Entropy, Baryon Asymmetry and Dark Matter from Heavy Neutrino Decays.

Entropy, Baryon Asymmetry and Dark Matter from Heavy Neutrino Decays. Kai Schmitz Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany Based on arxiv:1008.2355 [hep-ph] and arxiv:1104.2750 [hep-ph]. In collaboration with W. Buchmüller and G. Vertongen. 6. Kosmologietag, IBZ, Bielefeld University May 5, 2011

Outline 1 Idea Reheating through heavy neutrino decays Leptogenesis and gravitino dark matter 2 Scenario False vacuum decay Particle interactions 3 Analysis Parameter study Conclusion Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, 2011 2 / 10

Idea Reheating through heavy neutrino decays Origin of the hot phase of the early universe? Epoch dominated by energy in radiation: Evidence: CMB (T 0.25eV) and BBN (T 1MeV). Paradigm: Preceded by inflation (vacuum domination). Transition? Reheating mechanism and T RH unknown. Definition T RH : H (T =: T RH ) = Γ X T RH 0.2 Γ X M P. Γ X free parameter! Our idea: Entropy from heavy neutrino decays Assume dominant N 1 abundance after inflation. Type I seesaw: Add heavy Majorana neutrinos N i to the SM. At tree-level Γ N1 = m 1 8π (M 1/v EW ) 2, m 1 := ( m Dm D )11 /M 1. T RH = T RH ( m 1,M 1 ) 10 9 10 GeV for typical m 1 & M 1. Baryon asymmetry & dark matter are natural by-products. Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, 2011 3 / 10

Idea Reheating through heavy neutrino decays Origin of the hot phase of the early universe? Epoch dominated by energy in radiation: Evidence: CMB (T 0.25eV) and BBN (T 1MeV). Paradigm: Preceded by inflation (vacuum domination). Transition? Reheating mechanism and T RH unknown. Definition T RH : H (T =: T RH ) = Γ X T RH 0.2 Γ X M P. Γ X free parameter! Our idea: Entropy from heavy neutrino decays Assume dominant N 1 abundance after inflation. Type I seesaw: Add heavy Majorana neutrinos N i to the SM. At tree-level Γ N1 = m 1 8π (M 1/v EW ) 2, m 1 := ( m Dm D )11 /M 1. T RH = T RH ( m 1,M 1 ) 10 9 10 GeV for typical m 1 & M 1. Baryon asymmetry & dark matter are natural by-products. Consistent cosmology and non-trivial parameter relations! Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, 2011 3 / 10

Idea Leptogenesis and gravitino dark matter Baryon asymmetry and dark matter [Fukugita & Yanagida 86] [Buchmüller et al. 05] [Bolz et al. 01] [Steffen & Pradler 07] Baryogenesis through leptogenesis: η B := n B /n γ 6 10 10 η sym B 10 18. SM sphalerons convert L into B asymmetry (c sph ). Seesaw & neutrino data: M 1 T L 10 9 10 GeV. (Non-)thermal N 1 production: η B = η B ( m 1,M 1 ). ε 1 = Γ Γ Γ+ Γ CP-violating out-of-equilibrium N 1 neutrino decays Th. prod. of gravitinos in SUSY QCD: Do not spoil BBN or overclose the universe. DM for free if gravitino is heavy stable LSP. Ω Gh 2 (T RH,m G,m g ) 0.11 Ω DM h 2. Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, 2011 4 / 10

Idea Leptogenesis and gravitino dark matter Baryon asymmetry and dark matter [Fukugita & Yanagida 86] [Buchmüller et al. 05] [Bolz et al. 01] [Steffen & Pradler 07] Baryogenesis through leptogenesis: η B := n B /n γ 6 10 10 η sym B 10 18. SM sphalerons convert L into B asymmetry (c sph ). Seesaw & neutrino data: M 1 T L 10 9 10 GeV. (Non-)thermal N 1 production: η B = η B ( m 1,M 1 ). ε 1 = Γ Γ Γ+ Γ CP-violating out-of-equilibrium N 1 neutrino decays Connect the two sectors! Ω Gh 2 ( m 1,M 1,m G,m g ) = Ω DM h 2 Keep m g fixed & solve for M 1. M 1,T RH,η B = f ( m 1,m G). Th. prod. of gravitinos in SUSY QCD: Do not spoil BBN or overclose the universe. DM for free if gravitino is heavy stable LSP. Ω Gh 2 (T RH,m G,m g ) 0.11 Ω DM h 2. Impose η B ( m 1,m G) η obs B. Mutual bounds m 1 m G. Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, 2011 4 / 10

Scenario False vacuum decay Generating a dominant nonthermal N 1 abundance SSB of U(1) B L at v B L by gauge singlet S: ( Seesaw: 1 2 M i n C n Ri Ri + h.c. ) violates lepton number L. ( Interpretation: 1 2 h(n) i n C n Ri RiS + h.c. ), S v B L + 1 S. 2 Hybrid inflation = Chaotic inflation+ssb S be the field coupling to the inflaton φ in hybrid inflation. False vacuum decay breaks B L and ends inflation. Tachyonic preheating: [Felder et al. 01] [García-Bellido & Ruiz Morales 02] Instability for φ < φ crit causes explosive spinodal growth of long-wavelength S modes: Waterfall transition! False vacuum energy density transferred to non-relativistic S bosons and due to expected h (n) i to N 2,3 neutrinos. Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, 2011 5 / 10

Scenario False vacuum decay Generating a dominant nonthermal N 1 abundance SSB of U(1) B L at v B L by gauge singlet S: ( Seesaw: 1 2 M i n C n Ri Ri + h.c. ) violates lepton number L. ( Interpretation: 1 2 h(n) i n C n Ri RiS + h.c. ), S v B L + 1 S. 2 Hybrid inflation = Chaotic inflation+ssb S be the field coupling to the inflaton φ in hybrid inflation. False vacuum decay breaks B L and ends inflation. Tachyonic preheating: [Felder et al. 01] [García-Bellido & Ruiz Morales 02] Instability for φ < φ crit causes explosive spinodal growth of long-wavelength S modes: Waterfall transition! False vacuum energy density transferred to non-relativistic S bosons and due to expected h (n) i to N 2,3 neutrinos. Assume 2M 1 m S 2M 2,3 s.t. S decays after SSB yield dominant N 1 abundance. Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, 2011 5 / 10

Scenario Particle interactions Initial State after N 2,3 Decay Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, 2011 6 / 10

Scenario Particle interactions Decay of Non-Thermally Produced N 1 Neutrinos Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, 2011 6 / 10

Scenario Particle interactions Decay of Thermally Produced N 1 Neutrinos Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, 2011 6 / 10

Scenario Particle interactions Boltzmann equations (S) ˆLf S (t,p) = m S E S Γ 0 S f S (t,p) ( N S 1 ) ( N T 1 ) ˆLf S N 1 (t,p) = M 1 E N1 Γ 0 N 1 f S N 1 (t,p) + 2 π2 Γ 0 S N S δ(e N1 m S /2) a 3 EN 2 1 ( ) ah d da NT N 1 = Γ T N 1 NN T 1 N eq N 1 ( ) (B L) ah d da N B L = ε 1 Γ S N 1 NN S 1 + ε 1 Γ T N 1 NN T 1 N eq N 1 ( G) 1 (2M 1 /m S ) 2 Neq N 1 2N eq l ( ) [ ah d da N G = κ G a 3 (T ) m2 g 54ζ (3)gs 1 + 2 (T ) π 2 T 6 ln M p 3m 2 G ( ) (R) ah d da N R = r S R Γ S N 1 NN S 1 + r T R Γ T N 1 NN T 1 N eq N 1 Γ T N 1 N B L ( T 2 m 2 g(t ) ) ] + 0.8846 with ˆL = t Hp, Γ S/T p N 1 = M1 E N1 Γ S/T 0 N 1, κ G O(1) and r S/T R = 3ρS/T N n R 1. 4n S/T N ρ R 1 Coupled system of non-linear first-order partial differential eqns. Solve for phase space distr. funcs. & number densities in an expanding FLRW background. Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, 2011 7 / 10

Analysis Parameter study Reheating temperature and baryon asymmetry M 1 (v B L, m 1,m G,m g ) s. t. Ω Gh 2 = 0.11 η B (v B L, m 1,M 1 ) = η S B + η T B > η obs B Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, 2011 8 / 10

Analysis Parameter study Reheating temperature and baryon asymmetry M 1 (v B L, m 1,m G,m g ) s. t. Ω Gh 2 = 0.11 η B (v B L, m 1,M 1 ) = η S B + η T B > η obs B Appreciate: Thermal bounds significantly alleviated! Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, 2011 8 / 10

Analysis Parameter study Reheating temperature and baryon asymmetry M 1 (v B L, m 1,m G,m g ) s. t. Ω Gh 2 = 0.11 η B (v B L, m 1,M 1 (v B L, m 1,m G,m g )) > η obs B Appreciate: Thermal bounds significantly alleviated! Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, 2011 8 / 10

Analysis Parameter study Connection between SUGRA and neutrino parameters Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, 2011 9 / 10

Analysis Parameter study Connection between SUGRA and neutrino parameters Scenario works in large region of parameter space! T RH bound lowered: 10 9 GeV 10 7 GeV. m 1 and m G mutually constrain each other. Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, 2011 9 / 10

Analysis Conclusion All you need is neutrino decays! Idea: Neutrino decays produce all entropy of the hot early universe. Reheating temperature T RH determined by neutrino lifetime Γ N1 ( m 1,M 1 ). BAU through leptogenesis and gravitino DM follow naturally + interrelated. Scenario: Dominant nonth. N 1 abundance after false vacuum decay. Hybrid inflation ends in SSB of local U(1) B L and tachyonic preheating. Vacuum energy density Higgs bosons of B L breaking N 1 neutrinos. Analysis: Quantitative results after solving the Boltzmann equations. T RH, η B and Ω Gh 2 from Lagrangian parameters v B L, m 1, M 1, m G and m g. m 1 constrains m G and vice versa. Falsification: Measure m i 0.1eV. Connection b/t collider searches, laboratory exps. and cosmological obs. Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, 2011 10 / 10

Analysis Conclusion All you need is neutrino decays! Idea: Neutrino decays produce all entropy of the hot early universe. Reheating temperature T RH determined by neutrino lifetime Γ N1 ( m 1,M 1 ). BAU through leptogenesis and gravitino DM follow naturally + interrelated. Scenario: Dominant nonth. N 1 abundance after false vacuum decay. Hybrid inflation ends in SSB of local U(1) B L and tachyonic preheating. Vacuum energy density Higgs bosons of B L breaking N 1 neutrinos. Analysis: Quantitative results after solving the Boltzmann equations. T RH, η B and Ω Gh 2 from Lagrangian parameters v B L, m 1, M 1, m G and m g. m 1 constrains m G and vice versa. Falsification: Measure m i 0.1eV. Connection b/t collider searches, laboratory exps. and cosmological obs. Thank you for your attention! Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, 2011 10 / 10

Appendix Froggatt-Nielson flavor model Yukawa couplings Superpotential for matter fields in SU(5) notation: W M = h (u) ij 10 i 10 j H u + h (d) ij 5 i 10 j H d + h (ν) ij 5 i 1 j H u + h (n) i 1 i 1 i S. Fermion irreps: 10 i = (q i,ui c,ei c) ; 5 i = (di c,l i ) ; 1 i = (n i ) ; N i := n i + ni c. Froggatt-Nielson U(1) FN flavor symmetry: [Buchmüller & Yanagida 99] Yukawa terms are generated from non-renorm. U(1) FN -inv. higher-dim. operators: h ij η Q i +Q j ; η := v FN /Λ 1/ 300 ; Λ > Λ GUT. FN parameter η and charges Q i determined from quark and lepton mass hierarchies. ψ i 10 3 10 2 10 1 5 3 5 2 5 1 1 3 1 2 1 1 Q i 0 1 2 a a a + 1 b c d Specific example: a = 0.5, d = 1.5. Require M 1 M 2,3 = m S b = c = d 1 = 0.5. v B L 6 10 13 GeV ; M 1 10 10 Gev ; M 2,3 = m S v B L. Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, 2011 1 / 4

i Appendix f Exemplary parameter point Comoving number densities Inverse temperature M 1 T 10 1 10 0 10 1 10 2 N(a) = a 3 n(a) abs N a 10 40 10 35 10 30 10 25 N 1 T S N 1 eq N 1 S a RH a ts a t1 a trh a RH R B L 10 20 10 0 10 1 10 2 10 3 10 4 10 5 Scale factor a G v B L = 6 10 13 GeV M 1 = 1 10 10 GeV m 1 = 3 10 3 ev m G = 100GeV m g = 800GeV ε max 1 = +1 10 6 ε2,3 max = 4 10 4 η max B = 1.9 10 8 > η obs B Ω Gh 2 = 0.11 = Ω obs DM h2 6 10 10 10 34 10 32 10 30 10 28 10 26 10 24 N 1 eq N 1 T B L Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, 2011 2 / 4

Appendix Generalization to different gluino masses Rescaling the gravitino mass for m g 800GeV ( Solve Ω Gh 2 T RH,m 0 G,800GeV ) = Ω Gh 2 (T RH,m G,m g ). ( ) Quadratic eq. for m G m g,m 0 G w/ two solutions m ±. G For m 0 G m g : m G = m 0 G (m g /800GeV) 2. T RH and η B unaffected as long as v B L, m 1 and M 1 are kept constant. Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, 2011 3 / 4

Appendix Theoretical uncertainty in the gravitino production rate Connection between SUGRA and neutrino parameters Scenario works in large region of parameter space! T RH bound lowered: 10 9 GeV 10 7 GeV. m 1 and m G mutually constrain each other. Kai Schmitz (DESY Hamburg) Entropy, BAU and DM from Heavy Neutrino Decays 6. Kosmologietag Bielefeld May 5, 2011 4 / 4