Dissipative Effects on Reheating after Inflation Kyohei Mukaida - PowerPoint PPT Presentation

Dissipative Effects on Reheating after Inflation Kyohei Mukaida (Univ. of Tokyo) Based on: 1212.1985 , 1208.3399 with K. Nakayama ; [ JCAP01(2013)017 , JCAP03(2013)002], also 1304.6597 with T. Moroi , K. Nakayama and M. Takimoto; [ JHEP1306(2013)040] 1 Kyohei Mukaida - Univ. of Tokyo

2 Introduction

Introduction After the inflation, the inflaton should convert its energy to radiation: Reheating . How does the reheating proceed ? ‣ “Standard” picture of reheating: φ V φ Inflaton φ 0 3 Kyohei Mukaida - Univ. of Tokyo

Introduction After the inflation, the inflaton should convert its energy to radiation: Reheating . How does the reheating proceed ? ‣ “Standard” picture of reheating: φ Thermal Plasma V φ χ 0 , χ 00 Decay χ χ Inflaton λ φ χ χ ¯ · · · ˜ χ A µ φ 0 4 Kyohei Mukaida - Univ. of Tokyo

Introduction After the inflation, the inflaton should convert its energy to radiation: Reheating . # 1 / 4 q " 90 • Reheating temperature: T R ∼ M pl Γ (pert) How does the reheating proceed ? φ π 2 g ∗ ‣ “Standard” picture of reheating: @ H ∼ Γ (pert . ) ∼ λ 2 m φ φ Thermal Plasma φ V φ χ 0 , χ 00 Decay χ χ Inflaton λ φ χ χ ¯ · · · ˜ χ A µ φ 0 5 Kyohei Mukaida - Univ. of Tokyo

Introduction After the inflation, the inflaton should convert its energy to radiation: Reheating . This Simple Picture does NOT ALWAYS hold ! # 1 / 4 q " 90 • Reheating temperature: T R ∼ M pl Γ (pert) How does the reheating proceed ? However... φ π 2 g ∗ ‣ “Standard” picture of reheating: @ H ∼ Γ (pert . ) ∼ λ 2 m φ φ Thermal Plasma φ V φ χ 0 , χ 00 Decay χ χ Inflaton λ φ χ χ ¯ · · · ˜ χ A µ φ 0 6 Kyohei Mukaida - Univ. of Tokyo

Introduction Missing Two effects (at least): Thermal Plasma φ χχ ; ( λ 2 φ 2 | ˜ χ | 2 ) λφ ¯ χ 0 , χ 00 χ χ Interaction Real Scalar · · · Gauge int. ˜ χ A µ 0 7 Kyohei Mukaida - Univ. of Tokyo

Introduction Missing Two effects (at least): ‣ Before going into details, let us clarify our setup: L kin − 1 φ φ 2 + λφ (¯ 2 m 2 χ L χ R + h . c . ) + L other Thermal Plasma φ χχ ; ( λ 2 φ 2 | ˜ χ | 2 ) λφ ¯ χ 0 , χ 00 χ χ Interaction Real Scalar · · · Gauge int. ˜ χ A µ 0 8 Kyohei Mukaida - Univ. of Tokyo

Introduction Missing Two effects (at least): ‣ Before going into details, let us clarify our setup: L kin − 1 φ φ 2 + λφ (¯ 2 m 2 χ L χ R + h . c . ) + L other Thermal Plasma φ χχ ; ( λ 2 φ 2 | ˜ χ | 2 ) λφ ¯ χ 0 , χ 00 χ χ Interaction Real Scalar · · · Gauge int. ˜ χ A µ 0 9 Kyohei Mukaida - Univ. of Tokyo

Introduction Missing Two effects (at least): ‣ Before going into details, let us clarify our setup: L kin − 1 φ φ 2 + λφ (¯ 2 m 2 χ L χ R + h . c . ) + L other Thermal Plasma φ χχ ; ( λ 2 φ 2 | ˜ χ | 2 ) λφ ¯ χ 0 , χ 00 χ χ Interaction Real Scalar · · · Gauge int. ˜ χ A µ 0 10 Kyohei Mukaida - Univ. of Tokyo

Introduction Missing Two effects (at least): ‣ Before going into details, let us clarify our setup: L kin − 1 φ φ 2 + λφ (¯ 2 m 2 χ L χ R + h . c . ) + L other Thermal Plasma φ χχ ; ( λ 2 φ 2 | ˜ χ | 2 ) λφ ¯ χ 0 , χ 00 χ χ Interaction Real Scalar · · · Gauge int. ˜ χ A µ 0 11 Kyohei Mukaida - Univ. of Tokyo

Introduction Missing Two effects (at least): ‣ Before going into details, let us clarify our setup: L kin − 1 φ φ 2 + λφ (¯ 2 m 2 χ L χ R + h . c . ) + L other Thermal Plasma φ χχ ; ( λ 2 φ 2 | ˜ χ | 2 ) λφ ¯ χ 0 , χ 00 χ χ Interaction Real Scalar · · · Gauge int. ˜ χ A µ 0 12 Kyohei Mukaida - Univ. of Tokyo

Introduction Missing Two effects (at least): Γ (pert . ) ?? ‣ What if ?? m e ff , χ � m φ φ e ff , χ = λ 2 φ ( t ) 2 + m th m 2 χ ( T ) 2 ∼ g 2 T 2 Thermal Plasma φ χχ ; ( λ 2 φ 2 | ˜ χ | 2 ) λφ ¯ χ 0 , χ 00 χ χ Interaction Real Scalar · · · Gauge int. ˜ χ A µ 0 13 Kyohei Mukaida - Univ. of Tokyo

Introduction Missing Two effects (at least): Γ (pert . ) ?? ‣ What if ?? m e ff , χ � m φ φ e ff , χ = λ 2 φ ( t ) 2 + m th m 2 χ ( T ) 2 ∼ g 2 T 2 m e ff , χ ∼ λ ˜ 1. If φ � m φ ➡ Non-perturbative particle production ( Preheating ) e.g., [L. Kofman, A. Linde, A. Starobinsky] m e ff , χ ∼ m th 2. If � m φ χ ➡ Thermal dissipation into radiation (via Scatterings ) e.g., [J. Yokoyama; M. Drewes; A. Berera et al.] 14 Kyohei Mukaida - Univ. of Tokyo

Introduction Missing Two effects (at least): Γ (pert . ) ?? ‣ What if ?? m e ff , χ � m φ φ e ff , χ = λ 2 φ ( t ) 2 + m th m 2 χ ( T ) 2 ∼ g 2 T 2 m e ff , χ ∼ λ ˜ 1. If φ � m φ ➡ Non-perturbative particle production ( Preheating ) e.g., [L. Kofman, A. Linde, A. Starobinsky] m e ff , χ ∼ m th 2. If � m φ χ ➡ Thermal dissipation into radiation (via Scatterings ) e.g., [J. Yokoyama; M. Drewes; A. Berera et al.] 15 Kyohei Mukaida - Univ. of Tokyo

Introduction Missing Two effects (at least): Γ (pert . ) ?? ‣ What if ?? m e ff , χ � m φ φ e ff , χ = λ 2 φ ( t ) 2 + m th m 2 χ ( T ) 2 ∼ g 2 T 2 m e ff , χ ∼ λ ˜ 1. If φ � m φ ➡ Non-perturbative particle production ( Preheating ) e.g., [L. Kofman, A. Linde, A. Starobinsky] m e ff , χ ∼ m th 2. If � m φ χ ➡ Thermal dissipation into radiation (via Scatterings ) e.g., [J. Yokoyama; M. Drewes; A. Berera et al.] 16 Kyohei Mukaida - Univ. of Tokyo

Main Message Possible sketch of reheating after inflation w/ m φ ⌧ λφ i . End of inflation. ( m φ ⌧ λφ i ) Preheating High T plasma ; is produced and the m φ n T preheating terminates: k ∗ ∼ m th χ . Dissipation (Scat.) into high T plasma Reheating can be completed by T R Thermal Dissipation! Time 17 Kyohei Mukaida - Univ. of Tokyo

Outline Introduction Preheating (Non-perturb. production) Dissipation to Thermal Plasma Numerical Results 18 Kyohei Mukaida - Univ. of Tokyo

19 Preheating

Non-pert. Production The non-perturbative particle production occurs if [L. Kofman, A. Linde, A. Starobinsky] Φ ’s amplitude: ˜ φ m th χ ( T ) 2   λ ˜   φ � max  m φ ,       m φ  φ ∼ g 2 T 2 χ q k 2 + m th χ ( T ) 2 + λ 2 φ 2 ( t ) ω χ = vac. fluc. 20 Kyohei Mukaida - Univ. of Tokyo

Non-pert. Production The non-perturbative particle production occurs if [L. Kofman, A. Linde, A. Starobinsky] Φ ’s amplitude: ˜ φ m th χ ( T ) 2   λ ˜   φ � max  m φ ,       m φ  φ ∼ g 2 T 2 χ q k 2 + m th χ ( T ) 2 + λ 2 φ 2 ( t ) ω χ = 21 Kyohei Mukaida - Univ. of Tokyo

Non-pert. Production The non-perturbative particle production occurs if [L. Kofman, A. Linde, A. Starobinsky] Φ ’s amplitude: ˜ φ m th χ ( T ) 2   λ ˜   φ � max  m φ ,       m φ  ‣ Implies that the non-pert. production is “blocked” if q λ m φ ˜ m th χ ( T ) ∼ k ∗ = φ . [KM, K. Nakayama; K. Enqvist, D. Figueroa, R. Lerner] 22 Kyohei Mukaida - Univ. of Tokyo

Non-pert. Production If χ is not stable , then... Non-perterbatively produced χ can decay within each crossings of Φ ~0. e.g.,[J. Garcia-Bellido, D. Figueroa, J. Rubio] Γ χ ∼ κ 2 m χ ( φ ( t )) ∼ κ 2 λ | φ ( t ) | ; ‣ χ decays completely before the Φ moves back to its origin if κ 2 λ ˜ φ � m φ . • Parametric Resonance is absent in this case; even if χ is boson. 23 Kyohei Mukaida - Univ. of Tokyo

Non-pert. Production If χ is not stable , then... Non-perterbatively produced χ can decay within each crossings of Φ ~0. e.g.,[J. Garcia-Bellido, D. Figueroa, J. Rubio] Γ χ ∼ κ 2 m χ ( φ ( t )) ∼ κ 2 λ | φ ( t ) | ; ‣ χ decays completely before the Φ moves back to λ 2 m φ its origin if κ 2 λ ˜ φ � m φ . Γ φ ∼ N d . o . f . 2 π 4 | κ | . ‣ This process ends @ [ λ m φ ˜ φ ] 1 / 2 ∼ k ∗ ∼ m th χ ( T ) ∼ gT . [KM, K. Nakayama] 24 Kyohei Mukaida - Univ. of Tokyo

25 Thermal Effects

Thermal Effects ‣ Thermal Dissipation (Scattering): e.g.,[Hosoya, Sakagami; J. Yokoyama; M. Drewes] 2 φ = − ∂ F φ + (3 H + Γ φ ) ˙ ¨ φ + m φ ∂φ Π J ( ω , 0 ) Friction coefficient from Kubo-formula: Γ φ ' lim . 2 ω ω ! 0 - Small Φ : ⇒ scatterings including χ . χ λφ ⌧ T A µ … Γ φ ∼ λ 2 α T ⇣ ⌘ Γ φ ∼ λ 4 φ 2 / ( α T ) φ χ - Large Φ : A µ A µ ⇒ scatterings by gauge bosons. λφ � T Γ φ ∼ α 2 T 3 … φ A µ φ 2 [D. Bodeker; M. Laine] 26 Kyohei Mukaida - Univ. of Tokyo