Inflation and the LHC

Rouzbeh AllahverdiRouzbeh Allahverdi

University of New Mexico

PPC 2010: “4th International Workshop On The Interconnection Between 

Particle Physics And Cosmology ”, Torino, Italy

July 15, 2010

Outline:

• Introduction

• Inflation in MSSMInflation in MSSM

• Properties, predictions, and parameter space

• Cosmology/phenomenology complementarity

• LHC role

• SummarySummary

Introduction:

LHC will discover new physics beyond the SM.

Microphysical explanation of major problems in cosmology (darkp y p j p gy (matter, matter/antimatter asymmetry, inflation) requires physicsbeyond the SM.

LHC-Cosmology connection: Discovering new physics at the LHC can help us learnDiscovering new physics at the LHC can help us learnabout the early universe.

LHC-Cosmology connection studied for WIMP dark matter.(Talks by Bhaskar Dutta and Giacomo Polesello)

Key: Dark matter related to weak scale physics

How about other connections between LHC & cosmology?

Some connection between the models and TeV scale physics must exist.

Example: TeV scale leptogenesis can be probed at the LHCBlanchet, Chacko, Granor, Mohapatra arXiv:0904.2174Blanchet, Chacko, Granor, Mohapatra arXiv:0904.2174

What about inflation?What about inflation?(no studies until recently)

LHC connection suggests low scale models of inflation

Key: Embedding inflation in TeV scale physicsKey: Embedding inflation in TeV scale physics

1) Inflation driven by the visible sector

Example:MSSM inflation (Sparticles as the inflaton)( p )

Allahverdi, Enqvist, Garcia-Bellido, Mazumdar PRL 97, 191304 (2006)

One can

Directly probe the physics of inflation at colliders• Directly probe the physics of inflation at colliders

• Use particle physics to constrain inflation parametersUse particle physics to constrain inflation parameters

• Reliably describe post-inflationary processes y y

2) Inflation driven by the SUSY breaking sector

Example:Modular inflation (SUSY breaking modulus as the inflaton)( g )

Allahverdi, Dutta, Sinha PRD 81, 083538 (2010)

One can

• Test predictions of inflation for sparticle masses

• Probe new particles required for a successful post-inflationinflation

Allahverdi, Dutta, Sinha arXiv:1005.2804

Inflation: a period of superluminal expansion of the universe.

It is driven by a scalar field (inflaton)φIt is driven by a scalar field (inflaton).

Assumptions:

φ

Canonical kinetic terms, minimal coupling to gravity

)(V φ

Hubble expansion rate

0)(3 =′++ φφφ VH &&&2

2

3)(

PMVH φ

=:H Hubble expansion rate

1||||

:H

Slow-roll inflation :

221

⎟⎞

⎜⎛ ′V V ′′2

1|||,| <<ηε

2

21

⎟⎠⎞

⎜⎝⎛≡

VVM Pε

VVM P≡ 2η

Slow-roll inflation occurs within a field range :

)(e Na∫e

dVφ

φ1),( ei φφ

S l f t f th i

)exp( toti

e Na

= ∫ ′=

i

dVV

MN

Ptot

φ

φ2

1

:a Scale factor of the universe

needed to explain the isotropy and)6030(≈≥ NN

:a

needed to explain the isotropy and flatness problems of the big-bang model.

)6030( −≈≥ COBEtot NN

Observable: Density fluctuations (CMB temperature anisotropy).

H11

PH M

H inf

21

51

επδ = εη 621 −+= sn

Amplitude Scalar spectral index (COBE) (WMAP7) 5109.1 −×≈ 024.0963.0 ±

Successful inflation possible for .13inf 10≤H GeV

13In low-scale models .

Th i i h

13inf 10<<H GeV

δThen generating correct requires that:Hδ1|| <<ε

1||21

<<⇒+≈⇒

ηηsn

The second condition naturally satisfied near a point of inflection.

1|| <<η

Inflection point inflation provides a suitable framework for low scale models.

Inflation in MSSM:

MSSM h l fi ld (Hi k l )MSSM has many scalar fields (Higgses, squarks, sleptons).

Can MSSM lead to inflation?

Naive answer is “no”: slow-roll conditions not satisfied for TeV scale masses andslow-roll conditions not satisfied for TeV scale masses and known gauge/Yukawa couplings.

BUTBUT:Potential can be made sufficiently flat along various directions in the field space.the field space.

Two such directions can lead to successful inflation.

Allahverdi, Enqvist, Garcia-Bellido, Mazumdar PRL 97, 191304 (2006) Allahverdi, Enqvist, Garcia-Bellido, Jokinen, Mazumdar JCAP 0706, 019 (2007)

Inflaton candidates in MSSM are two flat directions: 

ddu ++~~~ γβα LL ba ~~~ddu kji ++

=3

ϕγβ eLL k

bj

ai ++

=3

ϕ

kj ≠≠≠ ,γβα kjiba ≠≠≠ ,

bβ 2,13,,13,1 ≤≤≤≤≤≤ baji γβα

in MSSM with unbroken SUSY.

Lifted by SUSY breaking and higher order terms:

0)( =ϕV

Lifted by SUSY breaking and higher order terms: Dine, Randall, Thomas NPB 458, 291 (1996)

||1 610222 ϕϕ .).

6(||||

21)( 36

222 chM

AM

mVPP

+++=ϕλϕλϕϕ φ

)exp(2

θφϕ i= )(~, TeVOAmφ

102

6221)( AmV φλφλφφ +=

2soft mass A-term

6362)(

PP MMAmV λλφφ φ +−=

Quantum corrections:

)]log(1[)]log(1[ 20120

2 φφφ KAAKmm +=+=

2A

00 μμφ

41

3

⎟⎞

⎜⎛ Mm

22 41

40α

φ

+≡m

A

0 10 ⎟⎟⎠

⎞⎜⎜⎝

⎛≅

λφ φ PMm

⇒<< 1α a point of inflection

inflationV inflationV

φ0φ

Inflection point0φ

0)( 0 =′′ φV

40

220 4)( φαφ φmV =′

20

20 15

4)( φφ φmV =

Properties, Predictions, and Parameter Space:

Density perturbations:Density perturbations: Bueno-Sanchez, Dimopoulos, Lyth JCAP 0701, 015 (2007) Allahverdi, Enqvist, Garcia-Bellido, Jokinen, Mazumdar JCAP 0706, 019 (2007) , q , , , , ( )

[ ]ΔΔ

≈ COBEP

H NMm 2

22 sin158

φπδ φ

Δ05 φπ

[ ]ΔΔ−= COBEs Nn cot41

⎟⎟⎞

⎜⎜⎛

+ 0 )(l1966 VN φ

2⎞⎛ M

⎟⎟⎠

⎜⎜⎝

+≈ 40 )(ln

49.66

PCOBE M

N φ

2A

0

30 ⎟⎟⎠

⎞⎜⎜⎝

⎛≡Δ

φα P

COBEMN 2

2 4140

αφ

+≡m

A

Allowed parameter space to generate acceptable perturbations:

)024.0963.0,109.1( 5 ±=×≈ −sH nδ ),( sH

700

800

700

800

500

600

700

] 500

600

700

]

610−≤Δ 400

500

0 [1

012 G

eV]

400

500

0 [1

012 G

eV]

200

300φ 0 [

200

300φ 0 [

0

100

0

100

0 0 500 1000 1500 2000

mφ [GeV]

0 0 500 1000 1500 2000

mφ [GeV])1000100(inf −≅H GeV

Important properties:

sn1) within the whole range allowed by WMAP can be generated(unlike other models of inflation).

2) CMB data alone cannot pinpoint the inflaton parameters (unlike other models of inflation).

sH n,δΔ,, 0φφmλφ ,, Am

Two observables:Three parameters: (can be traded for )φφ

Other experiments needed to fix inflaton parameters

How to determine the parameters experimentally?

have no bearing for phenomenology, relevant for inflation.relevant for inflation and phenomenology both.

λ,Aφm

Cosmology/Phenomenology Complementarity:Inflaton parameters are related to weak scale observables via RGEs. Allahverdi, Dutta, Mazumdar PRD 75, 075018 (2007)

In general various phenomenological constraints can beIn general, various phenomenological constraints can be translated into regions in the plane.

Combined with CMB measurements they narrow down the

0φφ −m

Combined with CMB measurements, they narrow down the allowed region of the plane.0φφ −m

ΔMore precise measurements can determine and .Eventually one can pinpoint .Am ,, λφ

Δ0,φφm

To explicitly demonstrate this, consider mSUGRA model.Allahverdi Dutta Santoso arXiv:1004 2741Allahverdi, Dutta, Santoso arXiv:1004.2741

mSUGRA-udd, tan β=10, A0=0, μ>0mSUGRA-udd, tan β=10, A0=0, μ>0mSUGRA-udd, tan β=10, A0=0, μ>0mSUGRA-udd, tan β=10, A0=0, μ>0mSUGRA-udd, tan β=10, A0=0, μ>0mSUGRA-udd, tan β=10, A0=0, μ>0

(T): Teubner, et al arXiv:1001.5401(D): Davier, et al arXiv:1004.2741

500mSUGRA-udd, tan β=10, A0=0, μ>0

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800mSUGRA-udd, tan β=50, A0=0, μ>0

800mSUGRA-udd, tan β=50, A0=0, μ>0

800mSUGRA-udd, tan β=50, A0=0, μ>0

800mSUGRA-udd, tan β=50, A0=0, μ>0

800mSUGRA-udd, tan β=50, A0=0, μ>0

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μ

800mSUGRA-LLe, tan β=50, A0=0, μ>0

800mSUGRA-LLe, tan β=50, A0=0, μ>0

800mSUGRA-LLe, tan β=50, A0=0, μ>0

800mSUGRA-LLe, tan β=50, A0=0, μ>0

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800mSUGRA-LLe, tan β=50, A0=0, μ>0

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Mass measurements at the LHC can also be used to constrain

LHC Role:Mass measurements at the LHC can also be used to constrain

plane.0φφ −m

Consider a SUSY reference point in the co-annihilation regionConsider a SUSY reference point in the co annihilation region (all masses are in GeV):

0,40tan,350,210 02/10 ==== Amm β

329,3.151,7.14021

0 ~~ ===⇒ ττχmmm

With of data LHC can determine high energy parameters:110 −fb

211ττχ

With of data, LHC can determine high energy parameters:

160,140tan,4350,4210 02/10 ±=±=±=±= Amm β

10 fb

Arnowitt, Dutta, Gurrola, Kamon, Krislock, Toback PRL 100, 231802 (2006)

100

200

300

200 250 300mφ[GeV]

φ 0[× 1

012 G

eV]

uddLLe

R.A., Dutta, Santoso arXiv:1004.2741

100

200

300

200 250 300mφ[GeV]

φ 0[× 1

012 G

eV]

uddLLe

100

200

300

200 250 300mφ[GeV]

φ 0[× 1

012 G

eV]

uddLLe

100

200

300

200 250 300mφ[GeV]

φ 0[× 1

012 G

eV]

uddLLe

100

200

300

200 250 300mφ[GeV]

φ 0[× 1

012 G

eV]

uddLLe

100

200

300

200 250 300mφ[GeV]

φ 0[× 1

012 G

eV]

uddLLe

100

200

300

200 250 300mφ[GeV]

φ 0[× 1

012 G

eV]

uddLLe

General approach:

1) Fi d SUSY1) Find SUSY.

2) Measure as many masses as possible (sparticles2) Measure as many masses as possible (sparticles, gauginos).

3) Use RGEs to extrapolate the inflaton mass to high scales.

4) Narrow down the allowed region in plane.0φφ −m

5) Use this to find .A,λ

Provides information about the underlying physics that induceshigher order term, SUSY breaking sector

Inflation from SUSY Breaking Sector:

M d l i fl ti ithi KKLT tModular inflation within a KKLT set up.Allahverdi, Dutta, Sinha PRD 81, 083538 (2010)

Inflection point inflation driven by the SUSY breaking modulus:

TeVmH 50~~ 2/3inf

This model gives rise to mirage mediation of SUSYbreaking to the observable sector.

Reheat temperature is very low in the model: . MeVTR 200~

Successful baryogenesis requires additional fields in the observablle sector, e.g.:TeV scale colored tripletsTeV scale colored triplets

Allahverdi, Dutta, Sinha arXiv:1005.2804

Predictions for LHC:

S f l l l i fl ti i li th tSuccessful low scale inflation implies that:

• Gaugino masses receive comparable contributionsg pfrom modulus and anomaly mediation.

• Scalar masses mainly come from anomaly mediation.

The mass pattern can be tested at the LHCThe mass pattern can be tested at the LHC.

I ddi iIn addition,

• Color triplets with mass accessible at LHC.)(TeVOColor triplets with mass accessible at LHC. )(TeVO

• LHC inflation connection possible for a realistic embedding of

Summary:• LHC-inflation connection possible for a realistic embedding of

inflation within TeV scale physics.

• Inflation can be realized within MSSM. The underlying parameters cannot be determined from CMB measurements alone. Particle physics experiments are also needed to p y ppinpoint the parameters.

• Mass measurements at the LHC are important CombinedMass measurements at the LHC are important. Combined LHC/ILC and PLANCK data can lead to precise determination of the parameters.

• Inflation can be driven by the SUSY breaking sector. Predicted sparticle masses, and new colored fields required for p , qbaryogenesis, can be probed at the LHC.

3

~~~ ddu ++=φ

3

2~

2~

2~2 ddu mmm

m++

=⇒ φ3 3

⎟⎠⎞

⎜⎝⎛ +−= 2

12

123

232

2

524

61 gMgM

ddm

πμμ φ

⎠⎝μ

⎟⎠⎞

⎜⎝⎛ +−= 2

112332 5

83

164

1 gMgMddA

πμμ

222 mmm ++~~~ eLL ++

⎠⎝ 534d πμ

3~~~2 eLL mmm

m++

=⇒ φ3eLL ++

=φ

⎞⎛2 931dm

⎟⎠⎞

⎜⎝⎛ +−= 2

12

122

222 10

923

61 gMgM

ddm

πμμ φ

⎞⎛ 931dA⎟⎠⎞

⎜⎝⎛ +−= 2

112222 5

923

41 gMgM

ddA

πμμ

The condition for successful inflation can be met dynamically dueto RGEs.

1,4140

22

2

<<+≡ ααφm

A

is scale-dependent, hence VEV-dependent.

φ

αobtained within the phenomenologically interesting range

for a wide range of input values.1514 1010 − GeV0=α

This scale must coincide with an inflection point:

41

3 ⎞⎛ M 43

0 10 ⎟⎟⎠

⎞⎜⎜⎝

⎛≅

λφ φ PMm

This condition will fix the value of very precisely. λ

1.75

2

1.5

1.75A

2

1

1.25

2�n�

1��A

0.75

1

8m

2�n

0.25

0.5

13 14 15 16

LogΜ

0.25

300250200150=mφ Log�Μ���������������GeV

�

1600300,250,200,150

=

=

Amφ

1.75

2

1.5

1.75

1

1.25

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2

0.75

1

40m

0.25

0.5

13 14 15 16Μ

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2200200018001600ALog�

���������������GeV

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4002200,2000,1800,1600

==

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2�A

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0.440m

0.2

12.5 13 13.5 14 14.5 15 15.5 16Μ

Log����������������GeV

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σσ BeAeWW baflux ++= −−

2, δδ CVVVV F =+= 2σ