What can the CMB tell about cosmic reheating? · WHAT CAN THE CMB TELL ABOUT COSMIC REHEATING?...
Transcript of What can the CMB tell about cosmic reheating? · WHAT CAN THE CMB TELL ABOUT COSMIC REHEATING?...
WHAT CAN THE CMB TELL ABOUT COSMIC REHEATING?
Marco DrewesTU München
based onJCAP 1603 (2016) no.03, 013
arXiv:1511.03280 [astro-ph.CO]
April 29th 2016XI. Kosmologietag, Bielefeld, Gremany
1 / 13WHAT CAN THE CMB TELL ABOUT COSMIC REHEATING?
Inflation and Reheating
0.1 0.2 0.5 1 2
0.3
0.4
0.5
0.6
0.7
0.80.9
ϕ
V(ϕ)
Inflation Era Reheating Era
explains homogeneity, isotropyand flatness of the universe
explains origin of densityfluctuations from blown-upquantum fluctuations
ϕ+ (3H + Γϕ)ϕ+ ∂ϕV(ϕ) = 0
effective potential V(ϕ) governs the dynamics of inflation
effective dissipation rate Γϕ leads to reheating
3 / 13WHAT CAN THE CMB TELL ABOUT COSMIC REHEATING?
How reheating affects the CMB
0.1 0.5 1 5 10 50
1
5
10
t
a
Inflation Era Reheating Era Radiation Era
equation of state p = wρ during reheating is neither that of inflation(w < −1/3) nor that of radiation (w = 1/3)
that affects the rate of cosmic expansion via H = −4π(1 + w)ρ/m2P
⇒ affects relation between observed angular size of perturbationsand size at their generation
4 / 13WHAT CAN THE CMB TELL ABOUT COSMIC REHEATING?
How to quantify this effect
1 + zend =areh
aend(1 + zreh) =
areh
aend
(ρreh
ργ
)1/4
=areh
aend
ρ1/4reh
ρ1/4end
ρ1/4end
ρ1/4γ
≡ 1Rrad
(ρend
ργ
)1/4
0.1 0.5 1 5 10 50
1
5
10
t
a
Inflation Era Reheating Era Radiation Era
Rrad parameterises the effect ofthe reheating era on the expan-sion history. Martin/Ringeval 2010
Rrad = 1 if reheating were instan-taneous
5 / 13WHAT CAN THE CMB TELL ABOUT COSMIC REHEATING?
The parameter Rrad
One can express
ln Rrad =1− 3wreh
12 (1 + wreh)ln(ρreh
ρend
)wreh, ρend are governed by V(ϕ)ρreh is governed by Γϕ and V(ϕ)(reheating stops when Γϕ > H)
1) Can one constrain Rrad from observations?
2) Can one learn anything about the inflaton couplings from that?
6 / 13WHAT CAN THE CMB TELL ABOUT COSMIC REHEATING?
Constraining Rrad Ireheating happened after inflation,
ρreh < ρend,
and before big bang nucleosynthesis,
ρBBN < ρreh.
If V(ϕ) ∝ (ϕ/MP)p, then wreh = p−2p+2 and
Rrad =
(ρreh
ρend
) 4−p12p
and (ρBBN
ρend
) 4−p12p
≷ Rrad ≷ 1 for p ≷ 4,
7 / 13WHAT CAN THE CMB TELL ABOUT COSMIC REHEATING?
Constraining Rrad IIRrad can be treated as a free parameter in addition to those inV(ϕ) and those of the ΛCDM model when constraininginflationary models with CMB data.
Martin/Ringeval/Vennin 2016
8 / 13WHAT CAN THE CMB TELL ABOUT COSMIC REHEATING?
Use Rrad to constrain inflaton couplings ?
ln Rrad =1− 3wreh
12 (1 + wreh)ln(ρreh
ρend
)depends on V(ϕ) via wreh, ρend, ρreh and on Γϕ via ρreh
⇒ For given V(ϕ) one can constrain Γϕ⇒ Γϕ is given by inflaton coupling(s) λ⇒ allows to constrain inflaton couplng λ!
9 / 13WHAT CAN THE CMB TELL ABOUT COSMIC REHEATING?
Backreaction and parametric resonanceTime dependence of Γϕ is not given by inflaton coupling λ alone,but depends on coupling constants α of the produced particles .
resonance→ complicated far from equilibrium dynamics→ no meaningful bound on λ or α from Rrad.
Example: Lint = λmφφχ2 + α
4!χ4
induced transitions Γϕ ' Γ0[1 + 2fχ(mφ/2)]
can lead to resonant production of χ-particlesefficiency depends on how quickly χ-particles rescatter into othermodes
⇒ depends on α
large effective χ-masses in the plasma modify particle kinematics⇒ depends on α
But what if λ� 1 and there is no resonance?
10 / 13WHAT CAN THE CMB TELL ABOUT COSMIC REHEATING?
Backreaction and parametric resonanceTime dependence of Γϕ is not given by inflaton coupling λ alone,but depends on coupling constants α of the produced particles .
resonance→ complicated far from equilibrium dynamics→ no meaningful bound on λ or α from Rrad.
Example: Lint = λmφφχ2 + α
4!χ4
induced transitions Γϕ ' Γ0[1 + 2fχ(mφ/2)]
can lead to resonant production of χ-particlesefficiency depends on how quickly χ-particles rescatter into othermodes
⇒ depends on α
large effective χ-masses in the plasma modify particle kinematics⇒ depends on α
But what if λ� 1 and there is no resonance?
10 / 13WHAT CAN THE CMB TELL ABOUT COSMIC REHEATING?
Backreaction and parametric resonanceTime dependence of Γϕ is not given by inflaton coupling λ alone,but depends on coupling constants α of the produced particles .
resonance→ complicated far from equilibrium dynamics→ no meaningful bound on λ or α from Rrad.
Example: Lint = λmφφχ2 + α
4!χ4
induced transitions Γϕ ' Γ0[1 + 2fχ(mφ/2)]
can lead to resonant production of χ-particlesefficiency depends on how quickly χ-particles rescatter into othermodes
⇒ depends on α
large effective χ-masses in the plasma modify particle kinematics⇒ depends on α
But what if λ� 1 and there is no resonance?10 / 13
WHAT CAN THE CMB TELL ABOUT COSMIC REHEATING?
Perturbative reheating
1 100 104 106 108 1010
0.001
0.100
10
1000
a
T
TR
Tmax
Reheating Era Radiation Era
MaD 2014thermal history without backreactionthermal history with backreactionbackreaction affects themal history, but not expansionhistory⇒ leaves ρreh unaffected!⇒ backreaction does not affect Rrad!
11 / 13WHAT CAN THE CMB TELL ABOUT COSMIC REHEATING?
Constraining the inflaton coupling: Example
Lint = λmφφχ2 + α
4!χ4
Γ0 ' λ2mφ/(16π)
V(ϕ) = 12 m2
φϕ2 → wreh = 0, ρend ' m2
φm2P/2
ρreh/ρend can be determined from Γϕ = H at ρ = ρreh
This yields
Rrad 'λ1/3
2and
TR '√
mφmP
g1/4∗
R3rad
12 / 13WHAT CAN THE CMB TELL ABOUT COSMIC REHEATING?
Conclusions
the CMB is sensitive to the expansion history during reheating
this effect can be parameterised by a single number Rrad
Rrad can be constrained from CMB data
in absence of a parametric resonance, a constraint on Rrad can betranslated into a constraint on the inflaton coupling(s) andreheating temperature
13 / 13WHAT CAN THE CMB TELL ABOUT COSMIC REHEATING?