Preheating in the Higgs as Inflaton Model

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1 Preheating in the Higgs as Inflaton Model Why is preheating interesting? Higgs as inflaton model Relevant physics: nonadiabatic particle production particle decay, thermalization of decay daughters medium effects on nonadiabaticity back reaction etc Conclusions McGill, 12 April 2010: page 1 of 28

2 Preheating is interesting! Energy must get out of Inflaton into normal thermal DOF Maximum T achieved is important for many problems: leptogenesis (and baryogenesis) Gravitino production Other relic production and decay (moduli, etc) T of reheating seems to be very model dependent. What is the space of possibilities? McGill, 12 April 2010: page 2 of 28

3 Preheating is rich physics! Models considered depend on physics of: Perturbative particle decay Parametric resonance Nonadiabatic particle production Tachyonic field evolution rescattering, feedback, backreaction Very model dependent. McGill, 12 April 2010: page 3 of 28

4 Unanswered Question No detailed preheating study has been conducted in a scenario where reheating occurs directly into particles with nonabelian gauge interactions of realistic strength. The physics could be quite different from what is studied: much stronger mutual interactions new, nonabelian phenomena? What is the simplest such model? McGill, 12 April 2010: page 4 of 28

5 Higgs as Inflaton Bezrukov and Shaposhnikov, arxiv: Consider the addition of a Higgs-curvature interaction S = d 4 x g [ L SM + ( ) ] M 2 P 2 + ξh H R L SM = g µν D µ H D ν H + λ(h H) Here ξ is a permissible dimensionless coupling. We will need ξ 10 5 [SEE SLIDE 8!] Further analysis easier in Einstein frame: McGill, 12 April 2010: page 5 of 28

6 Ω 2 M2 P + ξh2 M 2 P, (h 2 = 2H H) ĝ µν = Ω 2 g µν Substituting, (...)R M 2 ˆR plus P µ Ω type terms. Canonically normalized Higgs χ S Einstein = d 4 x ĝ provided one defines (skipping some details) ( ) M 2 P 2 ˆR + ĝµν 2 D µχd ν χ + V (χ) dχ dh = Ω2 + 6ξ 2 h 2 /M 2 P Ω 4, V (χ) = 1 Ω 4 λ 4 (h2 (χ)) 2 McGill, 12 April 2010: page 6 of 28

7 Three regimes: h M P /ξ: Everything normal. M P ξ < h < M P : here Ω 1 but its derivatives matter! ξ χ 3 2 ξh2 M P and V (χ) λm2 P 6ξ 2 χ2 h > M P / ξ: Ω is large, χ 6M P ln(h), potential flattens out. Ideal slow-roll potential, V (λ/ξ 2 )M 4 P δρ/ρ right if ξ = λ; predicts n s 0.966, r = McGill, 12 April 2010: page 7 of 28

8 But is this nuts?? Model depends on a large rescaling between χ,h arising from large Higgs-curvature coupling ξrh 2. Bezrukov & Shaposhnikov: matter-only loops, stable. Burgess, Lee, Trott (arxiv: ): gravity-in-loops, not self-consistent. Barbon & Espinosa (arxiv: ): description not radiatively stable. Burgess, Barbon et.al. probably right. We analyze anyway. McGill, 12 April 2010: page 8 of 28

9 End of inflation Field χ oscillating about potential minimum Essentially quadratic after a few half-oscillations McGill, 12 April 2010: page 9 of 28

10 Higgs VEV gives (un)usual masses to other particles: m 2 W = g2 4 h2 = g2 χ M P m 2 h = λm2 P 24ξ 3ξ 2 Mass squared is linear in χ which is strange. m 2 Z m 2 W = g 2 + g 2 g , m 2 t m 2 W = 2y2 g where µ MS GeV relevant scale. McGill, 12 April 2010: page 10 of 28

11 Nonadiabatic evolution of W field excitations W-field Excitation, wave number k, obeys SHO equation: H = φ 2 k 2 + k2 + m 2 (t) 2 φ 2 k with m 2 (t) = g2 M P χ 0 24ξ sin(m h t) (χ 0 peak χ value) Evolution nonadiabatic near sin(m h t) = 0 if k < k, with k 3 dm 2 (t)/dt = m 2 Wm h. Nonadiabatic evolution: 0 squeezed Random excited state: raises occupancy. McGill, 12 April 2010: page 11 of 28

12 Occupancy change on evolving m 2 = k 3 t through t = 0: Modes with k < 0.7k get appreciable amplification. Less than in m 2 t 2 case except at large k 2. McGill, 12 April 2010: page 12 of 28

13 Early oscillations: m W > m h /α: Γ W > m h adiabatically generated W decay before next zero-crossing: m W 2 number of W s W get made W get made time Occurs roughly first 80 oscillations. After that, W stimulate more W, start to pile up. McGill, 12 April 2010: page 13 of 28

14 Fate of W decay products? W created when light, density n W < k 3. Decay when heavy, m k : p decayproduct k n 1/3 W. Decay products: low density plasma of high energy particles W decay is 2/3 q q, 1/3 lν l. ǫ np, n fp 3, f 1 General question: how does such a plasma thermalize? McGill, 12 April 2010: page 14 of 28

15 Plasma has a few soft particles. Form thermal bath T p. Scattering of hard p particles dominated by scattering with T particles, NOT with each other. p T k gluon Dominant process: elastic scattering off bath (T) particle Main energy loss mechanism: Bremsstrahlung while scattering k showers: Energy goes into T bath. McGill, 12 April 2010: page 15 of 28

16 Subtleties Sudakov logs: normally k distribution is p 0 dk/k. Energy loss: kdk/k dominated by k p. Dense medium: LPM suppression of large k by (T/k) 1/2. Large k s take too long to shower: don t promptly add to T. Requires slight extension of AMY/McGill jet energy loss method hep-ph/ , hep-ph/ , arxiv: α s = 1/40: weak coupling justified first time! Summary: decay products thermalize after about 80 oscillations. McGill, 12 April 2010: page 16 of 28

17 Fraction of W decays is exp ( π/mh 0 Γ W dt ) = exp ( 3α W 4 m W,max m h π 0 sin tdt ) controlled by m W /m h ξ 1/2 χ 0 /M P. After about 80 oscillations, many W survive, stimulate (nonadiabatic) particle creation. W number starts growing exponentially. What cuts off exponential growth? How does presence of bath and other W bosons feed back on nonadiabaticity condition for m W zero-crossing? McGill, 12 April 2010: page 17 of 28

18 Example of plasma s effect on W s: Plasma oscillations Starting Configuration E Field Moment Later E Field Sum over Many Such Particles: E Field Canceled! + Approaching + and charge will be bent Bending of charges induces E field + + Particles Continue Flying Particles Bend Back Again Each E gets bigger: collectively reverse original E field! E field again canceled Original E field re induced, process repeats McGill, 12 April 2010: page 18 of 28

19 Full W evolution determined by action: S A = m2 (t) A µ A µ F ij F i0 2 A µ J µ J a x = ( m 2 (t) + k t ) A a x Current is sum of currents from particles in plasma: J a x = dωv 4π v x δf a (v) (retarded) δf a is induced by past E fields (D t + v D) δf a (v) = m 2 Dv E a Note straight-line propagation. McGill, 12 April 2010: page 19 of 28

20 Particle propagation Green function: δf a (x,t,v) = m 2 D 0 dl v E a (x lv,t l) Hard Thermal Loop (neglecting color rotation). J x = dωv 4π v x m 2 D dl v x t A x (t l)e iv zkl 0 3 A x(t) + m 2 dt D A 0 t x (t t ) [ 3 cos(kt ) + (k2 t 2 3) sin(kt ) k 2 t 2 k 3 t 3 = m2 D Leads to integro-differential equation of motion for A x! ] McGill, 12 April 2010: page 20 of 28

21 New nonadiabatic amplification of W s: McGill, 12 April 2010: page 21 of 28

22 Plasma effect is almost m 2 m 2 + ω 2 pl with ω 2 pl = m 2 D/3. So what is ω 2 pl? Thermal bath contribution, m W > 3T: g 2 T 2 /4 Thermal bath, m W < 3T: g2 T 2 (W in bath) Other IR W bosons: 3g 2 n W /m W. What m W? At χ = 0, use m W = ω pl. Note: IR bosons feed back on each other to make each other feel more massive. Production is self-limiting Other feedbacks (3W 2W etc) comparable but smaller McGill, 12 April 2010: page 22 of 28

23 Back-reaction on Higgs field W bosons contribute thermal mass to Higgs field: V (χ) = V vac (χ) + V bath (χ) dv bath dχ = d 3 k (2π) 3(6)f W(k) de k dχ Every half-oscillation begins with more W s Ends with fewer W s. Damps χ oscillations. Account for by bath energy gain via W decays. Late in preheating, m 2 h rises due to bath. Accelerates completion of thermalization. McGill, 12 April 2010: page 23 of 28

24 Roll everything together: Bath-corrected Particle production on zero-crossing W particle decay, energy gain to bath Hubble expansion diluting T and χ max W feedback on χ max Determine evolution of χ, bath, soft W s as function of time (number of half-oscillations of h) McGill, 12 April 2010: page 24 of 28

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28 Results First, weak thermal bath develops At 100 oscillations, soft W s start to pile up. Self-limit around 250 oscillations Thermal bath dominates energy after 350 half-oscillations Higgs field rapidly dies away after 500 half-oscillations Very rich set of physics contributes McGill, 12 April 2010: page 28 of 28