Inflationary models and scale invariance. Dmitry Gorbunov

Transcription

1 Inflationary models and scale invariance Dmitry Gorbunov Institute for Nuclear Research, Moscow, Russia Hot topics in Modern Cosmology Spontaneous Workshop VII IESC, Cargese, France, Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 1 / 30

2 Why inflation and scale invariance? Scale invariance Inflation solves horizon problem solves curvature problem provides with matter perturbations... Phenomenological problems gets rid of (classical) cosmological constant (need instead a quintessence? unimodular gravity?) eliminates quadratic divergences ( ) T µ µ Λ 2 + mh 2 h 2... Theoretical problems Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 2 / 30

3 Outline Outline 1 Higgs portal to new physics 2 Higgs portal to X 4 -inflation: light inflaton at LHCb 3 Natural completion of νmsm: neutrino mass and mixing, dark matter, baryon asymmetry of the Universe... 4 Further extension within scale invariance 5 Inflation in presence of dilaton: dilaton production at reheating Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 3 / 30

4 Outline True Extension of the Standard Model should Reproduce the correct neutrino oscillations Contain the viable DM candidate Be capable of explaining the baryon asymmetry of the Universe Have the inflationary mechanism operating at early times Guiding principle: use as little new physics as possible Why? No any hints observed so far! Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 4 / 30

5 Outline Higgs portal to new physics 1 Higgs portal to new physics 2 Higgs portal to X 4 -inflation: light inflaton at LHCb 3 Natural completion of νmsm: neutrino mass and mixing, dark matter, baryon asymmetry of the Universe... 4 Further extension within scale invariance 5 Inflation in presence of dilaton: dilaton production at reheating Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 5 / 30

6 Higgs portal to new physics New physics from the (still unknown) Higgs sector EW baryogenesis: not enough CP, not I order phase transition could be 2 Higgs doublets! Dark Matter candidate: stable due to Z 2 -symmetry Natural CDM from primordial plasma Singlet scalar field: (e.g. Burgess, Pospelov, ter Veldhuis, 2001) L = L SM ( µs) 2 m2 0 2 S2 λs 2 H H +... one of the SM portals to hidden sectors (SM-gauge singlets: no FCNC!) βb µν U(1) Y B µν U(1) Y αh H X X secluded U(1) renormalizable! fascinating example: Z Z, γ γ to be tested at h χ portal to inflaton! e.g. M.Pospelov any energy scale! F.Bezrukov, D.G. Phys Rev D80 (2009) JHEP 1005 (2010) 010 Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 6 / 30

7 Outline Higgs portal to X 4 -inflation 1 Higgs portal to new physics 2 Higgs portal to X 4 -inflation: light inflaton at LHCb 3 Natural completion of νmsm: neutrino mass and mixing, dark matter, baryon asymmetry of the Universe... 4 Further extension within scale invariance 5 Inflation in presence of dilaton: dilaton production at reheating Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 7 / 30

8 Higgs portal to X 4 -inflation Inflation & Reheating: simple realization X e > M Pl Ẍ+3HẊ + V (X) = 0 generation of scale-invariant scalar (and tensor) perturbations from exponentially stretched quantum fluctuations of X δρ/ρ 10 5 requires V = βx 4 : β reheating? renormalizable? the only choice: αh HX 2 X Chaotic inflation, A.Linde (1983) larger α larger T reh quantum corrections α 2 β No scale, no problem Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 8 / 30

9 Higgs portal to X 4 -inflation Inflation & Reheating: the model L XN = 1 2 µx µ X m2 X X 2 β 4 X 4 λ (H H α λ X 2) 2 The SM-like vacuum of the scalar potential 2α v = βλ m X = 246 GeV, m h = β 2λ v, m χ = m h 2α Higgs-inflaton (h χ) mixing angle ( ) 2α 2β v 100 MeV θ = λ = 10 3 m χ Amplitude of primordial perturbations: β F.Bezrukov, D.G. (2009) Only one free parameter! 30 MeV m χ 1.8 GeV study of reheating: T reh > 100 GeV, m h < 190 GeV A.Anisimov, Y.Bartocci, F. Bezrukov (2008) m χ Landau pole above inflation scale Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 9 / 30

10 Higgs portal to X 4 -inflation Phenomenlogy: Higgs-inflaton mixing! τ χ, s e-05 1e-06 1e-07 1e-08 1e-09 1e-10 Br(K->πχ) 1e-06 1e-07 1e-08 1e-09 1e-10 K + E949 K + E787 K + expected K L expected 1e m χ, GeV 1e m χ, GeV Branching e + e - ππ cc τ + τ KK µ + µ gg ss γγ µ + µ m χ, GeV β 1e-08 1e-10 CHARM 1e-12 β 0 1e-14 1e m χ, GeV m χ 250 MeV is already excluded! from K π χ and pn... χ(χ µ + µ ) Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 10 / 30

11 Higgs portal to X 4 -inflation Inflaton Phenomenlogy: direct searches V ts Vtb Br(B χx s ) 0.3 V cb 2 ( ( mt 1 m2 χ m 2 b ) 4 ( ) 2 θ 2 1 m2 χ M W mb 2 ) 2 (300 ) MeV 2, m χ Recent sensitivity: Br(B K ( ) l + l ) 10 7 Expectation for the Inflaton: scalar channel displaced decay vertex peaks at a given energy for Belle 250 MeV m χ 1.8 GeV B K χ c τ χ 3 30 cm µ + µ, π + π, K + K This INFLATIONARY model can be directly and fully explored thanks to B-physics! Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 11 / 30

12 Outline Natural completion of νmsm 1 Higgs portal to new physics 2 Higgs portal to X 4 -inflation: light inflaton at LHCb 3 Natural completion of νmsm: neutrino mass and mixing, dark matter, baryon asymmetry of the Universe... 4 Further extension within scale invariance 5 Inflation in presence of dilaton: dilaton production at reheating Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 12 / 30

13 Natural completion of νmsm True Extension of the Standard Model should Reproduce the correct neutrino oscillations Contain the viable DM candidate Be capable of explaining the baryon asymmetry of the Universe Have the inflationary mechanism operating at early times Guiding principle: use as little new physics as possible Why? No accidental hints observed so far! Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 13 / 30

14 Natural completion of νmsm Straightforward completion of νmsm Use as little new physics as possible Require to get the correct neutrino oscillations Explain DM and baryon asymmetry of the Universe Lagrangian Most general renormalizable with 3 right-handed neutrinos N I L νmsm = L MSM + N I i/ N I f Iα HN I L α M I 2 Nc I N I + h.c. Extra coupling constants: 3 Majorana masses M i 15 new Yukawa couplings (Dirac mass matrix M D = f Iα H has 3 Dirac masses, 6 mixing angles and 6 CP-violating phases) T.Asaka, S.Blanchet, M.Shaposhnikov (2005) T.Asaka, M.Shaposhnikov (2005) Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 14 / 30

15 Natural completion of νmsm ν Masses and Mixings: seesaw from f Iα HN I L α M I M D = f v says nothing about M I! dangerous: δm 2 h M2 I 3 heavy neutrinos with masses M I similar to quark masses Light neutrino masses M ν = (M D ) T 1 M I M D f 2 v 2 m U T M ν U = 0 m m 3 M I Mixings: flavor state ν α = U αi ν i + θ αi N c I Active-sterile mixings θ αi = (MD ) αi M I f v M I 1 Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 15 / 30

16 Natural completion of νmsm Lightest sterile neutrino N 1 as Dark Matter Non-resonant production (active-sterile mixing) is ruled out Resonant production (lepton asymmetry) requires M 2, GeV arxiv: , , sin 2 (2θ 1 ) Phase-space density constraints Ω N1 > Ω DM NRP Ω N1 < Ω DM L 6 =25 L 6 =70 L 6 max =700 BBN limit: L 6 BBN = 2500 X-ray constraints M 1 [kev] Dark Matter production from inflaton decays in plasma at T m χ M.Shaposhnikov, I.Tkachev (2006) M NI Nc I N I f I X N I N I Can be naturally Warm F.Bezrukov, D.G. (2009) ( ) mχ M 1 15 kev 300 MeV Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 16 / 30

17 Outline Further extension within scale invariance 1 Higgs portal to new physics 2 Higgs portal to X 4 -inflation: light inflaton at LHCb 3 Natural completion of νmsm: neutrino mass and mixing, dark matter, baryon asymmetry of the Universe... 4 Further extension within scale invariance 5 Inflation in presence of dilaton: dilaton production at reheating Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 17 / 30

18 Summary Further extension within scale invariance Renormalizable inflationary model βx 4 + αx 2 H H with viable reheating can be fully explored by direct searches of B X s + χ 250 MeV m χ 1.8 GeV F.Bezrukov, D.G. JHEP 1005 (2010) 010 Br(B χx s ) 10 6 χ µ + µ,π + π,k + K ( 1 m2 χ m 2 b c τ χ 3 30cm ) 2 ( ) 300 MeV 2 combined with νmsm (completed with right handed neutrinos) provides active neutrino masses and mixing angles kev neutrino as (warm) Dark Matter mechanism for baryon asymmetry generation seesaw and BAU are testable at fixed target experiments and B-factories: Br , c τ N 10 5 cm m χ D.G., M.Shaposhnikov, JHEP 0710 (2007) 015 LHC: Higgs mass from validity upto α λ M P θ M P GeV: 128 ± 4 GeV m h Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 18 / 30

19 Further extension within scale invariance Light inflaton: update in Accepting LHC8, SPT, ACT, WMAP9 and Planck 1 2 ξ R X 2 Note, it is also scale-invariant... Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 19 / 30

20 Further extension within scale invariance Light inflaton nonminimally coupled to gravity S XSM = g d 4 x ( L SM + L XH + L ext + L grav ), L XH = 1 2 µx µ X m2 X X 2 β ( 4 X 4 λ H H α λ X 2) 2, L grav = M2 P + ξ X 2 R, 2 g µν g µν = Ω 2 g µν, Ω 2 = 1 + ξ X 2 /M 2 P, U(X) = βx4 4Ω 4 const = β ξ 2 M4 P at X. X X : dx dx = Ω 2 + 6ξ 2 X 2 /MP 2 Ω 4 Outcome: β β m χ = m h 2α = λθ 2. θ 2 = 2βv 2 m 2 χ = 2α λ. β = τ χ, Br(B χ) easier to test! Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 20 / 30

21 r r Further extension within scale invariance WMAP9, 95% ξ=0 68% WMAP9+BAO, 95% 68% ξ= ξ= ξ= n s ξ ξ β n s ξ Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 21 / 30

22 1 e + e - Further extension within scale invariance ππ cc 1e-04 KK τ + τ 1e-06 Branching µ + µ gg τ χ, s 1e-08 1e-10 ξ=0.001 ξ=0.01 ss 1e-12 ξ= γγ µ + µ m χ, GeV ξ=1 1e m χ, GeV 10 6 ( 1 m2 χ m 2 b Br(B χx s) ) 2( )( β(ξ ) 300 MeV m χ ) 2 with ξ > 10 2 inflaton decays earlier, at production point and B-meson branching grows β Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 22 / 30

23 10 Further extension within scale invariance No reheating τ χ =10-9 s τ χ =10-10 s τ χ =10-11 s τ χ =10-12 s 10 τ χ =10-9 s τ χ =10-10 s τ χ =10-11 s τ χ =10-12 s ξ=0.01 ξ=0.1 ξ=1 m χ, GeV 1 m χ, GeV 1 No reheating CHARM Rad. corrections ξ<10-3 CHARM Rad. corrections ξ 0.1 1e-08 1e-07 1e-06 1e θ 2 10 No reheating B + K + µ + µ B + K + π 0 π 0 B + K + π + π B + K + K - K + 10 B + K + µ + µ B + K + π 0 π 0 B + K + π + π B + K + K - K + ξ=0.01 ξ=0.1 ξ=1 m χ, GeV 1 m χ, GeV 1 No reheating CHARM Rad. corrections ξ<10-3 CHARM Rad. corrections ξ 0.1 1e-08 1e-07 1e-06 1e θ 2 Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 23 / 30

24 Further extension within scale invariance The model of light inflaton simple renormalizable weakly coupled SM sector is scale-invariant directly testable!!! However both inflaton and gravity sectors contain dimensionful parameters (mass term m 2 X and Planck mass M 2 P ) hence they are scale non-invariant as 10 2 GeV m X M P GeV we get the hierarchy problem imaging gravity as QFT Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 24 / 30

25 Outline Inflation in presence of dilaton 1 Higgs portal to new physics 2 Higgs portal to X 4 -inflation: light inflaton at LHCb 3 Natural completion of νmsm: neutrino mass and mixing, dark matter, baryon asymmetry of the Universe... 4 Further extension within scale invariance 5 Inflation in presence of dilaton: dilaton production at reheating Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 25 / 30

26 Dilaton X gives to Inflation in presence of dilaton SM Higgs λ ( h 2 α 2 X 2) 2 λ (h 2 v 2) General Relativity ξ X 2 X 2 R M2 P 2 R For inflation one can resort to minimalistic setups provided all scale-invariant terms are introduced Higgs-inflation ξ h H HR Starobinsky model β R 2 Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 26 / 30

27 Inflation in presence of dilaton The same inflaton potential at inflation! In this two models inflatons couple to the SM fields in different ways R 2 -inflation: gravity, L φ/m P φ hh Higgs-inflation: finally, at φ M P /ξ like in SM h W + W D.G., A.Panin (2010) F.Bezrukov, D.G., M.Shaposhnikov (2008) T reh GeV T reh GeV with different length of the post inflationary matter domination stage: F.Bezrukov, D.G. (2011) somewhat different predictions for perturbation spectra n s = 0.965, r = n s = 0.967, r = break in primordial gravity wave spectra at different frequencies in R 2 perturbations 10 5 have enough time to enter nonlinear regime: gravity waves from inflaton clumps SM Higgs potenial is OK up to the reheating scale: m h 116 GeV m h 126 GeV Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 27 / 30

28 Inflation in presence of dilaton Two models with dilaton ξ h H HR J.Garcia-Bellido, J.Rubio, M.Shaposhnikov (2012) slightly shifted n s, r, R Major event: dilaton production by inflaton β R 2 D.G., A.Tokareva (in preparation) scalaron perturbative decays into dilatons Nonperturbative production (gravity driven by oscillating Higgs) δ ρ χ + (3H + )δ 2ḃ(h) ρ χ + k 2 a 2 δρ χ = 0 ( ) ρχ N eff = 10 7 ρ ν BBN Untestable ( 1 Γ hh = 6β ( 1 Γ χχ = 6β ) 3/2 4MP 192π (1 + 6ξ h) 2 ) 3/2 M P 192π N eff 2.85 ρ χ 0.71 = ρ h (1 + 6ξ h ) 2 Is already being tested!!! and for conformal Higgs H HR/6 it is forbidden Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 28 / 30

29 Inflation in presence of dilaton Border line between Higgs and R 2 If both terms are introduced (and hence all scale-invariant terms play) S 0 = d 4 x { 1 g 2 [βr2 + ( µ X) 2 ξ X X 2 R ξ h h 2 R + ( µ h) 2 ] λ } 4 (h2 α 2 X 2 ) 2. Which of nonminimal couplings ξ X, ξ h is larger? ξ h H HR β R 2 ξ 2 X < ξ 2 h, βλ < ξ 2 h ξ h < ξ X T r GeV T r GeV n s 1 8ξ X coth(4ξ X N), = ξ X < 0.01 Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 29 / 30

30 Conclusion Inflation in presence of dilaton On the way towards scale-invariant theory of everything there are simple inflationary models which are cosmologically and phenomenologically viable can be extended further to be phenomenologically complete cosmologically and phenomenologically testable Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 30 / 30

31 Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 31 / 30

32 Backup slides Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 32 / 30

33 νmsm parameter space with resonant DM CHARM NuTeV 10 6 NuTeV 10 6 CHARM U BAU BBN PS191 BAU constrained MSM BAU U BAU PS191 BBN BAU constrained MSM BAU Seesaw DM Seesaw DM M GeV M GeV L.Canetti, M.Drewes, M.Shaposhnikov Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 33 / 30

34 Inflaton mass as a function of ξ β z mi [GeV] I II III IV V y ξ ξ Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 34 / 30

35 Critical point: where EW-vacuum becomes unstable Strong coupling Λ 0.02 M h mmax M h m min Zero M Fermi M Planck Μ F.Bezrukov, M.Shaposhnikov (2009) F.Bezrukov, D.G. (2011) F.Bezrukov, M.Kalmykov, B.Kniehl, M.Shaposhnikov (2012) G. Degrassi et al (2012) Μ 0.06 m cr h > [ m t 172.9GeV 1.1GeV theoretical uncertainties 1-2 GeV present measurements at CMS and ATLAS: m h ± 0.9 GeV 2.2 αs(m Z ) ] 0.56 GeV Important for inflation, when usually h H Λ Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 35 / 30 Μ

36 Spectra 2 R = λ sinh2 (4ξ X N) 1152π 2 ξ 2 X ξ 2 h, n s 1 = 8ξ X coth(4ξ X N), U = λm 4 P (1 + 6ξ X ) 2 (ξ h ξ X ) 2 F.Bezrukov et al (2012) Dmitry Gorbunov (INR) Inflationary models and scale invariance , SW6 36 / 30