Conformal Standard Model and Inflation Jan H. Kwapisz 1 , 2 , - - PowerPoint PPT Presentation

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Conformal Standard Model and Inflation Jan H. Kwapisz 1 , 2 , - - PowerPoint PPT Presentation

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Introduction Conformal Standard Model and Inflation Outline Backup slides Conformal Standard Model and Inflation Jan H. Kwapisz 1 , 2 , Krzysztof A. Meissner 1 1 Faculty of Physics University of Warsaw 2 Faculty of Mathematics, Informatics and

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Introduction Conformal Standard Model and Inflation Outline Backup slides

Conformal Standard Model and Inflation

Jan H. Kwapisz1,2, Krzysztof A. Meissner1

1 Faculty of Physics University of Warsaw 2 Faculty of Mathematics, Informatics and Mechanics

University of Warsaw 9 February 2018 Yukawa Institute, Kyoto University

Jan H. Kwapisz1,2, Krzysztof A. Meissner11 Faculty of Physics University of Warsaw2 Faculty of Mathematics, Conformal Standard Model and Inflation

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Inflation - problems of Λ-CDM model

Horizon problem Flatness problem Nonhomogenous CMB radiation Introducing inflation era resolves these problems! However poses a question on a mechanism which drives it.

Jan H. Kwapisz1,2, Krzysztof A. Meissner11 Faculty of Physics University of Warsaw2 Faculty of Mathematics, Conformal Standard Model and Inflation

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Experimental tests - Planck data

Figure: Bounds on ns and r, credits: PLANCK satellite data

Jan H. Kwapisz1,2, Krzysztof A. Meissner11 Faculty of Physics University of Warsaw2 Faculty of Mathematics, Conformal Standard Model and Inflation

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Non-minimally coupled Higgs inflation: Bezrukov-Shaposhnikov model.

Action: SH =

  • d4x
  • |g|
  • −M2

P + ξh2

2 R+ (1) ∂µh∂µh 2 + h2∂µθ∂µθ 2 − λ 4

  • h2 − v22
  • ,

(2) This model model gives correct values of ns and r for N ≈ 60, e-folds. n ≃ 1 − 2/N ≃ 0.97, (3) r ≃ 12/N 2 ≃ 0.0033, (4) Unitary issue. Value of parameter ξ.

Jan H. Kwapisz1,2, Krzysztof A. Meissner11 Faculty of Physics University of Warsaw2 Faculty of Mathematics, Conformal Standard Model and Inflation

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Introduction Conformal Standard Model and Inflation Outline Backup slides

Conformal Standard Model

Only slight extension Relies on Softly Broken Conformal Symmetry Mechanism (SBCS) Right handed neutrinos Introduction of sterile complex scalar (coupled only to right handed neutrinos and Higgs). Higgs particle combined from two mass states Dark matter candidates Baryogengesis via leptogenesis

Jan H. Kwapisz1,2, Krzysztof A. Meissner11 Faculty of Physics University of Warsaw2 Faculty of Mathematics, Conformal Standard Model and Inflation

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Introduction Conformal Standard Model and Inflation Outline Backup slides

Inflation in Conformal Standard Model

Lagrangian in the Jordan frame: L = 1 2∂µh∂µh+ 1 2∂µs∂µs−

  • M2

P + ξ1h2 + ξ2s2

2 R−VJ(h, s), (5) with ξi > 0. With the potential: VJ(h, s) = 1 4λ1(h2 − v2

H)2 + 1

4λp(s2 − v2

φ)2

+1 2λ3

  • h2 − v2

H

s2 − v2

φ

  • ,

(6) Einstein frame transformation: ˜ gµν = Ω2gµν, Ω2 = 1 + ξ1h2+ξ2s2

M2

P

, (7)

Jan H. Kwapisz1,2, Krzysztof A. Meissner11 Faculty of Physics University of Warsaw2 Faculty of Mathematics, Conformal Standard Model and Inflation

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Inflation in Conformal Standard Model (2)

We assume that: ξ1h2 + ξ2s2 ≫ M2

P ≫ v2 i ,

(8) And define new fields: χ =

  • 3

2 log(ξ1h2 + ξ2s2), (9) τ =h s , (10)

Jan H. Kwapisz1,2, Krzysztof A. Meissner11 Faculty of Physics University of Warsaw2 Faculty of Mathematics, Conformal Standard Model and Inflation

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Behaviour of τ and χ

Lkin ≃ 1 2(∂µχ)2 + 1 2 ξ2

1τ 2 + ξ2 2

(ξ1τ 2 + ξ2)3 (∂µτ)2, (11) and the potential in new variables reads: VE(τ, χ) = U(τ)W(χ) = λ1τ 4 + λp + 2λ3τ 2 4(ξ1τ 2 + ξ2)2

  • 1 + e−2χ/

√ 6−2

. (12) Then τ drops to minimum. Since the heavy state decouples we are left with Bezrukov-Shaposhnikov like evolution: V (χ) = λeff 4ξ2 W(χ), (13) Since inflation parameters ns, r depends only on shape of the potential, so they fit data.

Jan H. Kwapisz1,2, Krzysztof A. Meissner11 Faculty of Physics University of Warsaw2 Faculty of Mathematics, Conformal Standard Model and Inflation

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Further work

Does this model posses a UV completion? Supergravity, string theory? Can SBCS mechanism still hold and up to which scale, when considering the inflation model?

Jan H. Kwapisz1,2, Krzysztof A. Meissner11 Faculty of Physics University of Warsaw2 Faculty of Mathematics, Conformal Standard Model and Inflation

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Thank you for your attention To contact me use my mail: j.kwapisz@student.uw.edu.pl

Jan H. Kwapisz1,2, Krzysztof A. Meissner11 Faculty of Physics University of Warsaw2 Faculty of Mathematics, Conformal Standard Model and Inflation

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Source material

Kwapisz, J. H. and Meissner, K. A., Conformal Standard Model and Inflation, year 2017, arXiv 1712.03778, To appear in Acta Physica Polonica B,

  • Vol. 49, No. 2
  • F. Bezrukov and M. Shaposhnikov, The Standard

Model Higgs boson as the inflaton, Phys. Lett. B659 (2007) 703.

  • A. Lewandowski, K. A. Meissner, and H. Nicolai,

Conformal Standard Model, Leptogenesis and Dark Matter, arXiv:1710.06149[hep-th].

Jan H. Kwapisz1,2, Krzysztof A. Meissner11 Faculty of Physics University of Warsaw2 Faculty of Mathematics, Conformal Standard Model and Inflation

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Source material(2)

  • A. Starobinsky, A new type of isotropic cosmological

models without singularity, Phys.Lett. B91 (1980) 99.

  • A. H. Guth, Inflationary Universe: A possible solution to

the horizon and flatness problem, Physical Review D23 (1981)

  • A. Latosinski, A. Lewandowski, K. A. Meissner,

and H. Nicolai, Conformal standard model with an extended scalar sector, JHEP 1510 (2015) 170.

  • P. H. Chankowski, A. Lewandowski, K. A.

Meissner, and H. Nicolai, Softly broken conformal symmetry and the stability of the electroweak scale, Mod.

  • Phys. Lett. A30 (2015) 1550006.

Jan H. Kwapisz1,2, Krzysztof A. Meissner11 Faculty of Physics University of Warsaw2 Faculty of Mathematics, Conformal Standard Model and Inflation

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Source material(3)

  • O. Lebedev and H. M. Lee, Higgs Portal Inflation, Eur.
  • Phys. J., C71 (2011) 1821.

J.-O. Gong, H. M. Lee, and S. K. Kang, Inflation and dark matter in two Higgs doublet models, J. High Energ.

  • Phys. (2012) 2012: 128.
  • D. I. Kaiser, Conformal transformations with multiple

scalar fields, Phys. Rev. D81 (2010) 084044.

Jan H. Kwapisz1,2, Krzysztof A. Meissner11 Faculty of Physics University of Warsaw2 Faculty of Mathematics, Conformal Standard Model and Inflation

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Softly borken conformal symmetry mechanism

There exist a cutoff scale Λ, determined by a UV complete fundamental theory. Two mechanisms: Quadratic divergences cancels out by some symmetry The putative fundamental theory singles out a particular scale Λ, the physical cutoff, at which m2

B(Λ) ≪ Λ2 and at

which the ∝ Λ2 corrections to the physical spin-zero boson(s) (and thus to the ratio M2

EW /M 2 P ) vanish. The

crucial fact, which is at the heart of this proposal is that the coefficient in front of Λ2 can be written as a function of the bare coupling(s) only: Second one: SBCS.

Jan H. Kwapisz1,2, Krzysztof A. Meissner11 Faculty of Physics University of Warsaw2 Faculty of Mathematics, Conformal Standard Model and Inflation

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CSM with extended scalar sector

The complex scalar sterile sextet φij = φji is introduced: Lscalar = (DµH)†(DµH) + Tr(∂µφ∗∂µφ) − V (H, φ), (14) and the potential is given by a formula: V (H, φ) = m2

1H†H + m2 2Tr(φφ∗) + λ1(H†H)2

+λ2[Tr(φφ∗)]2 + 2λ3(H†H)Tr(φφ∗) + λ4Tr(φφ∗φφ∗), (15) The potential is invariant under U(3) transformations.

Jan H. Kwapisz1,2, Krzysztof A. Meissner11 Faculty of Physics University of Warsaw2 Faculty of Mathematics, Conformal Standard Model and Inflation

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τ behaviour

Table: Minimal values of the radial part of inflation potential

τ0 values stable minimum condition U0 τ0 = 0 a > 0 and b < 0

λ1 4ξ2

1 ,

τ0 = +∞ a < 0 and b > 0

λp 4ξ2

2 ,

τ0 = ±

  • b

a

a > 0 and b > 0

λ1λp−λ2

3

4(λ1ξ2

2+λpξ2 1−2λ3ξ1ξ2),

τ = 0 or τ0 = +∞ a < 0 and b < 0

λ1 4ξ2

1 or

λp 4ξ2

2 .

Then we have two types of scenarios. Either we have single Inflaton case: Higgs or single “shadow” Higgs inflation, when τ0

  • btains zero or infinity value. Slow - roll such behaviour can be

showed explicitely.

Jan H. Kwapisz1,2, Krzysztof A. Meissner11 Faculty of Physics University of Warsaw2 Faculty of Mathematics, Conformal Standard Model and Inflation