Higgs-Dilaton Cosmology: From the Early to the Late Universe Mikhail Shaposhnikov Heraklion, 8 October 2012 Heraklion, 8 October 2012 – p. 1
Outline ETOE Dilaton-Higgs Cosmology Higgs mass, stability, inflation and asymptotic safety Conclusions Heraklion, 8 October 2012 – p. 2
An alternative to SUSY, large extra dimensions, technicolor, etc Effective Theory Of Everything Heraklion, 8 October 2012 – p. 3
Definitions “Effective”: valid up to the Planck scale, quantum gravity problem is not addressed. No new particles heavier than the Higgs boson. “Everything”: neutrino masses and oscillations dark matter baryon asymmetry of the Universe inflation dark energy Heraklion, 8 October 2012 – p. 4
Particle content of ETOE Particles of the SM + graviton + dilaton + 3 Majorana leptons Heraklion, 8 October 2012 – p. 5
Symmetries of ETOE gauge: SU(3) × SU(2) × U(1) – the same as in the Standard Model Heraklion, 8 October 2012 – p. 6
Symmetries of ETOE Restricted coordinate transformations: TDIFF , det [ − g ] = 1 (Unimodular Gravity). Equations of motion for Unimodular Gravity: R µν − 1 4 g µν R = 8 πG N ( T µν − 1 4 g µν T ) Perfect example of “degravitation" - the “ g µν " part of energy-momentum tensor does not gravitate. Solution of the “technical part" of cosmological constant problem - quartically divergent matter loops do not change the geometry. But - no solution of the “main" cosmological constant problem - why Λ ≪ M 4 P ? Scale invariance can help! Heraklion, 8 October 2012 – p. 7
Symmetries of ETOE Exact quantum scale invariance No dimensionful parameters Cosmological constant is zero Higgs mass is zero these parameters cannot be generated radiatively, if regularisation respects this symmetry Scale invariance must be spontaneously broken Newton constant is nonzero W-mass is nonzero Λ QCD is nonzero Heraklion, 8 October 2012 – p. 8
Lagrangian of ETOE Scale-invariant Lagrangian L ν MSM = L SM[M → 0] + L G + 1 2( ∂ µ χ ) 2 − V ( ϕ, χ ) � ¯ c N I χ + h . c . N I iγ µ ∂ µ N I − h αI ¯ ϕ − f I ¯ � + L α N I ˜ N I , Potential ( χ - dilaton, ϕ - Higgs, ϕ † ϕ = 2 h 2 ) : � 2 ϕ † ϕ − α � 2 λχ 2 + βχ 4 , V ( ϕ, χ ) = λ Gravity part � R ξ χ χ 2 + 2 ξ h ϕ † ϕ � L G = − 2 , Heraklion, 8 October 2012 – p. 9
For λ > 0 , β = 0 the scale invariance can be spontaneously broken. The vacuum manifold: 0 = α h 2 λ χ 2 0 Particles are massive, Planck constant is non-zero: M 2 H ∼ M W ∼ M t ∼ M N ∝ χ 0 , M P l ∼ χ 0 Phenomenological requirement: v 2 ∼ 10 − 38 ≪ 1 α ∼ M 2 P l Absence of gravity: the only choice leading to interacting particles is β = 0 . With gravity this argument is lost. Still, the choice of β = 0 will be made. Heraklion, 8 October 2012 – p. 10
Roles of different particles The roles of dilaton: determine the Planck mass give mass to the Higgs give masses to 3 Majorana leptons lead to dynamical dark energy Note: dilaton is a Goldstone boson of broken dilatation symmetry = ⇒ only derivative couplings to matter, no fifth force! Roles of the Higgs boson: give masses to fermions and vector bosons of the SM provide inflation Heraklion, 8 October 2012 – p. 11
New fermions: the ν MSM Role of N 1 with mass in keV region: dark matter Role of N 2 , N 3 with mass in 100 MeV – GeV region: “give” masses to neutrinos and produce baryon asymmetry of the Universe Heraklion, 8 October 2012 – p. 12
The couplings of the ν MSM Particle physics part, accessible to low energy experiments: the ν MSM. Mass scales of the ν MSM: M I < M W (No see-saw) Consequence: small Yukawa couplings, √ m atm M I ∼ (10 − 6 − 10 − 13 ) , F αI ∼ v here v ≃ 174 GeV is the VEV of the Higgs field, m atm ≃ 0 . 05 eV is the atmospheric neutrino mass difference. Small Yukawas are also necessary for stability of dark matter and baryogenesis (out of equilibrium at the EW temperature). Heraklion, 8 October 2012 – p. 13
Scale invariance + unimodular gravity Solutions of scale-invariant UG are the same as the solutions of scale-invariant GR with the action � R �� � � ξ χ χ 2 + 2 ξ h ϕ † ϕ d 4 x � S = − − g 2 + Λ + ... , Physical interpretation: Einstein frame g µν , ( ξ χ χ 2 + ξ h h 2 )Ω 2 = M 2 g µν = Ω( x ) 2 ˜ P Λ is not a cosmological constant, it is the strength of a peculiar potential! Heraklion, 8 October 2012 – p. 14
Relevant part of the Lagrangian (scalars + gravity) in Einstein frame: � � ˜ R � − M 2 L E = − ˜ g 2 + K − U E ( h, χ ) , P K - complicated non-linear kinetic term for the scalar fields, � 1 2( ∂ µ χ ) 2 + 1 � P ( ∂ µ Ω) 2 . K = Ω 2 2( ∂ µ h ) 2 ) − 3 M 2 The Einstein-frame potential U E ( h, χ ) : λ χ 2 � 2 h 2 − α � � � λ Λ U E ( h, χ ) = M 4 4( ξ χ χ 2 + ξ h h 2 ) 2 + , ( ξ χ χ 2 + ξ h h 2 ) 2 P Heraklion, 8 October 2012 – p. 15
U E U E Dilaton Dilaton Higgs Higgs Higgs Higgs Potential for the Higgs field and dilaton in the Einstein frame. Left: Λ > 0 , right Λ < 0 . 50% chance ( Λ < 0 ): inflation + late collapse 50% chance ( Λ > 0 ): inflation + late acceleration Heraklion, 8 October 2012 – p. 16
Inflation Chaotic initial condition: fields χ and h are away from their equilibrium values. Choice of parameters: ξ h ≫ 1 , ξ χ ≪ 1 (will be justified later) Then - dynamics of the Higgs field is more essential, χ ≃ const and is frozen. Denote ξ χ χ 2 = M 2 P . Heraklion, 8 October 2012 – p. 17
Redefinition of the Higgs field to make canonical kinetic term � h ≃ ˜ Ω 2 + 6 ξ 2 d ˜ h h 2 /M 2 h for h < M P /ξ h P dh = = ⇒ for h > M P / √ ξ Ω 4 � ˜ � h ≃ M P h √ ξ exp √ 6 M P Resulting action (Einstein frame action) � R + ∂ µ ˜ h∂ µ ˜ � − M 2 h 1 λ � 4 h (˜ P ˆ d 4 x � h ) 4 S E = − ˆ g − Ω(˜ 2 2 h ) 4 Potential: 4 ˜ λ h 4 for h < M P /ξ U (˜ h ) = . � 2 � 2˜ h λM 4 − √ 1 − e for h > M P /ξ P 6 MP 4 ξ 2 Heraklion, 8 October 2012 – p. 18
Potential in Einstein frame U( χ ) λ M 4 / ξ 2 /4 Reheating Standard Model λ v 4 /4 λ M 4 / ξ 2 /16 0 0 v 0 χ end χ COBE χ 0 Heraklion, 8 October 2012 – p. 19
Slow roll stage � 2 ǫ = M 2 � dU/dχ ≃ 4 4 χ � � P 3 exp − √ 2 U 6 M P d 2 U/dχ 2 ≃ − 4 2 χ � � η = M 2 3 exp − √ P U 6 M P Slow roll ends at χ end ≃ M P h 2 N − h 2 Number of e-folds of inflation at the moment h N is N ≃ 6 end M 2 8 P /ξ χ 60 ≃ 5 M P COBE normalization U/ǫ = (0 . 027 M P ) 4 gives √ � λ N COBE λ = 49000 m H ξ ≃ 0 . 027 2 ≃ 49000 √ 3 2 v Connection of ξ and the Higgs mass! Heraklion, 8 October 2012 – p. 20
CMB parameters—spectrum and tensor modes 0.4 50 60 WMAP5 0.3 ξ 2 SM+ h R 0.2 0.1 0.0 0.94 0.96 0.98 1.00 1.02 Heraklion, 8 October 2012 – p. 21
Experimental precision normalization prescription I 0.97 0.96 n s m t � 171.2 GeV, Α s � 0.1176 0.95 normalization prescription II 0.94 LHC & PLANCK precisions 127 128 129 130 131 132 m H ,GeV Heraklion, 8 October 2012 – p. 22
Naturalness of Higgs inflation Heraklion, 8 October 2012 – p. 23
Naturalness of Higgs inflation Standard Model: is the value ξ ∼ 10 3 − 10 4 “natural”? Heraklion, 8 October 2012 – p. 23
Naturalness of Higgs inflation Standard Model: is the value ξ ∼ 10 3 − 10 4 “natural”? SM: is M P /M W ∼ 10 17 “natural”? Heraklion, 8 October 2012 – p. 23
Naturalness of Higgs inflation Standard Model: is the value ξ ∼ 10 3 − 10 4 “natural”? SM: is M P /M W ∼ 10 17 “natural”? SM: is m t /m u ∼ 10 5 “natural”? Heraklion, 8 October 2012 – p. 23
Naturalness of Higgs inflation Standard Model: is the value ξ ∼ 10 3 − 10 4 “natural”? SM: is M P /M W ∼ 10 17 “natural”? SM: is m t /m u ∼ 10 5 “natural”? SM: is m τ /m e ∼ 10 3 “natural”? Heraklion, 8 October 2012 – p. 23
Naturalness of Higgs inflation Standard Model: is the value ξ ∼ 10 3 − 10 4 “natural”? SM: is M P /M W ∼ 10 17 “natural”? SM: is m t /m u ∼ 10 5 “natural”? SM: is m τ /m e ∼ 10 3 “natural”? Real physics question is not whether this or that theory is “natural” but whether it is realised in Nature... Heraklion, 8 October 2012 – p. 23
Naturalness of Higgs inflation Standard Model: is the value ξ ∼ 10 3 − 10 4 “natural”? SM: is M P /M W ∼ 10 17 “natural”? SM: is m t /m u ∼ 10 5 “natural”? SM: is m τ /m e ∼ 10 3 “natural”? Real physics question is not whether this or that theory is “natural” but whether it is realised in Nature... If ξ is large then chaotic inflation is inevitable in the Standard model, V inf ∝ λM 4 P /ξ 2 . Heraklion, 8 October 2012 – p. 23
What happens at large ξ ? Sibiryakov, ’08; Burgess, Lee, Trott, ’09; Barbon and Espinosa, ’09 Tree amplitudes of scattering of scalars above electroweak vacuum hit the unitarity bound at energies E > Λ ∼ M P ξ What does it mean? Heraklion, 8 October 2012 – p. 24
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