Inflation and the LHC

Transcription

1 Inflation and the LHC Rouzbeh Allahverdi University of New Mexico PPC 00: 4 th International Workshop On The Interconnection Between Particle Physics And Cosology, Torino, Italy July 5, 00

2 Outline: Introduction Inflation in MSSM Properties, predictions, and paraeter space Cosology/phenoenology copleentarity LHC role Suary

3 Introduction: LHC will discover new physics beyond the SM. Microphysical explanation of ajor probles in cosology (dark atter, atter/antiatter asyetry, inflation) requires physics beyond the SM. LHC-Cosology connection: Discovering new physics at the LHC can help us learn about the early universe. LHC-Cosology connection studied for WIMP dark atter. (Talks by Bhaskar Dutta and Giacoo Polesello) Key: Dark atter related to weak scale physics

4 How about other connections between LHC & cosology? Soe connection between the odels and TeV scale physics ust exist. Exaple: TeV scale leptogenesis can be probed at the LHC Blanchet, Chacko, Granor, Mohapatra arxiv: What about inflation? (no studies until recently) LHC connection suggests low scale odels of inflation Key: Ebedding inflation in TeV scale physics

5 ) Inflation driven by the visible sector Exaple: MSSM inflation (Sparticles as the inflaton) Allahverdi, Enqvist, Garcia-Bellido, Mazudar PRL 97, 904 (006) One can Directly probe the physics of inflation at colliders Use particle physics to constrain inflation paraeters Reliably describe post-inflationary processes

6 ) Inflation driven by the SUSY breaking sector Exaple: Modular inflation (SUSY breaking odulus as the inflaton) Allahverdi, Dutta, Sinha PRD 8, 0858 (00) One can Test predictions of inflation for sparticle asses Probe new particles required for a successful post- inflation Allahverdi, Dutta, Sinha arxiv:

7 Inflation: a period of superluinal expansion of the universe. It is driven by a scalar field (inflaton). Assuptions: Canonical kinetic ters, inial coupling to gravity & H & ( V ( V ) = 0 ) H = M H : P Hubble expansion rate ε, η << Slow-roll inflation : ε V V M η M P V P V

8 ( e i, ) Slow-roll inflation occurs within a field range : a e e exp( N ) tot a = V N = tot M V i P i a : a Scale factor of the universe d N tot N COBE (0 60) flatness probles of the big-bang odel. needed to explain the isotropy and Observable: Density fluctuations (CMB teperature anisotropy). H inf δ = n = η 6ε H 5π ε M s P Aplitude Scalar spectral index 5 (COBE) (WMAP7) ± 0. 04

9 inf 0 Successful inflation possible for. H H inf << 0 GeV In low-scale odels. δ H Then generating correct requires that: ε << η n s η << GeV The second condition naturally satisfied near a point of inflection. Inflection point inflation provides a suitable fraework for low scale odels.

10 Inflation in MSSM: MSSM has any scalar fields (Higgses, squarks, sleptons). Can MSSM lead to inflation? Naive answer is no : slow-roll conditions not satisfied for TeV scale asses and known gauge/yukawa couplings. BUT: Potential can be ade sufficiently flat along various directions in the field space. Two such directions can lead to successful inflation. Allahverdi, Enqvist, Garcia-Bellido, Mazudar PRL 97, 904 (006) Allahverdi, Enqvist, Garcia-Bellido, Jokinen, Mazudar JCAP 0706, 09 (007)

11 Inflaton candidates in MSSM are two flat directions: d d u ~ ~ ~ γ β α L L b a ~ ~ ~ d d u k j i = ϕ γ β e L L k b j a i = ϕ k j, γ β α k j i b a, b,,,, b a j i γ β α in MSSM with unbroken SUSY. Lifted by SUSY breaking and higher order ters: 0 ) ( = ϕ V Lifted by SUSY breaking and higher order ters: Dine, Randall, Thoas NPB 458, 9 (996) 6 0 ϕ ϕ.). 6 ( ) ( 6 h c M A M V P P = ϕ λ ϕ λ ϕ ϕ

12 ϕ = exp( iθ ) V ( ) A, A ~ O( TeV) soft ass A-ter 6 λ = λ Quantu corrections: 0 6 6M M P P = 0 [ K log( )] A = A0[ K log( μ 0 μ 0 )] A 40 4 α << 0 α M P 0λ 4 a point of inflection

13 V inflation V ( 0 ) = 0 0 Inflection point V = ( 0 ) 4α 0 4 V ( 0) = 0 5

14 Properties, Predictions, and Paraeter Space: Density perturbations: Bueno-Sanchez, Diopoulos, Lyth JCAP 070, 05 (007) Allahverdi, Enqvist, Garcia-Bellido, Jokinen, Mazudar JCAP 0706, 09 (007) δ H 8 M P sin 5 π 0 Δ [ N Δ] COBE n s [ N Δ] = 4Δ cot COBE N Δ COBE V ( 0 ) 66.9 ln 4 M P 4 0α N COBE M 0 P A 40 4 α

15 Allowed paraeter space to generate acceptable perturbations: 5 ( δ.9 0, = 0.96 ± 0.04) ( H n s [0 0 GeV] Δ H inf (00 000) GeV [GeV]

16 Iportant properties: ) n s within the whole range allowed by WMAP can be generated (unlike other odels of inflation). ) CMB data alone cannot pinpoint the inflaton paraeters (unlike other odels of inflation). δ H, n s, A,λ Two observables: Three paraeters: (can be traded for ),, 0 Δ Other experients needed to fix inflaton paraeters How to deterine the paraeters experientally? A, λ have no bearing for phenoenology, relevant for inflation. relevant for inflation and phenoenology both.

17 Cosology/Phenoenology Copleentarity: Inflaton paraeters are related to weak scale observables via RGEs. Allahverdi, Dutta, Mazudar PRD 75, (007) In general, various phenoenological constraints can be translated into regions in the plane. 0 Cobined with CMB easureents, they narrow down the allowed region of the plane. 0 More precise easureents can deterine and. Eventually one can pinpoint, λ, A., 0 Δ To explicitly deonstrate this, consider SUGRA odel. Allahverdi, Dutta, Santoso arxiv:004.74

18 (T): Teubner, et al arxiv: (D): Davier, et al arxiv: SUGRA-udd, tan β=0, A 0 =0, μ>0 0-8 pb 400 stau-coan 0 0 [ GeV] excluded n s, δ H pb g μ - bound (T) g μ - bound (D) [GeV]

19 500 SUGRA-LLe, tan β=0, A 0 =0, μ> pb stau-coan 0 [0 GeV V] excluded n s, δ H pb g μ - bound (T) 0 g μ - bound (D) [GeV]

20 (Focus point region not shown) pb SUGRA-udd, tan β=50, A 0 =0, μ>0 funnel 0 [0 [ GeV ev] excluded stau-coan n s, δ H pb g μ - bound (T) g μ - bound (D) [GeV] μ

21 (Focus point region not shown) SUGRA-LLe, tan β=50, A 0 =0, μ> pb funnel 600 stau-coan 0 [0 GeV ev] excluded n s, δ H pb g μ - bound (T) g μ - bound (D) [GeV]

22 LHC Role: Mass easureents at the LHC can also be used to constrain plane. 0 Consider a SUSY reference point in the co-annihilation region (all asses are in GeV): 0 = 0, / = 50, tan β = 40, A0 = χ = 40.7, τ = 5., τ ~ = 0 ~ fb With of data, LHC can deterine high energy paraeters: 0 = 0 ± 4, / = 50 ± 4, tan β = 40 ±, A0 = 0 ± 6 Arnowitt, Dutta, Gurrola, Kaon, Krislock, Toback PRL 00, 80 (006)

23 00 R.A., Dutta, Santoso arxiv: [ 0 GeV] 0 00 LLe udd [GeV]

24 General approach: ) Find SUSY. ) Measure as any asses as possible (sparticles, gauginos). ) Use RGEs to extrapolate the inflaton ass to high scales. 4) Narrow down the allowed region in 0 plane. 5) Use this to find λ, A. Provides inforation about the underlying physics that induces higher order ter, SUSY breaking sector

25 Inflation fro SUSY Breaking Sector: Modular inflation within a KKLT set up. Allahverdi, Dutta, Sinha PRD 8, 0858 (00) Inflection point inflation driven by the SUSY breaking odulus: H ~ 50 inf ~ / TeV This odel gives rise to irage ediation of SUSY breaking to the observable sector. T R ~ 00 MeV Reheat teperature is very low in the odel:. Successful baryogenesis requires additional fields in the observablle sector, e.g.: TeV scale colored triplets Allahverdi, Dutta, Sinha arxiv:

26 Predictions for LHC: Successful low scale inflation iplies that: t Gaugino asses receive coparable contributions fro odulus and anoaly ediation. Scalar asses ainly coe fro anoaly ediation. The ass pattern can be tested at the LHC. In addition, i Color triplets with ass accessible at LHC. O(TeV )

27 Suary: LHC-inflation connection possible for a realistic ebedding of inflation within TeV scale physics. Inflation can be realized within MSSM. The underlying paraeters cannot be deterined fro CMB easureents alone. Particle physics experients are also needed to pinpoint the paraeters. Mass easureents at the LHC are iportant. Cobined LHC/ILC and PLANCK data can lead to precise deterination of the paraeters. Inflation can be driven by the SUSY breaking sector. Predicted sparticle asses, and new colored fields required for baryogenesis, can be probed at the LHC.

28 ~ ~ ~ d d u = ~ ~ ~ d d u = = g M g M d d π μ μ μ = g M g M d da π μ μ ~ ~ ~ e L L 5 4 d π μ ~ ~ ~ e L L = e L L = 9 d = g M g M d d π μ μ 9 da = g M g M d da π μ μ

29 The condition for successful inflation can be et dynaically due to RGEs. A 40 α = 0 α 4α, α << is scale-dependent, hence VEV-dependent. obtained within the phenoenologically interesting range 5 for a wide range of input values GeV This scale ust coincide with an inflection point: 4 P M 4 0 0λ This condition will fix the value of very precisely. λ

30 .75.5 A 8 n A =50 50,00,50,00 50 A = Μ Log GeV

31 A A = 600,800,000, = Μ Log GeV

32 0.8 0 A A Μ Log GeV

33 W aσ = W Ae flux Be bσ C V = V δv, δv = F σ