R 2 -inflation vs Higgs-inflation: crucial tests in Particle physics and Cosmology. Dmitry Gorbunov

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1 R 2 -inflation vs Higgs-inflation: crucial tests in Particle physics and Cosmology Dmitry Gorbunov Institute for Nuclear Research, Moscow, Russia Hot topics in Modern Cosmology Spontaneous Workshop VI IESC, Cargese, France, Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 1 / 30

2 The essence of the matter on two slides: question There are two inflationary models without NEW scalar(s) in PARTICLE PHYSICS SECTOR: A.Starobinsky (1980) R 2 -inflation Higgs-inflation F.Bezrukov, M.Shaposhnikov (2007) S JF = M2 ) ( ) P g d 4 x (R R2 g 2 6 µ 2 + Smatter = JF, SJF d 4 x M2 P 2 R ξ H HR + Smatter JF with the same inflaton potential at inflation and right after 0.20 U(χ) λm 4 /ξ 2 / λm 4 /ξ 2 λ v 4 /4 / v 0 0 χ end χ WMAP χ How one can distinguish one model from another? Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 2 / 30

3 The essence of the matter on two slides: answer 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) R 2 -inflation vs Higgs-inflation , SW6 3 / 30

4 Outline Outline 1 Motivation: Phenomena Observed but Unexplained within the SM 2 Starting from R 2 -inflation: no new interactions 3 Starting from Higgs-inflation: no new fields 4 Distinguishing between the two models 5 Summary and minimal extensions: back to motivation Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 4 / 30

5 Motivation: Phenomena Observed but Unexplained within the SM Outline 1 Motivation: Phenomena Observed but Unexplained within the SM 2 Starting from R 2 -inflation: no new interactions 3 Starting from Higgs-inflation: no new fields 4 Distinguishing between the two models 5 Summary and minimal extensions: back to motivation Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 5 / 30

6 Motivation: Phenomena Observed but Unexplained within the SM Neutrino oscillations: masses and mixing angles Solar 2 2 subsector Atmospheric 2 2 subsector ) 2 ev 3 (10 2 m MINOS best oscillation fit MINOS 90% Super K 90% MINOS 68% Super K L/E 90% K2K 90% sin 2 (2θ) m 1 > ev DAYA-BAY, RENO: sin 2 2θ arxiv: m 2 > 0.05 ev Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 6 / 30

7 Motivation: Phenomena Observed but Unexplained within the SM Baryons and Dark Matter in Astrophysics Rotation curves Gravitational lensing X-rays from clusters Bullet cluster Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 7 / 30

8 Motivation: Phenomena Observed but Unexplained within the SM Baryons and Dark Matter in Cosmology Standard candles Angular distance BBN (m-m) (mag) (m-m) (mag) Ground Discovered HST Discovered Empty (Ω=0) Ω M=0.27, Ω Λ=0.73 "replenishing" gray Dust high-z gray dust (+Ω M=1.0) Ω M=1.0, Ω Λ=0.0 Evolution ~ z, (+Ω M=1.0) θ (mas) Yp D 0.24 H Li/H p He D/H p 3 He/H p Baryon density Ω b h BBN CMB z z Baryon-to-photon ratio η Structures BAO CMB fluctuations Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 8 / 30

9 Cosmological parameters: Ω DM = 0.22, Ω B = Baryon density Ω b h No Big Bang He Y p D 0.24 H Motivation: Phenomena Observed but Unexplained within the SM 1.0 SNe D/H p 3 He/H p BBN CMB Li/H p BAO Flat CMB arxiv: Baryon-to-photon ratio η Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 9 / 30

10 Motivation: Phenomena Observed but Unexplained within the SM Inflationary solution of Hot Big Bang problems Temperature fluctuations δt /T 10 5 Universe is uniform! conformal time conformal time space coordinate particle horizon casually connected regions inflationary expansion δρ/ρ 10 5 space coordinate Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 10 / 30

11 Motivation: Phenomena Observed but Unexplained within the SM 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 particle physics as possible Why? No any hints observed so far! No FCNC No WIMPs No Nothing new at all Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 11 / 30

12 Outline Starting from R 2 -inflation: no new interactions 1 Motivation: Phenomena Observed but Unexplained within the SM 2 Starting from R 2 -inflation: no new interactions 3 Starting from Higgs-inflation: no new fields 4 Distinguishing between the two models 5 Summary and minimal extensions: back to motivation Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 12 / 30

13 Starting from R 2 -inflation: no new interactions Inflation: R 2 term S JF = M2 P 2 g d 4 x ( R R2 6 µ 2 ) + S JF matter, Jordan Frame Einstein Frame A.Starobinsky (1980) ( ) g µν g µν = χ g µν, χ = exp 2/3φ/MP. S EF = g d 4 x [ M2 P 2 R gµν µ φ ν φ 3 µ2 MP 2 4 ( 1 1 ) ] 2 + Smatter EF χ (φ), 0.20 generation of (almost) scale-invariant scalar perturbations from exponentially stretched quantum fluctuations δρ/ρ 10 5 requires µ = m φ M P 0.05 Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 13 / 30

14 Starting from R 2 -inflation: no new interactions Post-inflationary Reheating: provided by gravity Smatter JF = S(g µν,ϕ,a µ,...) Smatter EF = S( g µν, ϕ,ãµ,...) ( ) g µν g µν = χ g µν, χ = exp 2/3φ/MP. for free (in the Jordan frame) scalar ϕ and fermion ψ fields: ( Sϕ EF = g d 4 1 x 2 gµν µ ϕ ν ϕ 1 2 χ m2 ϕ ϕ2 + ϕ2 S EF ψ = g d 4 x ( i ψ ˆDψ m ψ χ ψ ψ ). g µν 12MP 2 µ φ ν φ + ϕ ) g µν µ ϕ ν φ, 6MP ϕ ϕ = χ 1/2 ϕ, ψ ψ = χ 3/4 ψ, ˆD ˆD = χ 1/2 ˆD New scale m φ µ is screened: δl JF = M2 P 2µ 2 R2 Lφ EF 1/M P Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 14 / 30

15 Starting from R 2 -inflation: no new interactions Reheating: decay of scalarons ρ φ = µ 2 φ 2 /2 = µn φ ρ rad T 4 µ m ϕ,m ψ µ 3 Γ φ ϕϕ = 192π MP 2, µ m2 ψ Γ φ ψψ = 48π MP 2. ( T reh g 1/4 Nscalars µ 3 ) 1/2, M P for the SM with 4 scalar degrees of freedom: A.Starobinsky (1980,1981) T reh GeV D.G., A.Panin (2010) Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 15 / 30

16 Outline Starting from Higgs-inflation: no new fields 1 Motivation: Phenomena Observed but Unexplained within the SM 2 Starting from R 2 -inflation: no new interactions 3 Starting from Higgs-inflation: no new fields 4 Distinguishing between the two models 5 Summary and minimal extensions: back to motivation Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 16 / 30

17 Starting from Higgs-inflation: no new fields Higgs-driven inflation S = d 4 x ( g M2 P ( In a unitary gauge H T = 0,(h + v)/ ) 2 2 R ξ H HR + L SM (and neglecting v = 246 GeV) S = d 4 x ( g M2 P + ξ ) h2 R + ( µ h) 2 λ h F.Bezrukov, M.Shaposhnikov (2007) ) slow roll behavior due to modified kinetic term even for λ 1 Go to the Einstein frame: (M 2 P + ξ h2 )R M 2 P R g µν = Ω 2 g µν, Ω 2 = 1 + ξ h2 M 2 P with canonically normalized χ: dχ dh = M P MP 2 + (6ξ + 1)ξ h2 MP 2 + ξ, U(χ) = h2 λm 4 P h4 (χ) 4(M 2 P + ξ h2 (χ)) 2. we have a flat potential at large fields: U(χ) h M P / ξ Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 17 / 30

18 Starting from Higgs-inflation: no new fields U(χ) MP λm 4 /ξ 2 /4 log(χ) MP /ξ exact h 3/2ξh 2 /MP 6 log( ξh/mp ) MP / MP /ξ ξ log(h) Reheating by Higgs field after inflation: M P /ξ < h < M P / ξ λm 4 /ξ 2 λ v 4 /4 / v 0 0 χ end χ WMAP χ exponentially flat h M P / ξ : effective dynamics : h 2 χ U(χ) = λm4 P 4ξ 2 ( ( )) 2 2 χ 1 exp 3MP L = 1 2 µ χ µ χ λ 6 M 2 P ξ 2 χ2 Advantage: NO NEW interactions to reheat the Universe inflaton couples to all SM fields! coincides with R 2 -model! But NO NEW d.o.f , from WMAP-normalization: ξ λ Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 18 / 30

19 Starting from Higgs-inflation: no new fields U(χ) MP λm 4 /ξ 2 /4 log(χ) MP /ξ exact h 3/2ξh 2 /MP 6 log( ξh/mp ) MP / MP /ξ ξ log(h) Reheating by Higgs field after inflation: M P /ξ < h < M P / ξ λm 4 /ξ 2 λ v 4 /4 / v 0 0 χ end χ WMAP χ exponentially flat h M P / ξ : effective dynamics : h 2 χ U(χ) = λm4 P 4ξ 2 ( ( )) 2 2 χ 1 exp 3MP L = 1 2 µ χ µ χ λ 6 M 2 P ξ 2 χ2 Advantage: NO NEW interactions to reheat the Universe inflaton couples to all SM fields! coincides with R 2 -model! But NO NEW d.o.f , from WMAP-normalization: ξ λ Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 18 / 30

20 Starting from Higgs-inflation: no new fields F.Bezrukov, D.G., M.Shaposhnikov, log(χ) MP MP /ξ MP /ξ exact h 3/2ξh 2 /MP 6 log( ξh/mp ) log(h) MP / ξ Reheating by Higgs field after inflation: M P /ξ < h < M P / ξ mw 2 (χ) = g2 2 6 m t (χ) = y t M P χ (t) ξ M P χ (t) sign χ(t) 6ξ reheating via W + W, ZZ production at zero crossings then nonrelativistic gauge bosons scatter to light fermions W + W f f effective dynamics : h 2 χ L = 1 2 µ χ µ χ λ 6 M 2 P ξ 2 χ2 Advantage: NO NEW interactions to reheat the Universe inflaton couples to all SM fields! Hot stage starts almost from T = M P /ξ GeV: ( ) λ 1/ GeV < T r < GeV from WMAP-normalization: ξ λ Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 19 / 30

21 Starting from Higgs-inflation: no new fields Fine theoretical descriptions both in U(χ) UV: ( χ M P, U = const + O exp ( 2 χ/ )) 3M P λm 4 /ξ 2 /4 and in IR: h M P /ξ, U = λ 4 h4 no gravity corrections at inflation! (Unlike βx 4 ) All inflationary predictions are robust Obvious problem with QFT-description of IR/UV matching at intermediate χ < χ end and h < M P / ξ Hence no reliable prediction for the SM Higgs boson mass m h = 2λ v except absence of the Landau pole and wrong minimum of the Higgs potential (well) below M P /ξ 125GeV m h 195GeV λm 4 /ξ 2 /16 λ v 4 /4 0 0 v 0 0 χ end χ WMAP χ exponentially flat h M P / ξ : U(χ) = λm4 P 4ξ 2 coincides with R 2 -model! ( ( )) 2 2 χ 1 exp 3MP But NO NEW d.o.f , from WMAP-normalization: ξ λ Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 20 / 30

22 Starting from Higgs-inflation: no new fields Fine theoretical descriptions both in U(χ) UV: ( χ M P, U = const + O exp ( 2 χ/ )) 3M P λm 4 /ξ 2 /4 and in IR: h M P /ξ, U = λ 4 h4 no gravity corrections at inflation! (Unlike βx 4 ) All inflationary predictions are robust Obvious problem with QFT-description of IR/UV matching at intermediate χ < χ end and h < M P / ξ Hence no reliable prediction for the SM Higgs boson mass m h = 2λ v except absence of the Landau pole and wrong minimum of the Higgs potential (well) below M P /ξ 125GeV m h 195GeV λm 4 /ξ 2 /16 λ v 4 /4 0 0 v 0 0 χ end χ WMAP χ exponentially flat h M P / ξ : U(χ) = λm4 P 4ξ 2 coincides with R 2 -model! ( ( )) 2 2 χ 1 exp 3MP But NO NEW d.o.f , from WMAP-normalization: ξ λ Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 20 / 30

23 Starting from Higgs-inflation: no new fields Fine theoretical descriptions both in RG-evolution with energy scale µ: UV: ( χ M P, U = const + O exp ( 2 χ/ )) 3M P and in Λ dλ d log µ 2 + # λ 2 # Yt 4 IR: h M P /ξ, U = λ 4 h4 no gravity corrections at inflation! (Unlike βx 4 ) All inflationary predictions are robust m H 174 GeV Obvious problem with QFT-description of IR/UV matching at intermediate χ < χ end and h < M P / ξ Hence no reliable prediction for the SM Higgs boson mass m h = 2λ v except absence of the Landau pole and wrong minimum of the Higgs potential (well) below M P /ξ 125GeV m h 195GeV 0.5 m H GeV M P Μ,GeV U(χ) = λm4 P 4ξ 2 ( ( )) 2 2 χ 1 exp 3MP T reh GeV , from WMAP-normalization: ξ λ Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 21 / 30

24 Starting from Higgs-inflation: no new fields Strong coupling in Higgs-inflation: scatterings Jordan frame Einstein frame E Strong coupling E Strong coupling Λ Planck Λ g-s Λ Planck M P M P Λ g-s Λ gauge Λ gauge M P /ξ Weak coupling M P /ξ Weak coupling M P /ξ M P / ξ h gravity-scalar sector: M P ξ, for h M P ξ, ξ h Λ g s (h) 2 M, for M P P ξ h M P, ξ ξ h, for h M P. ξ M P /ξ M P / ξ h gravitons: Λ 2 Planck M2 P + ξ h2 gauge interactions: Λ gauge (h) { MP ξ, for h M P ξ, h, for M P ξ h, Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 22 / 30

25 Outline Distinguishing between the two models 1 Motivation: Phenomena Observed but Unexplained within the SM 2 Starting from R 2 -inflation: no new interactions 3 Starting from Higgs-inflation: no new fields 4 Distinguishing between the two models 5 Summary and minimal extensions: back to motivation Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 23 / 30

26 Distinguishing between the two models Upper limit on the Higgs boson mass R 2 -inflation: stability while the Universe evolves from Q = T reh GeV J.Espinosa, G.Giudice, A.Riotto (2007) F.Bezrukov, D.G. (2011) [ mh R2 > m t 172.9GeV 1.1GeV 2.6 αs(m Z ) ] 0.5 GeV Higgs-inflation: stability while the Universe evolves from Q = T reh GeV F.Bezrukov, M.Shaposhnikov (2009) F.Bezrukov, D.G. (2011) [ mh H > m t 172.9GeV 1.1GeV 2.1 αs(m Z ) ] 0.5 GeV stability while the Universe evolves right after inflation h GeV mh H >[ ] GeV present limit from CMS: m h < %CL Λ 2 1 m H 174 GeV m H GeV M P10 20 Uncertainties: about 2 3 GeV due to unknown QCD-corrections Important for further improvement: (N)NLO corrections in QCD coupling Μ,GeV measurement of m t and m h at LHC Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 24 / 30

27 Distinguishing between the two models Gravity waves from inflation and inflaton clumps Notice that at MD : ρ GW /ρ U 1/a, at RD : ρ GW /ρ U const One expects a break ( knee ) in inflationary GW spectrum at ν (T reh ) at MD : δρ/ρ a R 2 inflation : a reh a inf 10 7 F.Bezrukov, D.G. (2011) scalar perturbations enter nonlinear regime GW from: collapses at formation of clumps merging of clumps evaporation of clumps (scalaron decays) Since ρ GW /ρ U 1/a, the strongest signal in present GW spectrum is expected at ν (T reh ) K.Jedamzik, M.Lemoine, J.Martin (2010) Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 25 / 30

28 Distinguishing between the two models The power spectra of primordial perturbations The same potential, the same φ at the end of inflation e.g. F.Bezrukov, D.G., M.Shaposhnikov (2008) (4N + 9) n s 1 (4N + 3) 2, r 192 (4N + 3) But WMAP observes different N in the two models: k/a 0 = 0.002/Mpc exits horizon at different moments 0.05 ( ) N = 1 3 log π 2 30 log (k/a 0) 27 T 0 g 1/3 + log log Ve 1/ GeV 1 3 log 1013 GeV T reh V 1/2 Ve 1/4 M P inside horizon H(t) outside horizon inside horizon The difference is F.Bezrukov, D.G. (2011) N log 1013 GeV T reh,n R 2 = 54.37, N H = k q(t)= a(t) R 2 -inflation: n s = 0.965, r = , Higgs-inflation: n s = 0.967, r = Planck(?), CMBPol(1-2σ) inflation t e RD, MD epochs t Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 26 / 30

29 Outline Summary and minimal extensions: back to motivation 1 Motivation: Phenomena Observed but Unexplained within the SM 2 Starting from R 2 -inflation: no new interactions 3 Starting from Higgs-inflation: no new fields 4 Distinguishing between the two models 5 Summary and minimal extensions: back to motivation Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 27 / 30

30 Summary and minimal extensions: back to motivation Summary: Models without NEW scalar(s) in PARTICLE PHYSICS SECTOR A.Starobinsky (1980) R 2 -inflation Higgs-inflation F.Bezrukov, M.Shaposhnikov (2007) S JF = M2 ) ( ) P g d 4 x (R R2 g 2 6 µ 2 + Smatter = JF, SJF d 4 x M2 P 2 R ξ H HR + Smatter JF In this two models inflatons couple to the SM fields in different ways R 2 -inflation: gravity, L φ/m P Higgs-inflation: finally, at φ M P /ξ like in SM 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 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 enter nonlinear regime: gravity waves from inflaton clumps SM Higgs potenial is OK up to the reheating scale: m h 116 GeV m h GeV Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 28 / 30

31 Summary and minimal extensions: back to motivation Standard Model: Success and Problems Gauge fields (interactions): γ, W ±, Z, g Three generations of matter: L = ( ν L e L ), er ; Q = ( ul d L ), d R, u R Describes all experiments dealing with electroweak and strong interactions Does not describe Neutrino oscillations Dark matter (Ω DM ) Baryon asymmetry (ΩB ) Inflationary stage Dark energy (ΩΛ ) Strong CP: boundary terms, new topology,... Gauge hierarchy: No new scales! Quantum gravity Try to explain all above Planck-scale physics saves the day Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 29 / 30

32 Summary and minimal extensions: back to motivation Both models can be safely completed Universaly: e.g., with νmsm (3 sterile neutrinos) T.Asaka, S.Blanchet, M.Shaposhnikov (2005), T.Asaka, M.Shaposhnikov (2005) 2 neurinos at GeV scale are seesaw neutrnos, thus explainig neutrino oscillations and BAU via lepton asymmetry generation due to oscillations in primordial plasma 1 neutrino at kev scale serves as dark matter R 2 -inflation free fermion of m 10 7 GeV as dark matter 2 sterile seesaw neutrino of m GeV to explain neutrino oscillations and BAU via leptogenesis D.G., A.Panin (2010) Specifically Higgs-inflation At strong coupling scale Λ(h) one may expect nonrenormalizable operators neutrino oscillations due to (LH) 2 /Λ BAU via CP-violating Higgs decays due to (LH) 2 /Λ and LHE, LHE H 2 /Λ 2 dark matter with additional scalar or fermion F.Bezrukov, D.G., M.Shaposhnikov (2011) Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 30 / 30

33 Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 31 / 30

34 Backup slides Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 32 / 30

35 Straightforward completion of νmsm Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 33 / 30

36 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) R 2 -inflation vs Higgs-inflation , SW6 34 / 30

37 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) R 2 -inflation vs Higgs-inflation , SW6 35 / 30

38 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] Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 36 / 30

39 Production and Decays Ds ν µ µ ν µ N 2,3 µ N 2,3 π D ν µ µ π N 2,3 N 2,3 ν µ µ ν e e Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 37 / 30

40 Searches for sterile seasaw neutrinos N 2,3 Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 38 / 30

41 Searches for sterile seesaw neutrinos N 2,3 τ, s PS191 BBN CHARM, BEBC, BAU NuTeV See-saw M 2 Br(D ln) Br(D s ln) Br(D KlN) Br(D s ηln) Br(D K ln) Br(B DlN) Br(B D ln) Br(B s DslN) c τ N 10 5 cm D.G., M.Shaposhnikov (2007) Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 39 / 30

42 R 2 -inflation with dark matter, neutrino oscillations and BAU Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 40 / 30

43 Dark Matter production in scalaron decays The same universal messenger: gravity D.G., A.Panin (2010) ρ φ = µ 2 φ 2 /2 = µn φ ρ DM = m DM n DM µ 3 Γ φ ϕϕ = 192π MP 2, Γ φ ψψ = µ m2 ψ 48π MP 2. ( ) not Dark Matter Z 1/2 Nscalars ( g ) 1/4 m ϕ 7 kev, ( ) Cold Dark Matter Z 1/6 ( ) m ψ 10 7 Nscalars /12 GeV. 4 g Heavier stable particles are excluded! Scalars are overheated: p ϕ GeV at T reh GeV Still too fast for proper structure formation at 1 ev epoch... Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 41 / 30

44 Dark Matter production in scalaron decays The same universal messenger: gravity D.G., A.Panin (2010) ρ φ = µ 2 φ 2 /2 = µn φ ρ DM = m DM n DM µ 3 Γ φ ϕϕ = 192π MP 2, Γ φ ψψ = µ m2 ψ 48π MP 2. ( ) not Dark Matter Z 1/2 Nscalars ( g ) 1/4 m ϕ 7 kev, ( ) Cold Dark Matter Z 1/6 ( ) m ψ 10 7 Nscalars /12 GeV. 4 g Heavier stable particles are excluded! Scalars are overheated: p ϕ GeV at T reh GeV Still too fast for proper structure formation at 1 ev epoch... Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 41 / 30

45 Dark Matter production in scalaron decays The same universal messenger: gravity D.G., A.Panin (2010) ρ φ = µ 2 φ 2 /2 = µn φ ρ DM = m DM n DM µ 3 Γ φ ϕϕ = 192π MP 2, Γ φ ψψ = µ m2 ψ 48π MP 2. ( ) not Dark Matter Z 1/2 Nscalars ( g ) 1/4 m ϕ 7 kev, ( ) Cold Dark Matter Z 1/6 ( ) m ψ 10 7 Nscalars /12 GeV. 4 g Heavier stable particles are excluded! Scalars are overheated: p ϕ GeV at T reh GeV Still too fast for proper structure formation at 1 ev epoch... Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 41 / 30

46 Scalar Dark Matter: other ways out Two options within our paradigm of AVOIDING NEW INTERACTIONS IN PARTICLE PHYSICS: 1 switch on nonminimal (conformal) coupling to GRAVITY: ξ 2 Rϕ2 2 consider a SUPERHEAVY dark matter candidate: m ϕ > µ/2 Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 42 / 30

47 1: Light scalar with nonminimal coupling to gravity ( g Sϕ JF = d 4 1 x 2 gµν µ ϕ ν ϕ 1 2 m2 ϕϕ 2 + ξ ) 2 Rϕ2, introducing no new scales, not interfering with inflation: 0 < ξ < 1 ( ) g µν g µν = χ g µν, χ = exp 2/3φ/MP, ϕ ϕ = χ 1/2 ϕ. for free (in the Jordan frame) scalar field ϕ: [ 1 Sϕ EF = g d 4 x 2 gµν µ ϕ ν ϕ + ξ 2 R ϕ 2 1 2χ m2 ϕ ϕ ( 1 ) ϕ 2 6 ξ MP 2 g µν µ φ ν φ + 6 ( ) 1 ϕ 6 ξ g µν µ ϕ ν φ M P ]. Γ φ ϕϕ = ( 1 6ξ + 2 m2 ϕ µ 2 ) 2 µ 3 192πM 2 p. Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 43 / 30

48 1: Warm or Cold scalar dark matter Γ φ ϕϕ = ( ) 2 1 6ξ + 2 m2 ϕ µ 3 µ 2 192πMp 2 scalar production: p = µ 2 /4 mϕ, 2 a(t then redshifting p = p ) a(t reh ). Spectrum of produced dark matter particles: reheating f (p) 1 p 3/2, p (T reh) = 3 5 p T reh must be conformal with 20%-accuracy To be Warm (v DM 10 equilibrium, T 1 ev) we need: m φ 0.7MeV, then ξ 1/ , or ξ 1/ To be Cold (v DM 10 equilibrium, T 1 ev) we need: 1/ < ξ < 1/ , m φ = m φ (ξ ) > 0.7MeV Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 44 / 30

49 2: Superheavy dark matter candidate, m ϕ > µ/2 Particle production in the expanding Universe ( ds 2 = a 2 (η) dη 2 d x 2), ϕ = s/a(η), Main effect: production at the end of inflation { 2 η 2 2 x χ a2 mϕ 2 ( ) ( 1 6 ξ 6 a a + φ 2 6a 2 MP 2 + M P Calculation of Bogolubov s transformation coefficients: s(η, x) = e φ/m P m 2 ϕ ϕ2 )} V(φ) s(η, x) = 0, φ vacuum initial conditions 1 ( ) (2π) 3/2 d 3 p â p s p (η)e i p x + â ps p(η)e i p x, s p 1/ 2ω, s p iωs p. DM particle density in post-inflationary Universe m ϕ GeV to explain DM n ϕ = 1 (2πa) 3 d 3 p β p 2, β p 2 = s p 2 + ω 2 s p 2 1 2ω 2. Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 45 / 30

50 Summary on scalar Dark Matter: m ϕ (GeV) 3 1e+16 5e+15 µ/2 1e+12 1e+10 1e+08 1e+06 1e+04 1e+02 1e+00 1e-02 m ϕ, min 1e+10 1e+09 1e+08 Ω DM < Ω DM < 0.2 1/6-1e-7 1/6 + 1e-7 1 hot component, Ω DM < / ξ D.G., Panin, 1110.xxxx Minimal coupling to gravity, ξ = 0: Superheavy DM: m φ = GeV Conformal coupling to gravity, ξ = 1/6: Superheavy DM: m φ = GeV Heavy DM: m φ > 10 9 GeV is forbidden due to H m φ Warm Dark Matter: m φ 0.7 MeV Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 46 / 30

51 BAU via leptogenesis Add sterile neutrinos to explain active neutrino oscillations (OK) either νmsm (BAU via oscillations in primordial plasma) or use the same universal messenger to produce sterile neutrinos: gravity ρ φ = m 2 φ φ 2 /2 = m φ n φ ρ N = m N n N L JF = i N I γ µ µ N I y αi Lα N I Φ M I 2 N c I N I + h.c. ( ) n NI s (T reh) = M 2 I GeV seesaw mechanism: v m ν αβ = 2 y αi y 2M βi, I I neutrino of M N > GeV decays before reheating: Γ NI = M I 8π y αi 2 α m 2 atm 4π M 2 I v 2. Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 47 / 30

52 Lepton asymmetry from seesaw neutrino decays Only the lightest sterile neutrino contribution (I = 1,2, M 1 M 2 ) is enough δ L = Γ(N 1 hl) Γ(N 1 h l) Γ tot N 1 3M 1 matm 2 8πv 2 an order of magnitude estimate for the asymmetry right before the reheating L = n ( ) L s = δ L nn 1 s 1.5 M GeV we got B,0 = L / Cannot obtain much larger...! we need B, µ GeV Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 48 / 30

53 Is it sensitive to CP in active neutrino sector? One active neutrino is massless m 1 = 0, m 2 = m sol = ev, and we switch off all phases in PMNS θ 12 = 33.8, θ 23 = 45.5, α = 0, θ 13 = 0 (normal hierarchy) m 3 = m atm = ev Scan over parameters of sterile neutrino sector 1e-08 1e+16 B 1e-09 1e-10 OK M 2 (GeV) 1e+15 1e+14 1e+13 OK M 2 = M 1 1e-11 M 1 µ/2 1e-12 1e+12 1e+13 1e+14 1e+15 M 2 (GeV) M 1 = GeV Maximum B we can obtain at a given M 2 1e+12 1e+11 5e+12 1e e+13 M 1 (GeV) B,0 = Limit from above on M 2 at a given M 1 Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 49 / 30

54 Higgs-inflation with nonrenormalizable operators Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 50 / 30

55 U(χ) Fine theoretical descriptions both in λm 4 /ξ 2 /4 UV: ( χ M P, U = const + O exp ( 2 χ/ )) 3M P and in IR: h M P /ξ, U = λ 4 h4 Obvious problem with QFT-description of IR/UV matching at intermediate χ < χ end and h < M P / ξ Hence no reliable prediction for the SM Higgs boson mass m h = 2λ v λm 4 /ξ 2 /16 λ v 4 /4 0 0 v 0 0 χ end χ WMAP χ exponentially flat h M P / ξ : U(χ) = λm4 P 4ξ 2 ( ( )) 2 2 χ 1 exp 3MP coincides (apart of T reh GeV) with R 2 -model! But NO NEW d.o.f n s = 0.97, r = , N = 59 from WMAP-normalization: ξ λ Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 51 / 30

56 U(χ) Fine theoretical descriptions both in λm 4 /ξ 2 /4 UV: ( χ M P, U = const + O exp ( 2 χ/ )) 3M P and in IR: h M P /ξ, U = λ 4 h4 Obvious problem with QFT-description of IR/UV matching at intermediate χ < χ end and h < M P / ξ Hence no reliable prediction for the SM Higgs boson mass m h = 2λ v λm 4 /ξ 2 /16 λ v 4 /4 0 0 v 0 0 χ end χ WMAP χ exponentially flat h M P / ξ : U(χ) = λm4 P 4ξ 2 ( ( )) 2 2 χ 1 exp 3MP coincides (apart of T reh GeV) with R 2 -model! But NO NEW d.o.f n s = 0.97, r = , N = 59 from WMAP-normalization: ξ λ Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 51 / 30

57 Strong coupling in Higgs-inflation Jordan frame Einstein frame E Strong coupling E Strong coupling Λ Planck Λ g-s Λ Planck M P M P Λ g-s Λ gauge Λ gauge M P /ξ Weak coupling M P /ξ Weak coupling M P /ξ M P / ξ h gravity-scalar sector: M P ξ, for h M P ξ, ξ h Λ g s (h) 2 M, for M P P ξ h M P, ξ ξ h, for h M P. ξ M P /ξ M P / ξ h gravitons: Λ 2 Planck M2 P + ξ h2 gauge interactions: Λ gauge (h) { MP ξ, for h M P ξ, h, for M P ξ h, Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 52 / 30

58 What can nonrenormalizable operators do? F.Bezrukov, D.G., Shaposhnikov (2011) δl NR = a 6 Λ 2 (H H) β L 4Λ F αβ L α HH L c β + β B Λ 2 O baryon violating + + h.c. + β N 2Λ H H N c N + b L α Λ L α ( /DN) c H +, L α are SM leptonic doublets, α = 1,2,3, N stands for right handed sterile neutrinos potentially present in the model, H a = ε ab Hb, a,b = 1,2; and Λ = Λ(h) = { Λ g s (h), Λ gauge (h), Λ Planck (h) } couplings can differ significantly in different regions of h: today h < M P /ξ, at preheating M P /ξ < h < M P / ξ Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 53 / 30

59 Nonrenormalizable operators today Neutrino masses: easily hence L νν (5) = β Lv 2 F αβ 4Λ 2 ν ανβ c + h.c. ( ) Λ ev 2 1/2 GeV β L matm 2 when Λ = M P ξ can explain with GeV β L 0.2 Proton decay: probably then from experiments L (6) β B Λ 2 QQQL Λ ( ) β B τ 1/4 p π GeV 0 e years with the same one needs Λ = M P ξ GeV β B < Either B and L α are significantly different or we will observe proton decay in the next generation experiment Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 54 / 30

60 Nonrenormalizable operators today Neutrino masses: easily hence L νν (5) = β Lv 2 F αβ 4Λ 2 ν ανβ c + h.c. ( ) Λ ev 2 1/2 GeV β L matm 2 when Λ = M P ξ can explain with GeV β L 0.2 Proton decay: probably then from experiments L (6) β B Λ 2 QQQL Λ ( ) β B τ 1/4 p π GeV 0 e years with the same one needs Λ = M P ξ GeV β B < Either B and L α are significantly different or we will observe proton decay in the next generation experiment Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 54 / 30

61 Nonrenormalizable operators today Neutrino masses: easily hence L νν (5) = β Lv 2 F αβ 4Λ 2 ν ανβ c + h.c. ( ) Λ ev 2 1/2 GeV β L matm 2 when Λ = M P ξ can explain with GeV β L 0.2 Proton decay: probably then from experiments L (6) β B Λ 2 QQQL Λ ( ) β B τ 1/4 p π GeV 0 e years with the same one needs Λ = M P ξ GeV β B < Either B and L α are significantly different or we will observe proton decay in the next generation experiment Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 54 / 30

62 Leptogenesis, B L /3: can be successful i d dt ˆQ L = [Ĥint, ˆQ ] L, n L n L n L = Q L L Y = Y α Lα HE α + h.c., L νν (5) = β L 4Λ F αβ L α HH L c β + h.c. ( )) ( ) d n L /dt Im (βl 4 Tr FF FYYF YY βl 4 y τ 4 Im F 3β Fαβ F α3f33 for the gauge cutoff Λ = h one has β 4 L ( yτ 0.01 ) 4 ( 0.25 λ for gravity-scalar cutoff Λ = ξ h 2 /M P ( βl 4 yτ ) ( λ ) 5/4 ( < L < βl 4 yτ 0.01 ) 13/4 ( < L < βl 4 yτ 0.01 ) ( ) , λ In both cases the asymmetry can be (significantly) increased with operator δl τ = y τ L τ HE τ + β y L τ HE τ H H Λ 2 + ) ( ) λ one can fancy the hierarchy gives a factor up to 10 8! 1 β y y τ Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 55 / 30

63 Leptogenesis, B L /3: can be successful i d dt ˆQ L = [Ĥint, ˆQ ] L, n L n L n L = Q L L Y = Y α Lα HE α + h.c., L νν (5) = β L 4Λ F αβ L α HH L c β + h.c. ( )) ( ) d n L /dt Im (βl 4 Tr FF FYYF YY βl 4 y τ 4 Im F 3β Fαβ F α3f33 for the gauge cutoff Λ = h one has β 4 L ( yτ 0.01 ) 4 ( 0.25 λ for gravity-scalar cutoff Λ = ξ h 2 /M P ( βl 4 yτ ) ( λ ) 5/4 ( < L < βl 4 yτ 0.01 ) 13/4 ( < L < βl 4 yτ 0.01 ) ( ) , λ In both cases the asymmetry can be (significantly) increased with operator δl τ = y τ L τ HE τ + β y L τ HE τ H H Λ 2 + ) ( ) λ one can fancy the hierarchy gives a factor up to 10 8! 1 β y y τ Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 55 / 30

64 Dark matter: an example of sterile fermion L int = β N H H 2Λ N c N = β N 4 can be produced at preheating or at the hot stage h 2 Λ(h) N c N. DM fermion has to be light! (WDM?) Indeed, today b Lα Λ L α ( /DN) c H f α b Lα M N Λ. So, N is unstable with the γν partial width of the order Γ N γν 9b2 L α αg 2 F 512π 4 v 2 M 5 N Λ 2. EGRET gives τ γν > s, hence for Λ = M P : M N 200MeV, for Λ = M P /ξ : M N 4MeV Dmitry Gorbunov (INR) R 2 -inflation vs Higgs-inflation , SW6 56 / 30