Right-Handed Sneutrino Modification of D-term Hybrid Inflation in - - PowerPoint PPT Presentation

▶

Feb 11, 2024 88 likes •423 views

Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results Right-Handed Sneutrino Modification of D-term Hybrid Inflation in Non-mininal Supergravity Chia-Min Lin (with John McDonald) Cosmology

SLIDE 1

Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results

Right-Handed Sneutrino Modification of D-term Hybrid Inflation in Non-mininal Supergravity

Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster

Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation

SLIDE 2

Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results

Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results

Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation

SLIDE 3

Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results

Topics

◮ Inflation

Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation

SLIDE 4

Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results

Topics

◮ Inflation ◮ SUSY Inflation

Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation

SLIDE 5

Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results

Topics

◮ Inflation ◮ SUSY Inflation ◮ What is D-term inflation?

Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation

SLIDE 6

Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results

Topics

◮ Inflation ◮ SUSY Inflation ◮ What is D-term inflation? ◮ What are the problems with D-term Inflation?

Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation

SLIDE 7

Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results

Topics

◮ Inflation ◮ SUSY Inflation ◮ What is D-term inflation? ◮ What are the problems with D-term Inflation? ◮ Provide a solution.

Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation

SLIDE 8

Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results

Inflation

Once upon a time, the Universe was dominated by some mysterious vacuum energy: V (φ) = 3H2M2

Pl ≈ ρφ ≈ const.

∴ ˙ ρ ≈ 0 ⇒ H ≡ ˙ a a ≈ const. da a = Hdt ⇒ a ∝ eHt People named this dramatic expansion “Inflation”. The problem is, what in the world is V (φ) after all?!

Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation

SLIDE 9

Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results

Inflation

So people start to play the game of Inflation by inventing all kinds

f potentials...

Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation

SLIDE 10

Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results

Inflation

Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation

SLIDE 11

Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results

Inflation

Slow-roll inflation: A scalar potential of the field(s) V (φ, ...) tells you almost everything! η = M2V ′′/V and ǫ = (M2/2)(V ′/V )2 Spectral index: n = 1 + 2η − 6ǫ Curvature perturbation: Pζ = 1 12π2M6 V 3 V ′2 etc.

Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation

SLIDE 12

Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results

Supersymmetry (Boson↔Fermion)

Every particle corresponds to its superpartner, which must be HEAVY due to SUSY breaking.

Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation

SLIDE 13

Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results

Supersymmetry

Reasons for implanting SUSY into Inflation:

◮ Have scalar fields

Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation

SLIDE 14

Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results

Supersymmetry

Reasons for implanting SUSY into Inflation:

◮ Have scalar fields ◮ Quantum corrections could be suppressed.

Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation

SLIDE 15

Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results

Supersymmetry

Reasons for implanting SUSY into Inflation:

◮ Have scalar fields ◮ Quantum corrections could be suppressed. ◮ no SUSY, no good GUT.

Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation

SLIDE 16

Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results

Supersymmetry

Reasons for implanting SUSY into Inflation:

◮ Have scalar fields ◮ Quantum corrections could be suppressed. ◮ no SUSY, no good GUT. ◮ etc.

Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation

SLIDE 17

Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results

Supersymmetry

Scalar potential V = VF + VD SUSY: VF = |F|2 ≡ |Wm|2 VD = 1 2(g 2

qn|φn|2 + ξ)2 SUGRA: VF = eK/M2 (Wm + WKm M2 )K m†n(Wn + WKn M2 ) − 3|W |2 M2

VD = 1

2(Ref )−1g2(qnKnφn + ξ)2

Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation

SLIDE 18

Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results

Conventional D-term Inflation

The superpotential of D-term hybrid inflation is given by WD = λSΦ+Φ− One-loop potential: V (S) = V0 + g4ξ2 16π2 ln(|S|2 Λ2 )

Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation

SLIDE 19

Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results

Problems of conventional D-term Inflation

From WMAP n = 0.958 ± 0.016 However, n = 0.983 From cosmic string study (for example astro-ph:0702223): ξ1/2 < 3.9 × 1015GeV (assume an upper limit of 10%) However, ξ1/2 = 7.9 × 1015GeV

Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation

SLIDE 20

Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results

Non-minimal Supergravity

We consider the K¨ ahler potential of the form: K = |S|2 +|Φ+|2 +|Φ−|2 +f+(|S|2 M2

P

)|Φ+|2 +f−(|S|2 M2

P

)|Φ−|2 +b|S|4 M2

P

where f±(|S|2 M2

P

) = c± |S|2 M2

P

= c±s2 2 .

Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation

SLIDE 21

Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results

D-term Inflation

The effective scalar potential for the D-term inflationary model reads Veff (|S|) = g2ξ2 2

g2 16π2

2 ln(z g2ξ

Λ2 ) + fV (z)

where fV (z) = (z + 1)2 ln(1 + 1 z ) + (z − 1)2 ln(1 − 1 z ) and z ≡ λ2s2 2g2ξ exp(s2 2 + bs4 4 ) 1 (1 + f+)(1 + f−)

Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation

SLIDE 22

Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results

right-handed sneutrino correction

Wν = λνΦHuL + mΦ 2 Φ2 K = S†S + Φ†Φ + cS†SΦ†Φ M2 ∆V = −κ|S|2 2 + M2

φφ2

2 , where we have defined κ by κ ≡ (c − 1)M2

φ|φ|2

M2 .

Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation

SLIDE 23

Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results

results

Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation

SLIDE 24

Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results

results

Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation

SLIDE 25

Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results

results

c+ = c− = 3.0

Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation

SLIDE 26

Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results

results

c+ = 2.0, c− = 5.0

Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation

SLIDE 27

Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results

results

g = 0.6

Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation

SLIDE 28

Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results

results

Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation

SLIDE 29

Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results

results

Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation

SLIDE 30

Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results

results

Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation

SLIDE 31

Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results

results

Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation