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
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:
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
500mSUGRA-udd, tan β=10, A0=0, μ>0
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500mSUGRA-udd, tan β=10, A0=0, μ>0
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0 0 100 200 300 400 500 600 700 800
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0 0 100 200 300 400 500 600 700 800
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mφ [GeV]
gμ-2 bound (D) 0
0 100 200 300 400 500 600 700 800mφ [GeV]
0 0 100 200 300 400 500 600 700 800
mφ [GeV]
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
500mSUGRA-LLe, tan β=10, A0=0, μ>0
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500mSUGRA-udd, tan β=10, A0=0, μ>0
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500mSUGRA-udd, tan β=10, A0=0, μ>0
500mSUGRA-udd, tan β=10, A0=0, μ>0
500mSUGRA-udd, tan β=10, 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:
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.
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