Magnetic Phenomena at Preheating

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1 Magnetic Phenomena at Preheating Andres Díaz-Gil Universidad Autónoma de Madrid 31 July 2007 In collaboration with: J.García-Bellido, M. García Pérez, A González-Arroyo A. Díaz-Gil (UAM) Magnetic Phenomena at Preheating LATT 07 1 / 19

2 Outline 1 Preheating: Preheating. Why is it interesting? (For a physicist). Why is it interesting? (For a lattice physicist). Large Scale Magnetic fields. A. Díaz-Gil (UAM) Magnetic Phenomena at Preheating LATT 07 2 / 19

3 Outline 1 Preheating: Preheating. Why is it interesting? (For a physicist). Why is it interesting? (For a lattice physicist). Large Scale Magnetic fields. 2 The use of the Lattice: Lattice electromagnetism. A. Díaz-Gil (UAM) Magnetic Phenomena at Preheating LATT 07 2 / 19

4 Outline 1 Preheating: Preheating. Why is it interesting? (For a physicist). Why is it interesting? (For a lattice physicist). Large Scale Magnetic fields. 2 The use of the Lattice: Lattice electromagnetism. 3 Some results: Simulation characteristics. Turbulent behavior and Thermalization. Magnetic field generation and evolution. A. Díaz-Gil (UAM) Magnetic Phenomena at Preheating LATT 07 2 / 19

5 Outline 1 Preheating: Preheating. Why is it interesting? (For a physicist). Why is it interesting? (For a lattice physicist). Large Scale Magnetic fields. 2 The use of the Lattice: Lattice electromagnetism. 3 Some results: Simulation characteristics. Turbulent behavior and Thermalization. Magnetic field generation and evolution. 4 Conclusions and future work. A. Díaz-Gil (UAM) Magnetic Phenomena at Preheating LATT 07 2 / 19

6 Preheating: Preheating. The Hybrid Inflation Model. Our Hybrid Inflation Model: Minimal extension of SM. to allow inflation. Inflation driven by a scalar field χ (Inflaton). Coupled to the S.M. Higgs field Φ. SU(2)xU(1) gauge group. Lagrangian of the system: ] L = 1 4 Ga µν G a µν 1 4 F µν Y F µν Y [(D + Tr µ Φ) D µ Φ V(Φ,χ) = V (g2 χ 2 m 2 ) Φ 2 + λ 4 Φ µ2 χ ( µχ) 2 V (Φ,χ) A. Díaz-Gil (UAM) Magnetic Phenomena at Preheating LATT 07 3 / 19

7 Preheating: Preheating. The Hybrid Inflation Model. The dynamics of inflaton field modifies the Higgs potential: Inflation ends at T crit : m Heff = 0 Universe is cold and empty. Preheating and Reheating Transference of energy from the inflaton to other fields. A. Díaz-Gil (UAM) Magnetic Phenomena at Preheating LATT 07 4 / 19

8 Preheating: Why is it interesting? (For a physicist). Why is it interesting? (For a physicist). Alternative to the electroweak phase transition High sphaleron rate at s.s.b, and suppressed after it (T rh < T ew ). Non-linear non perturbative process. Rich phenomenology: Topological defects (strings, domain walls, textures, monopoles). Gravitational waves production. (J.García-Bellido, D.Figeroa and A.Sastre, 2007) Magnetic field production. A. Díaz-Gil (UAM) Magnetic Phenomena at Preheating LATT 07 5 / 19

9 Preheating: Why is it interesting? (For a lattice physicist). Why is it interesting? (For a lattice physicist). Strong non-linearites arise from the equations. This makes mandatory the use of lattice techniques. Peculiarities: Non-equilibrium system: difficult direct lattice approach. But: Non-linear and gauge coupling terms can be neglected at the very beginning (t < t λ ): Exact quantum evolution. t = tλ Non-linearities become important. Tachyonic instability: Fast growth of infrared modes allows: Classical approximation: Evolution described by lattice classical equations of motion. A. Díaz-Gil (UAM) Magnetic Phenomena at Preheating LATT 07 6 / 19

10 Preheating: Large Scale Magnetic fields. Large Scale Magnetic fields. There is experimental evidence of coherent large scale magnetic fields: Scales going from galaxies to clusters Intensity µg Hypothesis: primordial origin. It is possible to generate them at preheating? Important ingredients present: Non-equilibrium Chern-Simons creation (J.García-Bellido,M.García Pérez, A.González-Arroyo (2003)) Charge and topological defects A. Díaz-Gil (UAM) Magnetic Phenomena at Preheating LATT 07 7 / 19

11 The use of the Lattice: Lattice electromagnetism. The photon field: Electric and Magnetic fields. Lattice expression for the photon electromagnetic tensor: We use a gauge invariant definition of the Z lattice field and tensor: ( Φ Ẑµ (n) = itr τ (n) Φ(n+µ) 3 φ(n) Ûµ(n) ˆB ) a 0 φ(n+µ) µ (n) a µ g Z Z µ ˆF µν Z (n)= a 0 µẑν(n) ν Ẑ µ (n) clov a µ a ν g Z Fµν Z Providing a gauge invariant definition for the electromagnetic tensor: ˆF µν γ (n) = g2 Y g ˆF 2 Y +g2 µν Z (n) ˆF Y a 0 µν (n) a µ a ν efµν γ W Ambiguities arise at points with non-broken symmetry. Gauge invariant and satisfying Bianchi identities everywhere: I B = 0, I E + 0 B = 0 A. Díaz-Gil (UAM) Magnetic Phenomena at Preheating LATT 07 8 / 19

12 Some results: Simulation characteristics. Simulation characteristics. Lattice parameters: N 3 = 100 3,80 3,64 3. p min /m = 0.15,0.12,0.1 Model parameters: g W = g Y = g 2 = 2λ v χ = m H /m W m w a s , ,0,25, , 0.20, 0, 30 A. Díaz-Gil (UAM) Magnetic Phenomena at Preheating LATT 07 9 / 19

13 Some results: Simulation characteristics. The evolution regions. S.S.B Baryo. Magneto. Turbulence Phot. Termalization The evolution presents two regions: SSB and bubble colliding region. Turbulence and thermalization region. mt Higgs 0.8 Simulation data Higgs ma=0.65, pmin= 0.1m ma=0.52, pmin=0.125m ma=0.52, pmin= 0.15m ma=0.42, pmin= 0.15m Inflaton ma=0.65, pmin= 0.1m ma=0.52, pmin=0.125m ma=0.52, pmin= 0.15m ma=0.42, pmin= 0.15m Inflaton mt A. Díaz-Gil (UAM) Magnetic Phenomena at Preheating LATT / 19

14 Some results: Turbulent behavior and Thermalization. The Turbulent behavior. 1 Inflaton ma=0.65, pmin= 0.1m ma=0.52, pmin=0.125m ma=0.52, pmin= 0.15m ma=0.42, pmin= 0.15m Higgs ma=0.65, pmin= 0.1m ma=0.52, pmin=0.125m ma=0.52, pmin= 0.15m ma=0.42, pmin= 0.15m 0.1 Inflaton t -2/ Higgs t -2/ mt Expected behavior from R. Micha and I.Tkachev: φ 2 φ 2 t ν ; ν = 2/(2m 1) 3 dimensions, m-particle interactions. From data: φ: m=5,χ: m=4 A. Díaz-Gil (UAM) Magnetic Phenomena at Preheating LATT / 19

15 Some results: Turbulent behavior and Thermalization. Thermalization of photons from B, mt=85 from E, mt=85 free radiation log (1+1/n k ) Thermal ( radiation: ) n k = e k 1 T 1 T fit m w v /m mt=10 mt=25 mt=40 mt=65 mt=105 Maxwellian fit T/m= Maxwellian distribution: D(B) = B 2 e 3B2 /(2 B 2 10 ) 8 B 2 = 30T4 6 2π 2 4 T fit m w 2 0 D( B ) B A. Díaz-Gil (UAM) Magnetic Phenomena at Preheating LATT / 19

16 Some results: Magnetic field generation and evolution. Three essential items. A generation mechanism for the magnetic field. A large correlation length. Time persistence A. Díaz-Gil (UAM) Magnetic Phenomena at Preheating LATT / 19

17 Some results: Magnetic field generation and evolution. Magnetic field generation. Mechanism for generating magnetic field: Colliding bubbles String-like Higgs minima distribution. θ W 0 sphalerons at Higgs minima get a magnetic dipole moment.(m.hindmarsh and M.James (1994)) These dipoles align into a magnetic string. A. Díaz-Gil (UAM) Magnetic Phenomena at Preheating LATT / 19

Some results: Magnetic field generation and evolution. Magnetic field generation. Relation between higgs minima and magnetic energy density maxima.

18 Some results: Magnetic field generation and evolution. Magnetic field generation. Relation between higgs minima and magnetic energy density maxima. mt = 15 just after SSB(mt 13): Higgs minima B maxima A. Díaz-Gil (UAM) Magnetic Phenomena at Preheating LATT / 19

19 Some results: Magnetic field generation and evolution. Correlation. Smeared fields. Smear distance s m = 4a s < ρ t 7a s helps: Smooth the central singularities of the strings showing the leading structure. Clears the radiation background. Similar structures appears in Z Vachaspati s mechanism in EW phase transition. A. Díaz-Gil (UAM) Magnetic Phenomena at Preheating LATT / 19

20 Some results: Magnetic field generation and evolution. Spatial and Temporal correlation. 140 mt=10 mt=20 l 2 <B 2 > l Spatial correlation: String like behavior: Implies L dx3 B 2 (x) cte.l l Time average: R B T = 1 T dtb(t) Radiation: B R T 2 1 V dk Bk 2 W(k,T) 2 W = sin( k T/2) k T/2 Time av. eliminates k /m > (mt) 1. B t rms mt=105 mt=145 mt=185 Order today: B(t) 2 [10 3,10 4 ] [6, 0.6]µG mt A. Díaz-Gil (UAM) Magnetic Phenomena at Preheating LATT / 19

21 Conclusions and future work. Conclusions and future work. Relationship between generation of magnetic strings Sphalerons and bubble collisions. First estimations: Large correlation length. µg intensities. Work in progress: Detailed time evolution. Study of m H m W dependence. A. Díaz-Gil (UAM) Magnetic Phenomena at Preheating LATT / 19

22 Conclusions and future work. A discussion about m H /m W Compromise of several parameters: To avoid lattice artifacts ma s << 1. p min small as possible classical approximation. p min /m = 2π N.ma s. N 100. Maximal empirical value: pmin/m 0.15 m H a s No restriction for a s m h /a s m w in principle. But Strong dependence in mw a s because ρ sph (m w a s ) 1. Constraint ma s < 0.3 That makes mh /m w > 2 in our best lattice. A. Díaz-Gil (UAM) Magnetic Phenomena at Preheating LATT / 19

EW preheating & primordial magnetic fields

EW preheating & primordial magnetic fields EW preheaing & primordial magneic fields CFT&S, Cambridge UK 3-6h July 006 Juan García-Bellido Física Teórica UAM 6h July 006 Kofman, Linde, Sarobinsy PRL73, 395 994 PRD56, 358 997 Khlebniov, Tachev PRL77,