Inflation and the LHC

Rouzbeh Allahverdi

University of New Mexico

Santa Fe 2010 Summer Workshop

“LHC: From Here to Where? ”

July 7, 2010

Outline:

• Introduction

• Inflation in MSSMInflation in MSSM

• Properties, predictions, and parameter space

• Cosmology/phenomenology complementarity

• LHC role

• SummarySummary

Introduction:

LHC-Cosmology connection studied in the context ofWIMP dark matter:

• See the WIMP (missing energy) and measure its mass

• Make measurements and identify a point in the dark matter allowed region for a given model (e.g., mSUGRA)

• Measure as many parameters as possible, and calculate thermal relic density

Nojiri, Polesello, Tovey JHEP 0603, 063 (2005)Baltz, Battaglia, Peskin, Wizanski PRD 74, 103521 (2006)Arnowitt, Dutta, Gurrola, Kamon, Krislock, Toback PRL 100, 231802 (2008)Arnowitt, Dutta, Gurrola, Kamon, Krislock, Toback PRL 100, 231802 (2008)

How about other connections between LHC & cosmology?

Standard Cosmological Model: LCDM+ Inflation (the best paradigm of the early universe cosmology)

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

Example: Probing TeV scale leptogenesis at the LHCBlanchet Chacko Granor Mohapatra arXiv:0904 2174Blanchet, Chacko, Granor, Mohapatra arXiv:0904.2174

Lets focus on inflation.

LHC connection suggests low scale models of inflationLHC connection suggests low scale models of inflationKey: Embedding inflation in TeV scale physics

Most direct connection:Inflation driven by the visible sectorInflation driven by the visible sector

Example:pMSSM inflation

R.A., Enqvist, Garcia-Bellido, Mazumdar PRL 97, 191304 (2006)R.A., Enqvist, Garcia Bellido, Mazumdar PRL 97, 191304 (2006)

One can

• Directly probe the physics of inflation at colliders

• Use particle physics to constrain inflation parameters

• Reliably describe post-inflationary processes

Less direct: Inflation driven by the SUSY breaking sectorInflation driven by the SUSY breaking sector

Example:pKahler modulus inflation

R.A., Dutta, Sinha PRD 81, 083538 (2010)R.A., Dutta, Sinha PRD 81, 083538 (2010)

One can probe

Predictions of inflation for sparticle masses• Predictions of inflation for sparticle masses

• New particles required for a successful post-inflationNew particles required for a successful post inflation

R.A., Dutta, Sinha arXiv:1005.2804

Inflation: a period of superluminal expansion o 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

Inflation occurs in the slow-roll regime :

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 ±

Slow-roll inflation possible for .13inf 10≤H GeV

13In low-scale inflation .

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 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.

R.A., Enqvist, Garcia-Bellido, Mazumdar PRL 97, 191304 (2006) R.A., 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 superpotential terms:

0)( =ϕV

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

6ϕ36 PM

W ϕλ⊇

6

102

3

622 )6cos(

21)(

MMAmV φλφθλφϕ φ ++=

2 PP MM)exp(

2θφϕ i= )(~, TeVOAmφ

1061 φφ

2 φ

soft mass A-term

62

322

21)(

PP MMAmV φλφλφφ φ +−=

22

2

4140

α+≡A

41

3

⎟⎞

⎜⎛

φ φ PMm

240 φm

0 10 ⎟⎟⎠

⎜⎜⎝

≅λ

φ φ P⇒<< 1α is 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) R.A., 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

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] 500

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300φ 0 [

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mφ [GeV]

0 0 500 1000 1500 2000

mφ [GeV])1000100(inf −≅H GeV

Important properties:

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

sn

2) Creation of matter after inflation is guaranteed, and can be treated reliably (inflaton is a linear combination of sparticles).

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

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

sH n,δΔ0φφmλAmThree parameters: (can be traded for )

Oth i t i d t fi i fl t t

Δ,, 0φφmλφ ,, Am

Other experiments required to fix inflaton parameters

Cosmology/Phenomenology Complementarity:The inflaton mass is connected to low energy masses via RGEsThe inflaton mass is connected to low energy masses via RGEs.R.A., Dutta, Mazumdar PRD 75, 075018 (2007)

3

~~~ ddu ++=φ

3

2~

2~

2~2 ddu mmm

m++

=⇒ φ3 3~~~ eLL ++φ

2~

2~

2~2 eLL mmm ++

⇒3

=φ3

2 eLLm =⇒ φ

However have no bearing for phenomenology. Their only role is to give rise to successful inflation.

λ,Ag

How to determine the parameters experimentally?

3

~~~ ddu ++=φ

3

⎟⎠⎞

⎜⎝⎛ +−= 2

12

123

232

2

524

61 gMgM

ddm

πμμ φ

⎠⎝ 56d πμ

⎟⎠⎞

⎜⎝⎛ +−= 2

112332 5

83

164

1 gMgMddA

πμμ

~~~ eLL ++

⎠⎝μ

3eLL ++

=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

⎟⎞

⎜⎛ Mm 4

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

0m

2�A

2

0.75

1

40m

0.25

0.5

13 14 15 16Μ

0.25

2200200018001600ALog�

���������������GeV

�

4002200,2000,1800,1600

==

φmA

0.8

0.6

0.8A

2 0.6

0m

2�A

2

0.440m

0.2

12.5 13 13.5 14 14.5 15 15.5 16Μ

Log����������������GeV

�

mSUGRA-udd, tan β=10, A =0, >0mSUGRA-udd, tan β=10, A =0, >0mSUGRA-udd, tan β=10, A =0, >0mSUGRA-udd, tan β=10, A =0, >0mSUGRA-udd, tan β=10, A =0, >0mSUGRA-udd, tan β=10, A =0, >0

The RGEs can be used to map mSUGRA parameter space into plane: R.A., Dutta, Santoso arXiv:1004.27410φφ −m

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mSUGRA-LLe, tan β=10, A =0, >0mSUGRA-LLe, tan β=10, A =0, >0mSUGRA-LLe, tan β=10, A =0, >0mSUGRA-LLe, tan β=10, A =0, >0mSUGRA-LLe, tan β=10, A =0, >0mSUGRA-LLe, tan β=10, A =0, >0

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

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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

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012 G

eV]

uddLLe

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eV]

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eV]

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eV]

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200

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200 250 300mφ[GeV]

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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:

K hl d l i fl ti ithi KKLT tKahler modulus inflation within a KKLT set up:σσ BeAeWW ba

flux ++= −−

2, δδ CVVVV F

flux

=+=

I fl ti i t b f d lti i l l i fl ti

2,σF

Inflection point can be found, resulting in a low-scale inflationdriven by :σ

T VT VH 300050

This model gives rise to mirage mediation of SUSY

TeVmTeVmH 3000~,50~~ 2/3inf σ

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

Predictions for LHC:

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

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

• Scalar masses mainly come from anomaly mediation.

Reheat temperature is very low in the modelReheat temperature is very low in the model

(challenge for baryogenesis)MeVTR 200~

Successful baryogenesis with R.A., Dutta, Sinha arXiv:1005.2804

• TeV scale color triplet fields

• 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.