1 Inflationary Cosmology and Particle Physics Qaisar Shafi Bartol Research Institute Department of Physics and Astronomy University of Delaware Cambri...

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Cambridge August, 2009

1 / 67

Outline

Introduction Standard Model Inflation Non-Supersymmetric GUTs and Inflation Supersymmetry, Supergravity and Inflation Radiative Corrections and Precision Cosmology Conclusions

2 / 67

Hot Big Bang Cosmology (SM+GR)

Standard Model (SM) + General Relativity (GR) gives rise to highly successful ‘Hot Big Bang Cosmology’ Redshift of distant galaxies Cosmic Microwave Background (CMB) Primordial nucleosynthesis

3 / 67

Hot Big Bang Cosmology (SM+GR) But Hot Big Bang Cosmology cannot explain:

High degree of CMB isotropy Origin of

δT T

‘Flatness’ nB /s ∼ 10−10 (baryon asymmetry) Cold Dark Matter (CDM)

WMAP Collaboration 2008

··· 4 / 67

Hot Big Bang Cosmology (SM+GR) In recent years ΛCDM has become the leading candidate for the description of the universe. WMAP Collaboration 2008

Where does ΛCDM come from? 5 / 67

Inflationary Cosmology [Guth, Linde, Albrecht & Steinhardt, Starobinsky, Mukhanov, Hawking, ... ]

Successful Primordial Inflation should: Explain flatness, isotropy; Provide origin of

δT T ;

Offer testable predictions for ns , r, dns /d ln k; Recover Hot Big Bang Cosmology; Explain the observed baryon asymmetry; Offer plausible CDM candidate Physics Beyond the SM? 6 / 67

Physics Beyond the SM Solar and atmospheric neutrino oscillation experiments require new physics beyond the SM Simplest Extensions 1

2

Just add 2-3 SM singlet (‘right handed’) neutrinos and use seesaw mechanism to understand why mν ≪ mcharged matter Gauge U (1)B−L global symmetry of SM ⇒ requires 3 RH-ν’s to cancel anomalies

Will discuss these two possible extensions of the SM in the context of inflation Gauge hierarchy problem (MW ≪ MP ) Electric charge quantization

Strong CP problem (axions)

7 / 67

Beyond the SM Supersymmetry (Gauge hierarchy problem, LSP dark matter) Grand Unification (Charge quantization, proton decay, gauge coupling unification) Technicolor (Complicated models) Large Extra Dimensions (Black holes at LHC?) Warped Extra Dimensions (TeV scale KK excitations) Universal Extra Dimensions (KK dark matter candidate)

8 / 67

Slow-roll Inflation The slow-roll parameters may be defined as ′′ ′ 2 ′ ′′′ m2 ǫ = 2p VV , η = m2p VV , ξ 2 = m4P V VV2 . Assuming slow-roll approximation (i.e. (ǫ, |η|, ξ 2 ) ≪ 1), the spectral index ns , the tensor to scalar ratio r and the running of the spectral index dns /d ln k are given by ns ≃ 1 − 6ǫ + 2η, r ≃ 16ǫ,

dns d ln k

≃ 16ǫη − 24ǫ2 − 2ξ 2 .

The number of e-folds after the comoving scale l0 = 2 π/k0 has crossed the horizon is given by Rφ N0 = m12 φe0 VV ′ dφ. p

Inflation ends when ǫ(φe ) ∼ 1 or η(φe ) ∼ 1.

The amplitude of the curvature perturbation is given by 3/2 V 1 = 4.91 × 10−5 (WMAP5 normalization) ∆R = 2√3πm 3 V′ p

φ=φ0

9 / 67

Standard Model Inflation? [Bezrukov, Magnin and Shaposhnikov; De Simone, Hertzberg and Wilczek.] [Barvinsky, Kamenshchik, Kiefer, Starobinsky and Steinwachs.]

Consider the following action with non-minimal coupling: SJ = R 4√ dx −g{|∂H|2 + λ H † H −

v2 2

2

− 21 m2P R − ξH † H R}

In the Einstein frame the potential turns out to be: λG 4 Rt φ VE (φ) ≃ 4ξφ2 2 ; G(t) = exp[−4 0 dt′ γ(t′ )/(1 + γ(t′ ))] (1+

where H T =

m2 P

)

√1 (0, v 2

+ φ), t = log[ Mφt ] and γ(t) is the

anomalous dimension of the Higgs field. For large φ values, VE (φ) gives rise to inflation. 10 / 67

Standard Model Inflation? Mt = 175 GeV, Ξ = 2893, mh = 134.0 GeV

0.00180

Mt = 172.4 GeV, Ξ = 6379, mh = 134.1 GeV 0.01854

0.00175 0.00170

0.01852 0.00165 ΛHtL*GHtL 0.00160

0.01850

0.00155 0.01848

0.00150 0.00145 0.00140

ΛHtL*GHtL

0.01846 33.5

34.0

34.5

35.0

33.0

33.5

t = logHΦMt L

34.0

34.5

35.0

t = logHΦMt L

φe φ0 ] and inflation end scale te = log[ M ] λ(t) G(t) vs. t, between pivot-scale t0 = log[ M t

t

The spectral index is with

ns ≃ 1 − ∆2R ≃

λ G Ne2 ξ 2 72π 2

2 Ne

+

1 3

∂ψ0 (λ G) (λ G)

⇒ ξ≃

;

√ Ne 6 2 π ∆R

ψ0 ≡ √

√ ξ φ0 mP

λ G ∼ 104 (!) 11 / 67

Standard Model Inflation?

0.980

Mt = 173 GeV

GeV

1 GeV

169

0.985

Mt = 172.4 GeV

Mt = 17

Mt =

0.990

0.05

0.04

Λ @Φ0 D

V

ns

0.975

69

0.03

Mt

Ge

=1

V

0.970

71

0.02 Mt = 175 G eV

Mt

0.965 0.960 122

124

126

128

130

mhGeV

132

134

Ge

=1

Mt

V

Ge

73

V

.4 72

0.01

Ge

Mt

=1

=1

V

75

Mt

Ge

=1

0.00 136

122

124

126

128

130

132

134

136

mhGeV

Green curve is the tree level result (independent of Higgs mass). Blue and red include quantum corrections.

12 / 67

Challenges for SM inflation

[Burgess, Lee and Trott; Barbon and Espinosa, 09] hµν mP ,

Consider gµν = ηµν + ξ mP

so that the term ξ φ2 R yields

φ2 η µν ∂ 2 hµν + · · ·

This suggests an effective cut-off scale Λ ≈

mP ξ

≪ mP .

The energy scale of inflation is estimated to be 1/4

Ei ≃ V0

=

λ1/4 m √P 41/4 ξ

≫Λ=

mP ξ

.

Thus it is not clear how reliable are the calculations.

13 / 67

Non-Supersymmetric GUTs and Inflation [Q. Shafi and A. Vilenkin, 1984]

Consider Coleman-Weinberg (CW) and Higgs Potentials for inflation in Non-Supersymmetric GUTs h i 4 φ V (φ) = A φ4 ln M − 14 + A M (CW Potential) 4 2 2 φ V (φ) = V0 1 − M (Higgs Potential)

Here φ is a gauge singlet field. Coleman-Weinberg Potential

Higgs Potential

V HΦL

V HΦL

M

Φ

[Rehman, Shafi and Wickman, 08]

M

Φ

[Kallosh and Linde, 07] 14 / 67

Non-Supersymmetric GUTs and Inflation [V. N. Senoguz, Q. Shafi, 2007]

1

ns

0.98 0.96 0.94 0.92 6

8

14 10 12 Log10 @V0 14 HGeVLD

16

18

Below vev inflation 15 / 67

Non-Supersymmetric GUTs and Inflation 1.02 1.00

ns

0.98 0.96 0.94 0.92 15.0

15.2

15.4

15.6 15.8 Log10 @VHΦ0 LD

16.0

16.2

Below vev inflation 16 / 67

Predictions for CW and Higgs Potentials [M. Rehman, Q. Shafi and J. Wickman, 2008]

CW Potential HBVL

0.5

CW Potential HAVL

r

Higgs Potential HBVL

0.4

Higgs Potential HAVL

0.3

~Φ4

0.2 ~Φ2 0.1

~1-Φ

2

~1-Φ4 0.0 0.92

0.94

0.96

0.98

1.00

1.02

1.04

ns 17 / 67

Proton Decay and WMAP5 CW Potential HBVL CW Potential HAVL Higgs Potential HBVL Higgs Potential HAVL

0.96

~Φ2

ns

0.95

~Φ4

0.94

~1-Φ4

0.93

~1-Φ2

1/4

0.92 15.4

15.6

15.8

16.0

16.2

16.4

14

[email protected]Φ0L GeVD

1/4

V0 (GeV) 1.75 × 1016 2. × 1016 2.25 × 1016 2.5 × 1016 2.75 × 1016 3. × 1016 4. × 1016 4. × 1016 3. × 1016

V (φ0 )1/4 (GeV) 1.61 × 1016 1.74 × 1016 1.83 × 1016 1.89 × 1016 1.93 × 1016 1.96 × 1016 2.03 × 1016 2.14 × 1016 2.17 × 1016

ns 0.9613 0.9630 0.9637 0.9638 0.9636 0.9635 0.9628 0.9607 0.9600

r 0.0538 0.0730 0.0889 0.101 0.110 0.117 0.133 0.165 0.174

MX ∼ 2-4 V0 ∼ 1016 GeV (CWP) ⇒ τp ∼ 1034 -1038 years (proton lifetime)

18 / 67

Magnetic Monopoles and Inflation [Q. Shafi and A. Vilenkin, 1984; G. Lazarides, Q. Shafi, 1984]

Consider the breaking G ≡ SO(10) → H → SM where H ≡ SU (4) × SU (2) × SU (2). First breaking produces superheavy monopoles carrying one unit of Dirac charge; these will be inflated away. π2 (G/H) = Z2 ; The second breaking at scale Mc produces monopoles which carry two units of Dirac magnetic charge. These are intermediate mass monopoles and they may survive inflation. 19 / 67

Magnetic Monopoles and Inflation Consider the quartic coupling −cφ2 χ† χ, with c ∼ (Mc /M )2 . Here χ vev breaks 4-2-2 to 3-2-1 and φ is the inflaton. Monopole formation occurs when cφ2 ∼ H 2 → H(t − tχ ) ≡ η ∼ 3c/λ. Initial monopole number density ∼ H 3 , which gets diluted by

inflation down to H 3 exp(−3η); thus,

rM = nM /TR3 ∼ (H/TR )3 exp(−3η) . 10−30 . Roughly 25–30 e-folds can yield a flux close to or below the Parker bound. 20 / 67

Why Supersymmetry?

Resolution of the gauge hierarchy problem Unification of the SM gauge couplings at MGU T ∼ 2 × 1016 GeV Cold dark matter candidate (LSP) Other good reasons: Radiative electroweak breaking String theory requires susy Leading candidate is the MSSM (Minimal Supersymmetric Standard Model)

21 / 67

Why Supersymmetry?

60 Α-1 1

MSSM

Αi-1

50 40 Α-1 2

30 20

Α-1 3

10 2

4

6

8 10 12 [email protected]GeVD

14

16

22 / 67

MSSM Inflation [Allahverdi, Enqvist, Garcia-Bellido, Mazumdar]

Numerous flat dimensions exist in MSSM. Utilize UDD and LLE. By suitable tuning of soft susy breaking parameters A and mφ , an inflationary scenario may be realized. Flat directions lifted by higher dimensional operators W =

λ Φn , mn−3 P

Φ is flat direction superfield. n

λn φ V = 21 m2φ φ2 + A cos(nθ + θA ) nm n−3 + P

λ2n φ2(n−1) 2(n−3)

mP

For A2 ≥ 8(n − 1)m2φ , there is a secondary minimum at 1

φ = φ0 ∼ (mφ mPn−3 ) (n−2) ≪ mp , with 2

V ∼ m2φ φ20 ∼ m2φ (mφ mPn−3 ) n−2 (this can drive inflation) 23 / 67

MSSM Inflation Hinf ∼

(mφ φ0 ) mP

m

1

∼ mφ ( mPφ ) (n−2) ≪ mφ

To implement realistic inflation, one wants both the first and second derivatives of V to vanish at φ0 : Thus V (φ) ∼ V (φ0 ) +

1 ′′′ 3! V (φ0 )(φ

− φ0 )3 + · · ·

Using slow roll approximations (take n = 6, φ0 ∼ 1014 GeV, mφ ∼ 1 − 10 TeV) ns ∼ 1 −

dns dlnk

≃

r∼

4 N

≃ 0.92

− N42 ≃ −0.002 H −16 mP ∼ 10 24 / 67

CMSSM and Inflation

CMSSM is a special case of MSSM in which we assume that SUSY is spontaneously broken in some ‘hidden’ sector and this information is transmitted to our (visible) sector via gravity One employs universal soft SUSY breaking terms (say at MGU T ); these include scalar masses, gaugino masses, trilinear couplings, etc In our discussion of SUSY hybrid inflation we will follow this minimal SUGRA scenario for the soft terms

25 / 67

Susy Hybrid Inflation [Dvali, Shafi, Schaefer; Copeland, Liddle, Lyth, Stewart, Wands ’94]

Attractive scenario in which inflation can be associated with symmetry breaking G −→ H SUSY hybrid inflation is defined by the superpotential W = κ S (Φ Φ − M 2 ) inflaton (singlet) = S, waterfall field = (Φ , Φ) ∈ G R-symmetry Φ Φ → Φ Φ, S → eiα S, W → eiα W ⇒ W is unique renormalizable superpotential Some examples of gauge groups: G = U (1)B−L , (Supersymmetric superconductor) G = 3c × 2L × 2R × 1B−L , (Φ , Φ) = ((1, 1, 2, +1) , (1, 1, 2, −1)) G = 4c × 2L × 2R , (Φ , Φ) = ((4, 1, 2) , (4, 1, 2)) G = SO(10), (Φ , Φ) = (16 , 16) 26 / 67

Susy Hybrid Inflation SUSY vacua |hΦi| = |hΦi| = M, hSi = 0 Potential VF = κ2 (M 2 − |Φ2 |)2 + 2κ2 |S|2 |Φ|2 4

ÈSÈM 2

0 2.0

1.5

VΚ2 M 4

1.0

0.5

0.0 1 0

ÈFÈM

-1

27 / 67

Susy Hybrid Inflation

Mass splitting in Φ − Φ

m2± = κ2 S 2 ± κ2 M 2 ,

m2F = κ2 S 2

One-loop radiative corrections ∆V1loop =

2 1 Str[M4 (S)(ln MQ(S) 2 64π 2

In the inflationary valley (Φ = 0) V ≃ κ2 M 4 1 +

κ2 N 8π 2

− 32 )]

F (x)

where x = |S|/M and F (x) =

1 4

4

x + 1 ln

(x4 −1) x4

2

+ 2x ln

x2 +1 x2 −1

+ 2 ln

κ2 M 2 x 2 Q2

−3

28 / 67

Susy Hybrid Inflation Tree Level plus radiative corrections:

-4

1.02

-6

1.00

-8 ns

log10 r

0.98 0.96

-10 -12 -14

0.94

-16

0.92 -5

-4

ns ≃ 1 −

-3 log10 Κ

mp 2 M

-2

-1

0.980

0.985

0.990

0.995

1.000

1.005

ns

κ2 N 8π 2

x ≫1

0 |F ′′ (x0 )| −− −→ 1 −

1 N0

≃ 0.98

′

0) r ≃ 4 (1 − ns ) |FF′′(x (x0 )| 29 / 67

Minimal Sugra Hybrid Inflation The minimal K¨ahler potential can be expanded as 2 K = |S|2 + |Φ|2 + Φ

The SUGRA scalar potential is given by

2 2 −1 Dzi W Dzj∗ W ∗ − 3m−2 |W | VF = eK/mp Kij p where we have defined Dzi W ≡

∂W ∂zi

∂K + m−2 p ∂zi W ; Kij ≡

∂2K ∂zi ∂zj∗

and zi ∈ {Φ, Φ, S, ...} 30 / 67

Minimal Sugra Hybrid Inflation

Take into account SUGRA corrections, radiative corrections and soft SUSY breaking terms, the potential is given by V ≃ 4 M κ2 M 4 1 + m p

x4 2

+

κ2 N 8π 2

F (x) + a

m3/2 x κM

+

m3/2 x 2 κM

where a = 2 |2 − A| cos[arg S + arg(2 − A)] and S ≪ mP . Note: No ‘η problem’ with minimal K¨ ahler potential [V. N. Senoguz, Q. Shafi ’04; A. D. Linde, A. Riotto ’97]

31 / 67

Minimal Sugra Hybrid Inflation

a = +1, x0 = 1.040 1

1

VΚ2 M 4

1

1

1

1

1

1

1

1

1

1 1

1 1.00

a = -1, x0 = 1.023

a = 0, x0 = 1.037 1

1.02

1.04

1.06 xl

1.08

1 1.10 1.00

1.02

1.04

1.06 xl

1.08

1 1.10 1.00

1.02

1.04

1.06

1.08

1.10

xl

Hybrid vs. Hilltop Solutions (κ = 4 × 10−4 ) [L. Boubekeur and D. H. Lyth, 2005]

32 / 67

Minimal Sugra Hybrid Inflation [M. Rehman, Q. Shafi, J. Wickman, in preparation.]

a = -1

1.00

a = +1

ns

0.98

0.96 a = -1 0.94

0.92 -6

ns ≃ 1 + 6

M mP

-5

2

x20 +

-4 -3 log10 Κ

mP 2 M

2

-2

-1

− κ8πN2 |F ′′ (x0 )| + 2

m3/2 κM

2 33 / 67

Minimal Sugra Hybrid Inflation

a = -1

1.02 1.00

ns

a=0 0.98 0.96 a = -1 0.94 0.92 -6

ns ≃ 1 + 6

M mP

-5

2

x20

+

-4 -3 log10 Κ

mP 2 M

-2

2 − κ8πN2 |F ′′ (x0 )| +

-1

2

m3/2 κM

2 34 / 67

Minimal Sugra Hybrid Inflation

17.0 17.0

a = -1

log10 HM GeVL

log10 HM GeVL

16.5

16.0 a = +1 15.5

16.5 a = -1 16.0

15.5 a=0 a = -1

15.0 -6

-5

-4 log10 Κ

a = -1

15.0 -3

-2

-1

-6

-5

-4 log10 Κ

-3

-2

-1

35 / 67

Minimal Sugra Hybrid Inflation

17.0 17.0 a = -1 16.5 log @M GeVD

log @M GeVD

16.5 16.0

15.5

a = +1

16.0

15.5

a = -1

a = -1

15.0 0.92

15.0 0.94

0.96

0.98 ns

1.00

0.92

a=0 0.94

0.96

0.98

1.00

1.02

ns

36 / 67

Minimal Sugra Hybrid Inflation

-4

log10 r

-6 -8 -10 a = -1

-12

a = +1 -14 0.92

0.94

0.96

0.98

1.00

ns

r≃4

mP 2 M

4 2 mMP x30 +

κ2 N 8π 2

F ′ (x

0) +

am3/2 κM

+2

m3/2 κM

2

x0

2

37 / 67

Minimal Sugra Hybrid Inflation

-4 -6

log10 r

-8 -10 -12 a = -1

-14

a=0 -16 0.92

r≃4

mP 2 M

0.94

0.96

4 2 mMP x30 +

κ2 N 8π 2

0.98 ns

F ′ (x

0) +

1.00

am3/2 κM

1.02

+2

m3/2 κM

2

x0

2

38 / 67

Minimal Sugra Hybrid Inflation

-3

log10 Èdns dlnkÈ

-4

a = -1

-5 a = +1

-6 -7 -8 0.92

0.94

0.96

0.98

1.00

ns

dns d ln k

√ ∝− ǫ 39 / 67

Minimal Sugra Hybrid Inflation

-2 -3

log10 Èdns dlnkÈ

-4

a = -1

-5 -6 -7 -8 a=0

-9 0.92

0.94

0.96 dns d ln k

0.98 ns

1.00

1.02

√ ∝− ǫ 40 / 67

WMAP and Cosmic Strings [Battye, Bjorn, Adam] 1.02

ns

1.00

0.98

0.96

0.94 10-5

10-4

10-3

10-2

10-1

Κ

ns vs. κ for N = 1 susy hybrid inflation with string contribution included. The

contours represent the 68% and 95% confidence levels for a 7 parameter fit to the WMAP5+ACBAR data [arXiv:astro-ph/0607339]. δT T

=

q

δT 2 T inf

+

δT 2 T cs ,

δT T cs

∝ Gµ = 2π

M MP

2

2.4 ln(2/κ2 ) 41 / 67

Reheat Temperature and Non-Thermal Leptogenesis

17.0 10

8

log10 HM GeVL

log10 HTr GeVL

16.5 9

a = -1 a=0

7

a = -1 16.0

15.5

a = -1

a=0 15.0

-6

-5

-4 log10 Κ

Tr & 1.6 × 107 GeV

-3

-2

1016 GeV M

-1

1/2

9

a = -1 10

11

12 13 log10 Hminf GeVL

3/4 minf 1011 GeV

0.05 eV mν3

14

15

1/2

42 / 67

Reheat Temperature and Non-Thermal Leptogenesis

17.0 10

8

log10 HM GeVL

log10 HTr GeVL

16.5 9

a = -1 a = +1

7

a = -1 16.0 a = +1 15.5

a = -1 15.0 -6

-5

-4 log10 Κ

Tr & 1.6 × 107 GeV

-3

-2

1016 GeV M

-1

1/2

a = -1 11

12 13 log10 Hminf GeVL

3/4 minf 1011 GeV

0.05 eV mν3

14

15

1/2

43 / 67

Non-Minimal Sugra Hybrid Inflation [M. Bastero-Gil, S. F. King, Q. Shafi; M. Rehman, V. N. Senoguz, Q. Shafi 06]

The K¨ahler potential including non-minimal terms can be expanded as 2 K = |S|2 + |Φ|2 + Φ +κS

|S|4 4m2p

+ κSφ

|S|2 |Φ|2 m2p

+ κSφ

|S|2 |Φ| m2p

2

+ κSS

The potential is of the following form 4 2 M M 2 4 2+γ V ≃ κ M 1 − κS m x S mp p m3/2 x m3/2 x 2 +a κM + κM , where

γS = 1 −

7κS 2

|S|6 6m4p

x4 2

+

+ ···.

κ2 N 8π 2

F (x)

+ 2κ2S .

44 / 67

Non-Minimal Sugra Hybrid Inflation

1.00

0.98

n

s

0.96

0.94

s

s

0.92

s

s

s

0.90 -11

10

-10

10

-9

10

= 0 = 0.002 = 0.005 = 0.01 = 0.02

-8

10

nS ≃ 1 − 2κS + 6γS

-7

10

M mp

-6

10

2

-5

10

x20 −

-4

10

-3

10

mp 2 M

-2

-1

10

10

κ2 N 8π 2

|F ′′ (x0 )| 45 / 67

MSSM µ Problem

In MSSM, the term µHu Hd is both supersymmetric and also gauge invariant, and we require that |µ| ∼ 102 –103 GeV in order to implement radiative EW breaking µ, in principle, could be of order MGU T /MP ? In SUSY hybrid inflation models, the R-symmetry forbids the ‘bare’ µ term. However, λHu Hd S is allowed, λ a dimensionless coefficient. After SUSY breaking, hSi ∼ −m3/2 /κ, so that µ ∼ −m3/2 λ/κ.

46 / 67

Shifted Hybrid Inflation [R. Jeannerot, S. Khalil, G. Lazarides, Q. Shafi ’2000]

Useful for inflating away troublesome objects. Shifted hybrid inflation is defined by the superpotential W = κ S (Φ Φ − M 2 ) −

S (Φ Φ)2 MS2

Potential VF = κ2 (M 2 − |Φ|2 + ξ |Φ|4 )2 + 2κ2 |S|2 |Φ|2 (M 2 − 2 ξ |Φ|2 )2 where ξ = M 2 /κ MS2 Inflationary trajectories |Φ| = 0 and |Φ| =

p

1/2 ξ M with |S| > M 47 / 67

Shifted Hybrid Inflation Monopoles produced in the shifted directions get inflated away 4 3

ÈSÈM

2

1

0

2

1

2

0

-2

VΚ2 M 4

0

ÈFÈM

48 / 67

Shifted Hybrid Inflation

Including 1-loop radiative corrections in the shifted direction p (|Φ| = 1/2 ξ M ) 2 V ≃ κ2 Mξ4 1 + κ8πN2 F (xξ ) where xξ = |S|/Mξ and Mξ = M

p

1/4 ξ − 1

Same results/predictions are obtained as that of regular SUSY/SUGRA inflation Mξ ⇔ M

49 / 67

Chaotic Inflation

(Linde)

0.4

Driven by potentials m2 φ2 or λφ4 r

Where does φ come from?

Λ Φ4

0.3

0.2

1 2

m2 Φ2

0.1

One promising candidate is right handed sneutrino: WN ⇒V

˜2 ⊃ mN

0.0 0.92

0.94

0.96

0.98

1.00

1.02

ns

Komatsu et al, WMAP Collaboration 2008

⊃ m2 |N |2 ; m ∼ 1013 GeV

Challenge: Does this survive SUGRA corrections? (since N > MP during inflation) Answer: With N > MP during inflation, SUGRA corrections overwhelm this scenario: W = mΦ2 ⇒ large vev of W during inflation ⇒ potential negative/no inflation 50 / 67

Chaotic Inflation

Shift symmetry imposed on the inflaton (removes the nasty expotential factor in the inflaton potential) K(Φ, Φ∗ ) invariant for Φ → Φ + i c M , so K is a function of Φ + Φ∗ , i.e., K(Φ + Φ∗ ) However, with W = m Φ2 , chaotic inflation will not take place due to the large vev of W . To cure this introduce a field X with W = m X Φ. During inflation, X is assumed to be stablized at the origin, so that W vanishes. (Kawasaki, Yamaguchi, Yanagida) Why is W = m X Φ the only relevant term?

51 / 67

Chaotic Inflation Gravitino Problem If Φ transforms under a shift symmetry, the following term is allowed: K = c (Φ + Φ∗ ), with c ∼ O(1) in Planck units The inflaton Φ decays into susy breaking sector as well as the MSSM sector, leading to thermal and non-thermal gravitino overproduction. One possible solution: Introduce a discrete symmetry which suppresses/eliminates the linear term.

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Chaotic Inflation

If Φ is RH sneutrino, it is charged under the shift symmetry. It does not have a Majorana mass, so it is not clear how leptogenesis/ν oscillations work out.

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Radiative Corrections and Precision Cosmology Chaotic: potential is quadratic (V ∼ m2 φ2 ) or quartic (V ∼ λφ4 ) Simplest (renormalizable) potential Predicts significant primordial gravity waves

Hybrid: inflation driven by φ field, vacuum energy provided by second scalar field χ 2 2 2 2 2 2 2 V (φ, χ) = κ2 M 2 − χ4 + m 2φ + λ χ4 φ Compelling and robust Translates well to SUSY Non-SUSY model results in ns > 1 (unless in chaotic-like regime) — SUSY case has ns < 1 54 / 67

Tree Level Inflation Models vs. WMAP5

0.4

0.4 Φ0 = 1

4

ΛΦ

0.2

1 2

0.3

m2 Φ2

r

r

0.3

0.2

Flat Potential Φ0 < 0.67

Not Allowed

0.1

0.0 0.92

Φ0 >> 1

0.1

0.94

0.96

0.98

ns

1.00

1.02

0.92

0.94

0.96

0.98

1.00

1.02

ns

Komatsu et. al. (WMAP Collaboration), 2008

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Radiative Corrections in Chaotic Inflation 2

Quadratic: V (φ) = 12 m2 φ2 ± Aφ4 ln µφ2 2

Quartic: V (φ) = λφ4 ± Aφ4 ln φµ2

Fermion-dominated corrections (−) (say from right handed neutrinos) V HΦL

Φ

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Radiative Corrections in Chaotic Inflation — Results [V. N. Senoguz and Q. Shafi, 2008]

0.4 Λ Φ4

r

0.3

0.2

1 2

m2 Φ2

0.1

0.0 0.92

0.94

0.96

0.98

1.00

1.02

ns 57 / 67

Radiative Corrections in Hybrid Inflation [M. Rehman, Q. Shafi and J. Wickman, 2009] 2

V (φ, χ) = κ

χ2 M − 4 2

2

m2 φ2 λ2 χ2 φ2 + + ± Aφ4 ln 2 4

φ φc

,

where φ ≡ ‘inflaton’ field, χ ≡ ‘waterfall’ field (χ = 0 during inflation) -1 ΦP = 2.5

log10r

-2 ΦP = 1 -3

-4

ΦP = 0.25

-5 0.92

0.94

0.96

0.98

1.00

ns 58 / 67

Radiative Corrections & Precision Cosmology

Radiatively-corrected inflation models; Chaotic Inflation Permits low values of r (e.g. 0 . r . 0.2 to agree with WMAP5 2σ bound)

Hybrid Inflation Red spectrum (ns < 1) can be produced for Planckian or sub-Planckian values of the inflaton

Better agreement with WMAP5 Generically 2 solutions of ns for each A

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Brane Inflation

In the simplest brane inflation models the inflaton φ is a field which parametrizes the distance r between two brane worlds embedded in the extra dimensions. If the distance between these two branes is much bigger than the string scale, the potential between them is essentially governed by the infrared bulk supergravity. Assuming the effects of higher string excitations are decoupled, the potential is expected to be V ∼ Ms4 a − (Ms r)b N−2 , where Ms is the string scale, and a, b are constants.

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Brane Inflation Thus, in this picture inflation in four dimensions is driven by brane motion in the extra-dimensional space. Positive powers of φ are absent because the inter-brane interaction falls off with the distance. For a D3 brane - anti D3 brane system, assuming the extra dimensions have been suitably compactified (say T 6 ) and remain frozen during inflation, √ V (φ) ∼ Ms4 1 − φα4 , φ = T3 r, α = 16T3π2 . (contributions from dilaton, graviton and RR field) In this case δT T

∝ Mc /MP , Mc ∼ 1012 GeV (intermediate compactification scale), ns ≃ 1 − N20 ≈ 0.96.

NOTE: No very compelling/realistic model so far!!

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D-brane Inflation Brane-Antibrane Dvali & Tye; Dvali,Shafi,Solganik; Burgess,Majumdar,Nolte,Quevedo,Rajesh,Zhang; Alexander;. Branes at Angles Garcia-Bellido, Rabadan, Zamora; Blumenhagen, K¨ors, L¨ ust, Ott; Dutta, Kumar, Leblond. D3-D7 Dasgupta,Herdeiro,Hirano, Kallosh; Hsu,Kallosh, Prokushkin; Hsu & Kallosh; Aspinwall & Kallosh; Haack, Kallosh, Krause, Linde, L¨ ust, Zagermann. warped brane-antibrane Kachru,Kallosh,Linde,Maldacena,L.M.,Trivedi; Firouzjahi & Tye; Burgess,Cline,Stoica,Quevedo; Iizuka & Trivedi,... DBI Silverstein & Tong; Alishahiha,Silverstein,Tong; Chen; Chen; Shiu & Underwood; Leblond & Shandera,... Monodromy Silverstein & Westphal. Adapted from McAllister, 2008 62 / 67

D-brane Inflation Closed string inflation models, e.g.: Racetrack Blanco-Pillado, Burgess, Cline, Escoda, Gomez-Reino, Kallosh, Linde, Quevedo. K¨ahler moduli Conlon & Quevedo. N-flation Dimopoulos, Kachru, McGreevy, Wacker; Easther & L.M. Adapted from McAllister, 2008

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Chaotic inflation in string theory [Silverstein, Westphal, 2008]

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Brane Inflation and Cosmic Strings Prior to brane annihilation the associated gauge symmetry is U (1) × U (1). One linear combination gives rise to D-strings, while the orthogonal combination is associated with F (fundamental)-strings. It has been argued that a substantial fraction of energy of the annihilating branes is used up in the production of a network of cosmic D and F strings. If one assumes that brane inflation gives rise to the observed inhomogeneities, estimates suggest that 10−11 . Gµ . 10−6 . With some(?) luck it may be possible to observe these primordial strings with LIGO/LISA.

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Conclusions One of the most important challenges in our field is to find a “Standard Model of Inflationary Cosmology”. A large class of realistic inflation models, based on grand unification and/or low scale supersymmetry are consistent with the data currently available from WMAP and other observations. Non-supersymmetric GUT inflation models typically predict an ‘observable’ value for the tensor to scalar ratio r. Supersymmetric hybrid inflation, on the other hand, predicts a ‘tiny’ r value (. 10−4 ), even though the symmetry breaking scale associated with inflation is comparable to MGU T . 66 / 67

Conclusions Hopefully, the PLANCK Satellite will soon shed light on this fundamental parameter r. In addition, we expect the LHC to provide answers to the following long-standing and very basic questions: Is there a SM Higgs boson and what is its mass? Is there low scale supersymmetry? Is the LSP stable? Mass?

To achieve truly significant progress in particle physics and cosmology we need both the LHC and the PLANCK Satellite. They hold the key to future developments in these fields. 67 / 67

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