/(2π)
tsp
HestimateL
5
6
D-term inflation: data and theory
— Valerie Domcke — SISSA — 02.10.2014 — Page 6
Classical evolution: backreaction
Backreaction sets in once we overshoot the minimum:
1 2 2
λ2 2
g2
2
ϕ̈ + 3H ϕ̇ + λ s ϕ = 0 , s̈ + 3H ṡ − g ξ − ϕ s + s3 = 0
2
2
2
Time t @1  Hc D
1.5
smin
1.0
with backreaction
0.5
0.0
tdec
sHtL
matching
1
2
3
4
Time t @1  Hc D
5
6
15
600
500 0
V Hj, sL
0
Time t @1  H c D
2
10
s AMPl ‘ 10 4 E
2.0
5
1
100
0
2.0
1.5
1.0
200
tdec
0.5
0.0
22.714 22.715 22.716
j @MPl D
0
0
500
Inflaton field j @MPl D
5
10
15
Number of e-folds Ne
800 700
without backreaction
Waterfall field s AMPl ‘ 103 E
100 < s2 HtL >12  s0
2.5
20
inflaton field tracks local minimum. λ/g sets ratio of semi-axes.
D-term inflation: data and theory
— Valerie Domcke — SISSA — 02.10.2014 — Page 7
Implications for cosmology and particle physics
After the critical point: V (ϕ, smin (ϕ)) = 21 λ2 ξ ϕ2 1 −
2
1ϕ
2 ϕ2c
m2 ϕ2 inflation + small correction!
with ϕc ∝ g/λ > MP . →
predictions:
As '
λ4 ϕ4∗ ϕ2c
192π 2 g 2
1 ϕ2∗
1+
,
2 ϕ2c
ns ' 1−
8
ϕ2∗
1−
1 ϕ2∗
4 ϕ2c
,
r'
32
ϕ2∗
ϕ2
1 − ∗2 .
ϕc
e.g. g 2 = 21 , λ = 5 · 10−4 : ϕ∗ = 14.5 MP , ns = 0.963, r = 0.083
constraints:
√
sufficient inflation after ϕc : λ . 10−3 , ξ & 2 × 1016 GeV
√
validity of this formalism: λ & 10−4 , ξ . 2 × 1017 GeV
no cosmic string problem!
chaotic inflation with slightly reduced r. GUT scale FI-term.
D-term inflation: data and theory
— Valerie Domcke — SISSA — 02.10.2014 — Page 8
Final remarks on D-term ’hybrid’ inflation
We retrieve chaotic inflation from D-term hybrid inflation
Inflation is linked to the decay of a GUT-scale false vacuum
Interplay of quantum and classical dynamics
If BICEP is dust, ’usual’ D-term hybrid inflation is still viable for λ/g
large enough (but tension with cosmic string bound)
[Buchmüller, VD, Kamada ’13]
Supergravity embedding of FI-term tricky
[Komargodski, Seibergy ’09 and ’10; Dienes, Thomas ’10]
D-term inflation: data and theory
— Valerie Domcke — SISSA — 02.10.2014 — Page 9
Dynamical supersymmetry breaking
based on strong SP (1) ' SU (2) gauge group
[Izawa, Yanagida ’96, Intriligator, Thomas ’96]
field content below Λ: 4 ‘quarks’ Q, 6 ‘mesons’ M , 6 singlets Z
perturbative superpotential W = λi Mi Zi
deformed moduli constraint
P f (M ) = M1 M2 − M3 M4 + M5 M6 = Λ2 , [P f (M )]2 = det(M )
⇒ hMi i =
6 0 → hFZi i =
6 0 ⇒ susy breaking
scale Λ via dimensional transmutation:
Λ = MP exp −
e.g. gs (MP ) = 1...4π
8π 2
b gs (MP )
→ Λ = 1010 ..1018 GeV
supersymmetry breaking by strong dynamics at scale Λ
D-term inflation: data and theory
— Valerie Domcke — SISSA — 02.10.2014 — Page 10
Dynamical ‘FI-term’
Gauge a U (1) subgroup of the flavour symmetry
work in progress w K. Schmitz and T. Yanagida
fields
U (1)
M+
M−
z}|{
Q1
Q2
+1/2 +1/2
z}|{
Q3
Q4
−1/2 −1/2
Za0
0
Z+
+1
Z−
−1
D-term potential:
VD =
with hM± i2 '
λ∓ 2
λ± Λ
1 2
g (|M+ |2 − |M− |2 + . . . )2
2
(and all other fields stabilized at zero):
ξ = Λ2
λ−
λ+
−
λ+
λ−
(1 − O(g 2 ))
Effective GUT-scale FI-term generated
D-term inflation: data and theory
— Valerie Domcke — SISSA — 02.10.2014 — Page 11
Conclusion and Outlook
Realization of D-term hybrid inflation with dynamical FI-term
consistent in supergravity
no cosmic string problem
GUT scale arises naturally
chaotic regime of D-term inflation with sizeable r
Outlook
Further applications of dynamical FI-term
U (1)FI ↔ GGUT ?
more results on the search of primordial B-modes coming soon !
D-term inflation: data and theory
— Valerie Domcke — SISSA — 02.10.2014 — Page 12
Thank you!
Questions?
D-term inflation: data and theory
— Valerie Domcke — SISSA — 02.10.2014 — Page 13