Reheating of the universe after inflation with f( )R gravity - PowerPoint PPT Presentation

COSMO 08, Madison, 28 Aug. 2008 Reheating of the universe after inflation with f( φ φ φ φ )R gravity Yuki Watanabe (Univ. of Texas, Austin) with Eiichiro Komatsu Based on PRD 75, 061301 (2007), [arXiv:qr-qc/0612120] PRD 77, 043514 (2008), [arXiv:0711.3442]

Y. Watanabe, Reheating of the universe after inflation with f(phi)R gravity COSMO 08, Madison, 28 Aug. 2008 Why Study Reheating? • The universe was left cold and empty after inflation. • But, we need a hot Big Bang cosmology. • The universe must reheat after inflation. Successful inflation must transfer energy in inflaton to radiation, and heat the universe to at least ~1 MeV for successful nucleosynthesis. …however, little is known about this important epoch….

Y. Watanabe, Reheating of the universe after inflation with f(phi)R gravity COSMO 08, Madison, 28 Aug. 2008 Why Study Reheating? • The universe was left cold and empty after inflation. • But, we need a hot Big Bang cosmology. • The universe must reheat after inflation. Successful inflation must transfer energy in inflaton to radiation, and heat the universe to at least ~1 MeV for successful nucleosynthesis. …however, little is known about this important epoch…. Outstanding Questions • Can one reheat universe successfully/naturally? • How much do we know about reheating? • What can we learn from observations (if possible at all)? • Can we use reheating to constrain inflationary models? • Can we use inflation to constrain reheating mechanism?

Y. Watanabe, Reheating of the universe after inflation with f(phi)R gravity COSMO 08, Madison, 28 Aug. 2008 Slow-roll Inflation : Standard Picture ( φ V ) potential shape is arbitrary here, as long as it is flat. φ inflaton Oscillation Phase: around the potential Energetics: minimum at the end of 4 inflation ρ ~ T rad rh What determines 4 4 2 2 φ ~ g V ( ) ~ g M H inf Pl inf “energy-conversion � 2 T ~ g M H efficiency factor”, g? rh Pl inf

Y. Watanabe, Reheating of the universe after inflation with f(phi)R gravity COSMO 08, Madison, 28 Aug. 2008 Perturbative Reheating Dolgov & Linde (1982); Abbott, Farhi & Wise (1982); Albrecht et al. (1982) Inflaton decays and thermalizes through the tree-level � � 1 λφ interactions like: � � 2 4 � = − φ ψ ψ + φχ + + L g g ψ χ int � � 4 ψ χ g g χ ψ φ φ χ χ ψ ψ Inflaton can decay if allowed kinematically with the widths given by Pauli blocking φ φ φ φ Bose condensate Thermal medium φ effect φ φ φ

Y. Watanabe, Reheating of the universe after inflation with f(phi)R gravity COSMO 08, Madison, 28 Aug. 2008 Reheating Temperature from Energetics � � tot � − 2 3 / 2 φ + + Γ φ + φ = >> ∝ ( 3 H ) m 0 H H a σ φ inf osc � > Γ 3 H Inflaton dominates the energy density. osc tot � < Γ 3 H Decay products dominate the energy density. osc tot 2 2 2 Γ π M 2 2 2 2 4 4 ρ ρ = = = = Pl Pl tot tot = = ( ( t t ) ) 3 3 M M H H g g ( ( T T ) ) T T rad rh Pl osc * rh rh 3 30 − 1 / 4 � � Γ M ( ) g T � � Pl tot = * rh T rh � � 2 1 / 4 π ( 10 ) 100 Coupling constants determine the decay width, Γ. But, what determines coupling constants?

Y. Watanabe, Reheating of the universe after inflation with f(phi)R gravity COSMO 08, Madison, 28 Aug. 2008 What are coupling constants? Problem: arbitrariness of the nature of inflaton fields • Inflation works very well as a concept, but we do not understand the nature (including interaction properties) of inflaton. e.g. Higgs-like scalar fields, Axion-like fields, Flat directions, RH sneutrino, Moduli fields, Distances between branes, and many more… • Arbitrariness of inflaton = Arbitrariness of couplings • Arbitrariness of inflaton = Arbitrariness of couplings • Can we say anything generic about reheating? Universal reheating? Universal coupling? Gravitational coupling is universal � too weak to cause reheating with GR. In the early universe, however, GR would be modified. What happens to “gravitational decay channel”, when GR is modified?

Y. Watanabe, Reheating of the universe after inflation with f(phi)R gravity COSMO 08, Madison, 28 Aug. 2008 Conventional Einstein gravity during inflation 2 M − ∇ µ ∇ φ φ g L Pl ν matt Einstein-Hilbert term generates GR. Inflaton minimally couples to gravity. ( ) 2 2 2 � = − φ ψ ψ + φχ + λφ χ + L g g ψ χ int Conventionally one introduced explicit couplings between inflaton and matter.

Y. Watanabe, Reheating of the universe after inflation with f(phi)R gravity COSMO 08, Madison, 28 Aug. 2008 Modifying Einstein gravity during inflation Instead of introducing explicit coupling by hand, ( ) 2 2 2 � = − φ ψ ψ + φχ + λφ χ + L g g ψ χ int − ∇ µ ∇ φ φ g L ν matt Non-minimal gravitational coupling: common in effective Lagrangian from extra dimensional theories 2 = f ( v ) M In order to ensure GR after inflation, Pl ( φ V ) Matter (everything but gravity and inflaton) completely decouples from σ inflaton and minimally coupled to gravity as usual. φ v

Y. Watanabe, Reheating of the universe after inflation with f(phi)R gravity COSMO 08, Madison, 28 Aug. 2008 New decay channel through “scalar gravity waves” − 1 / 2 � + � 2 ~ F ( v ) 3 [ f ' ( v )] � � = + − σ = g g h g , F ( v ) f ' ( v ) 1 � � µν µν µν µν 2 2 � � 2 M M Pl Pl Fermionic (spinor) matter field: Yukawa interaction F ( v ) m ψ µα � = − ψ γ + ψ + + σ ψ ψ L e [ e D m ] e ψ α µ ψ 2 ψ 2 M Pl g g ψ ψ σ g Bosonic (scalar) matter field: ψ � ψ 1 µν � = − ∂ χ ∂ χ + χ + L e g U ( ) � χ µ ν � χ 2 Trilinear interaction g � χ F ( v ) σ ( ) � µν − σ χ + ∂ χ ∂ χ 4 U ( ) g µ ν 2 � 2 M Pl F ( v ) χ

Y. Watanabe, Reheating of the universe after inflation with f(phi)R gravity COSMO 08, Madison, 28 Aug. 2008 Magnitude of Yukawa coupling ψ g ψ F ( v ) σ ψ � For f( φ ) = ξφ 2 , g ψ = ξ(1+6ξ) −1/2 (v/M pl )(m ψ /M pl ) � Natural to obtain a small Yukawa coupling, g ψ ~10 -7 , for e.g., m ψ ~10 -7 M pl � The induced Yukawa coupling vanishes for massless fermions: � The induced Yukawa coupling vanishes for massless fermions: conformal invariance of massless fermions. � Massless, minimally-coupled scalar fields are not conformally invariant. Therefore, the three-legged interaction does not vanish even for massless scalar fields: F ( v )

Y. Watanabe, Reheating of the universe after inflation with f(phi)R gravity COSMO 08, Madison, 28 Aug. 2008 Decay Width Summary (Kinematical and thermal factors are neglected.) Fermions − 1 � � [ ] 2 ′ 2 2 ′ f ( v ) m m 3 [ f ( v )] � � ψ σ Γ = + 1 � � 4 2 π 32 M 2 M � � pl pl Scalar Bosons Probably the − 1 � � � � [ [ ] ] 2 2 3 3 2 2 ′ ′ ′ ′ f ( v ) m 3 [ f ( v )] � � most dominant σ Γ = + 1 � � decay channel 4 2 π 128 M 2 M � � pl pl g F Gauge Bosons g ψ σ − 1 � � [ ] 2 2 3 2 ′ ′ α F ( ) f v m 3 [ f ( v )] � � ( g ) σ Γ = + × 1 # of internal fermions etc � � 3 4 2 π 256 M 2 M � � pl pl

Y. Watanabe, Reheating of the universe after inflation with f(phi)R gravity COSMO 08, Madison, 28 Aug. 2008 Constraint on f( φ φ φ φ )R gravity from reheating − 1 / 4 � � Γ M g ( T ) � � Pl tot = * rh T rh 2 1 / 4 � � π ( 10 ) 100 + Γ σ FF − 1 / 2 � � 3 / 2 � � 1 / 4 � � ′ 2 M ( ) 3 [ f ( v )] g T � � � � � � pl 1 / 4 ′ + < π * rh | f ( v ) | 1 8 ( 40 ) T � � � � rh � � � � 2 � � � � M M m m 100 100 � � � � σ σ pl pl 2 2 (c.f.) Constraints from φ = M + ξφ e.g. f ( ) chaotic inflation − 1 / 2 � � 2 2 − 3 ξ ξ > − 6 v 10 � � ξ + | | 1 � � 2 M � � Futamase & Maeda(1989 ) pl 4 ξ > × λ 3 / 2 | | 5 10 � � 1 / 4 � � M T g ( T ) � � � � pl 1 / 4 rh * rh < π 4 ( 40 ) � � Komatsu & Futamase(1 999) � � � � v m 100 σ