The inflaton field as a dark matter candidate
● Incomplete decay mechanism after inflation: Inflaton coherent oscillations ~ (non-thermal) DM
● Single field models
● Hybrid models
● Inflaton thermal relic
M. Bastero-Gil with R. Cerezo and J.G. Rosa (1406.xxxx) Inflation vs Dark Matter
Inflation (early period of accelerated expansion)
● Horizon problem ● Flatness problem ● Relics ● Galaxy rotation curves ● CMB anisotropies ● Galaxy clusters ● Gravitational lensing ● Structure formation Dark Matter (massive, neutral, stable particle)
Single description? very different energy scales.... Inflation & Reheating
V(φ)∼φ2
−3 ρφ∼a dark matter?
[Turner'83; Kofman, Linde&Starobinsky'94] drastic but incomplete reduction of ρ + thermal bath (SM) T > T φ RH BBN ρDM −28 ξ0≃ ≃2.4×10 mP nγ 0 Preheating Reheating g2 φ2 χ2 gMφ χ2 parametric resonance decay φ→χ χ
not efficient complete decay
[Liddle&Ureña-Lopez'06] Possible solutions
● Plasma mass effects ?? [Cardenas'07; Panotopoulos'07] ● Thermal inflation after preheating [Liddle, Pahud & Ureña-Lopez'08] ● Reheating through PBH [Hidalgo, Ureña-Lopez & Liddle'11] ● Non-standard kinetic term [Bose & Majumdar'09; De-Santiago & Cervantes-Cota'11]
● Incomplete (fermionic) decay simpler Incomplete decay mechanism
LI∼mf ψ̄ ψ+h φ ψ̄ ψ mf >mφ /2
mψ=∣mf +hφ∣
mψ 2 mφ 2 h =1,m =10−3 m ,m =0.55 m V(φ)= φ +⋯ φ φ P f φ 2 4 ρφ /mP ρ rad Thermalization annihilations ρφ mP t Γφ≠0 Inflaton-to-entropy ratio n /s φ Ωφ 0 4 mφ nφ Γφ=0 = Ω R0 3 T0 s mP t Parameter space 1.78 0.12 h gR mφ≃52 TeV f 1.49(δ) nφ / s m (gR=no. of relativistic dof) m = φ (1+δ) f 2 f (δ)=1+4.8 δ1/2+0.5 δ mφ /mP mφ∼O(TeV) mφ (TeV) mf∼mφ h≃O(1) δ Temperature ρφ=ρ TRH (GeV) R TRH≫TBBN∼100 MeV δ h1.59 g−0.16 T ≃4×107 R GeV RH f (δ)1.12 −7 −6 (TRH≥TBBN for h>10 −10 ) Inflation? mφ ~ 1 TeV too low to match the amplitude of primordial spectrum 13 (mφ ~ 10 GeV) in canonical, minimally coupled single field models Non-minimal coupling+ λφ4 2 2 4 mP+ξ φ 1 μ ν S=∫d x √−g − R− g ∂μ φ ∂ν φ−V(φ) [ 2 2 ] h>(10−19−10−16)√ξ ξ plays no role during reheating/inflaton decay N =50 ξ e N =60 [Bezrukov & Shaposhnikov '08] e [Lerner & McDonald '09] [Okada, Rehaman & Shafi '10] ns How to recover SM: decay decay into SM induced decay Protected by symmetry: L= ψ̄ (i γμ ∂ −m )ψ −h φ ψ̄ ψ j −V(φ)+... ∑j=1,2 [ j μ f j j j ] φ −φ ψ1 ψ2 h1=−h2=h ψ1,2 Dirac fermions: decay before BBN m 1/ 2 T =4×109 g−1/4 h( f ) GeV≫T dec R 100GeV BBN How to recover SM: annihilations hidden U(1) 'dark photon' + kinetic mixing with γ Milicharged fermions Q= ε e ψj ψj →γ→qq,ll Thermalization of the SM dof at a given T: Γann>H T 1/ 2 (1) ϵ⩾0.46α−1 N−1/ 2 em Q (m ) P (2) ρφ=ρR (1) TSM= T≃mf (2) −8 −2 [mf∼GeV−TeV , ϵ∼10 −10 ] [Vogel & Redondo 1311.2600] SUSY hybrid inflation g 2 g 2 V(φ ,χ)= (χ2−M2)2+ φ2 χ2 8 2 LI=mf ψ̄ ψ+hφ φ ψ̄ ψ+hχ χ Ψ̄ Ψ tachyonic preheating no radiation domination incomplete decay mf >mφ /2 −2 M=10 mP , −5 −5 −2 hφ=1,hχ=10 , g=10 , δ=10 ρ ρ rad χ Γφ≠0 ρφ Γφ=0 Γχ≠0 Parameter space: an example 2 Ωφ 0 h0=0.12 hφ∼O(1) −10 −14 late χ decay hχ∼10 −10 6 9 mf ∼mφ∼mχ∼10 −10 GeV -6 hχ g=10-8 hχ g=10-5 g=10 g=10-4 g=10-6 -3 g=10-5 g=10 g=10-4 M/mP M/mP Inflation? Standard SUSY hybrid inflation n s ≃ 0.98 Planck 2013: ns≃0.960±0.007 Non-minimal Kähler potential 4 2 2 2 2 ∣Φ∣ ∣Φ∣ ∣Χ∣ K(Φ, Χ)=∣Φ∣ +∣Χ∣ +κΦ 2 +κΦΧ 2 +⋯ mP mP (κS=κΦ ) ns hχ g g [Rehman, Senoguz & Shafi PRD75 '07] [MBG, King & Shafi PLB'07] Inflaton Dark Matter: thermal relic? ● The condensate can be depleted by fermion scatterings ψ (T≫mf ,mφ) φ ● Radiation ~ inflaton + fermion particles + SM mψ=mf >mφ /2 ● Inflaton is stable ● −4 Inflaton ~ WIMP thermal relic : mφ∼O(GeV−TeV), hφ⩾10 (?) m 1/2 T ≃5×109 h g−1/4 φ GeV RH φ R ( 100GeV ) [Lerner & McDonald '09; Okada & Shafi '10; Mukaida & Nakayama '14] Summary Incomplete (fermonic) decay mechanism: mf > mφ/2 ρ ● DM −28 Consistent with DM abundance ξ0≃ ≃2.4×10 mP nγ 0 ● 7 9 Consistent with BBN TRH>TBBN∼O(100MeV), (TRH∼10 −10 GeV) ● Compatible with different models of inflation (consistent with inflationary observables) ● DM: inflaton condensate or WIMP thermal relic?