Tribrid Inflation: A Framework For Connecting Inflation With Particle ...

Outline

Hybrid Inflation

Tribrid Inflation

Application to Model Building

Summary

Tribrid Inflation: A Framework For Connecting Inflation With Particle Physics David Nolde University of Basel 14. August 2012 SUSY 2012, Beijing

based on S. Antusch, M. Ur Rehman, D.N. [arXiv:1205.0809] JCAP 1208 (2012) 004, S. Antusch, D.N. [arXiv:1207.6111], and references therein

Outline

Hybrid Inflation

Tribrid Inflation

1

Hybrid Inflation Basic Idea Supersymmetric Hybrid Inflation

2

Tribrid Inflation From Hybrid to Tribrid Inflation Tribrid Superpotential The Three Regimes Predictions

3

Application to Model Building General Recipe Toy Model Example

4

Summary

Application to Model Building

Summary

Outline

Hybrid Inflation

Tribrid Inflation

Application to Model Building

Summary

Basic Idea


W = κΦ H 2 − µ2 2 ⇒ VF = κ2 H 2 − µ2 + 4κ2 |HΦ|2 | {z } | {z } vacuum energy for |H| 6= µ

stabilizes H = 0 for |Φ| > Φc

Slow-roll inflation in Φ, H = 0 during inflation Inflation ends when Φ < Φc → waterfall transition in H After inflation, hHi = 6 0

Φ: inflaton H: waterfall field

Outline

Hybrid Inflation

Tribrid Inflation

Application to Model Building

Summary

Supersymmetric Hybrid Inflation

Promising features phase transition at µ ' 1016 GeV Φ  MPl ⇒ Planck-suppressed operators stay under control Unsatisfactory feature κµ2 Φ needed in superpotential → Φ must be a singlet under all symmetries (except R symmetry) → inflaton mostly disconnected from matter sector Look for variant of hybrid inflation where Φ can be a charged field

Outline

Hybrid Inflation

Tribrid Inflation

Application to Model Building

Summary

From Hybrid to Tribrid Inflation

SUSY hybrid model:
W = κΦ H 2 − µ2

SUSY tribrid model:   W = κS H ` − µ2 + λ H m Φn | {z } | {z } vacuum energy for |H| 6= µ

stabilizes H = 0 for |Φ| > Φc

singlet field S is still present, but no longer the inflaton inflaton Φ need not be a singlet, as long as Φn is some D-flat combination of fields

Outline

Hybrid Inflation

Tribrid Inflation

Application to Model Building

Tribrid Superpotential


W = κS H ` − µ2 + λ H m Φn Inflaton potential from: 1

loop corrections (Coleman-Weinberg potential)

2

Planck-suppressed operators from the K¨ahler potential

3

small hHi = 6 0 already during inflation (only for m > 2)

→ different regimes depending on which contribution dominates

Summary

Outline

Hybrid Inflation

Tribrid Inflation

Application to Model Building

The Three Regimes

Regime depends on the superpotential:

`=2 `=3 `=4

m=2 K¨ahler-driven or loop-driven K¨ahler-driven or loop-driven K¨ahler-driven or loop-driven

m=3

m=4

not possible

not possible

pseudosmooth

not possible

pseudosmooth or smooth

pseudosmooth

`, m = 1 do not feature successful tribrid inflation. `, m > 4 are possible, but lead to hHi & 1017 GeV.

Summary

Outline

Hybrid Inflation

Tribrid Inflation

Application to Model Building

Summary

The Three Regimes

Φ

V

X H\

0

V

H

Potential for K¨ahler- and loop-driven regime

0

H

Potential for pseudosmooth regime (H 6= 0)

Outline

Hybrid Inflation

Tribrid Inflation

Application to Model Building

Predictions

For generic model parameters, we find: hHi & 1016 GeV r . 0.01 αs ' 0 for loop-driven and pseudosmooth tribrid inflation αs > 0 for K¨ahler-driven tribrid inflation We can therefore exclude tribrid inflation if r > 0.01 or αs < 0 should be measured. A measurement of αs could also distinguish between the K¨ahler-driven and the other regimes.

Summary

Outline

Hybrid Inflation

Tribrid Inflation

Application to Model Building

Predictions

Detailed predictions depend on regime of tribrid inflation. Example: K¨ahler-driven regime with
W = κS H ` − µ2 + λ H m Φn K = |Φ|2 + |H|2 + |S|2 + (1 − 2a)|Φ|2 |S|2 + ...
−→ Veff (Φ) = V0 1 + 2a|Φ|2 + 4b|Φ|4 + ..., where b depends on several higher-order terms in K . Inflation provides predictions for CMB observables (r and αs ) and model parameters (λ and hHi), depending on a, b and ns .

Summary

Outline

Hybrid Inflation

Tribrid Inflation

Application to Model Building

Summary

Predictions

Predictions for ` = n = 3, m = 2 (example). Red band: ns = 0.98, blue band: ns = 0.94. The width of the bands is due to the dependence on b. l ³ 3, n = 3 1 100

0.05

0.03

Λ

Αs

0.04 10-2

0.02 10-4 0.01 0

0.02

0.04

0.06

10-6

0.01

0.02

a

0.03

a l=3 1 ´ 1016

0.004

XH \min

3 ´ 1016

r

1 ´ 1016

0.002

3 ´ 1015 0

0.02

0.04

a

0.06

1 ´ 1015

0

0.02

0.04

a

0.06

Outline

Hybrid Inflation

Tribrid Inflation

Application to Model Building

Summary

General Recipe

Recipe for model building: 1

identify models which can contain the tribrid superpotential

2

check table to find the regime for the model’s superpotential (`, m) use the predictions for the corresponding regime to either:

3

... determine CMB observables for given model parameters ... constrain the model parameters for given CMB observables

Outline

Hybrid Inflation

Tribrid Inflation

Application to Model Building

Toy Model Example

n o Superpotential: W = κS H 3 − M 2 + λH 2 LHu N +... | {z } → ` = 3, m = 2: K¨ahler-driven regime

Φ3

Example: assume αs ' 0.01 was measured. Predictions for our tribrid toy model: r < 10−3 hHi & 2 × 1016 GeV λ'1 → neutrino Yukawa coupling yν & 10−4 Further constraints may be derived from reheating, so that in principle, tribrid models can become very predictive.

Summary

Outline

Hybrid Inflation

Tribrid Inflation

Application to Model Building

Tribrid inflation can happen for a broad class of superpotentials Three regimes with different dynamics and predictions Retains the nice features of SUSY hybrid inflation → small-field model (Planck-scale effects under control) → GUT scale phase transition The inflaton can be a D-flat combination of matter fields → CMB constraints on the inflaton potential can constrain low-energy particle physics Tribrid inflation as a framework for connecting inflation with particle physics

Summary