Lattice Simulations of Preheating. Gary Felder KITP February 2008

Transkript

1 Lattice Simulations of Preheating Gary Felder KITP February 008

2 Outline Reheating and Preheating Lattice Simulations Gravity Waves from Preheating Conclusion

3 Reheating and Preheating Reheating is the decay of the homogeneous inflaton field. Preheating is a burst of exponentially rapid decay that occurs at the beginning of reheating in many models. (Kofman, Linde,, and Starobinsky,, 1994.)

4 Parametric Resonance k t χ + ω χ = ω k k k k k + g a 0 φ ln n k t *Figure taken from Kofman, Linde, and Starobinsky, hep-ph/

5 Tachyonic Preheating In many models of inflation such as new inflation and hybrid inflation the scalar fields at the end of inflation fall down a slope with negative curvature. V *G.F., et al, 001. Φ

6 Preheating in Inflationary Models Chaotic Inflation Parametric Resonance, Tachyonic Resonance Hybrid Inflation Tachyonic Preheating New Inflation Parametric Resonance, Tachyonic Preheating, Tachyonic Resonance

7 The Results of Preheating Parametric Resonance Tachyonic Preheating Parametric Resonance + Tachyonic Preheating Tachyonic Resonance

8 Stages of Reheating Preheating Turbulence Non-linear bubbly stage Thermalization

9 Bubble Formation in Tachyonic Preheating

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11 && Lattice Simulations a& 1 V + 3 & + = 0 a a a a a φ φ φ 4π a a&& + ( p+ 3 ρ) = 0 3 During and shortly after preheating, the field dynamics is purely classical. (Khlebnikov and Tkachev Tkachev,, 1996; Prokopec and Roos,, 1997; Tkachev, Khlebnikov, Kofman,, and Linde,, 1998; Berges, Rothkopf,, and Schmidt, 008.) φ a

12 Lattice Simulations LATTICEEASY - A lattice simulation program for interacting scalar fields in an expanding universe. User enters potential and run parameters. LATTICEEASY solves evolution equations and generates outputs. The only approximations are classicality and discretization.

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14 LATTICEEASY Accuracy *Figure generated by Zhiqi Huang

15 Lattice Simulations So Far: A Small Sample Parametric Resonance (Kofman and Tachyonic Preheating Phase Transitions (Khlebnikov and Defect Formation (Tkachev 1998.). Baryogenesis (Kolb, Kofman, Linde,, and Starobinsky,, 1994.) Preheating (G.F., et al 001.). Khlebnikov, Kofman, Linde,, and Tkachev,, 1998.) Tkachev, Khlebnikov, Kofman,, and Linde, (Kolb, Riotto,, and Tkachev,, 1998.).

16 Lattice Simulations LATTICEEASY - A lattice simulation program for interacting scalar fields in an expanding universe. CLUSTEREASY The parallel programming version of LATTICEEASY. Has completed runs of up to points with nine fields.

17 Gravity Waves: Motivation Gravity waves decouple instantly and pass through the universe unimpeded. The intermediate stages from inflation to thermalization constitute the most poorly understood epoch in cosmological history. Easther, Giblin, and Lim Figueroa, Garcia-Bellido, and Sastre Bergman, G.F., Dufaux, Kofman, Navros, and Uzan

18 Calculation of Gravity Waves ρ = 3 1 gw ij ij π G + = 16π TT ij ij ij ij TT = ij ijlm lm hh & & a h&& & h& h GT a T O T

19 Results: Chaotic Inflation

20 Hybrid Inflation 1 1 V( φ, σ) = λ( σ v ) + g φ σ + V ( φ) inf 4

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23 Hybrid Inflation 1 1 V( φ, σ) = λ( σ v ) + g φ σ + V ( φ) inf 4 3/4 1 f *,min ( λ) λ (10 Hz)

24 Future Prospects These same techniques can be applied to many other scenarios: Early structure formation Phase transitions Defect formation

25 Conclusions The epoch from inflation to thermalization is highly important and poorly understood. In many models of inflation that epoch begins with a stage of preheating. During and shortly after preheating the universe can be accurately modeled by classical lattice simulations.

26 Additional Slides

27 Tachyonic Preheating, cont. x V Φ Φ

28 *Slide taken from Juergen Berges

29 A Closer Look at Preheating: Parametric Resonance

30 Gravity Waves on the Lattice && a& 1 V + 3 & + = 0 a a a a a φ φ φ 4π a a&& + ( p+ 3 ρ) = 0 3 φ a h&& & h& h GT a + = 16π TT ij ij ij ij a

31 Hybrid Inflation 1 1 V( φ, σ) = λ( σ v ) + g φ σ + V ( φ) inf 4 Free Parameters : λ, g, v, φ & 0 g ~ λ f f v λ 1/4 Φ& 1/3, Ω h * 0 gw Φ & /3 0 *,min 3/4 1 ( λ) λ (10 Hz) 0 φ Φ& & φ 0 cr λ v