Quintessential Cosmology and Cosmic Acceleration - Department of
Quintessential Acceleration and its End
Transcript of Quintessential Acceleration and its End
Quintessential Acceleration and its End
arXiv: 1108.1793
Mustafa Amin
with P. Zukin and E. Bertschinger
Massachusetts Institute of Technology (MIT)supported by a Pappalardo Fellowship
Aug 10, 2011
Thursday, August 11, 2011
Scale dependent growth from a late (z<0.2) transition in dark energy dynamics
(similar to (p)reheating after inflation, but from quintessence)
Thursday, August 11, 2011
synopsis
• overview
• why?
• phenomenology:
end of accelerated expansion
resonant growth of structure
• observational consequences
• comment and To Do list
Thursday, August 11, 2011
a(t) > 0
75%70%
w = P/ρ ∼ −1
a(t)a(t)
= −4πG
3(ρ + 3P ) > 0
“we” are not importantor liked
image: High Z Supernova Search Team, HST
Thursday, August 11, 2011
a working model: ΛCDM
L =1
16πG[R−2Λ] + [Lsm+LWIMP ]
image: NASA/WMAP Science Team
Thursday, August 11, 2011
an alternative
quintessence
L =1
16πGR + [Lsm + LWIMP +L(ϕ)]
L(ϕ) =12(∂ϕ)2 + U(ϕ)
• Important: does not solve the Λ problem, it is an alternative, not a solution.
Thursday, August 11, 2011
what is needed
a(t)a(t)
= −4πG
3(ρ + 3P ) > 0
slow roll !ϕ2 U
w =P
ρ=
12 ϕ2 − U12 ϕ2 + U
∼ −1
Thursday, August 11, 2011
quintessence potential
slow roll
oscillatory
ϕ ∼M
U (ϕ) ∼ m2
U(ϕ)
ϕ2 U
w =P
ρ=
12 ϕ2 − U12 ϕ2 + Uϕ→
A. Mantz, S. W. Allen, D. Rapetti, and H. Ebeling (2010)
Thursday, August 11, 2011
end of quintessential acceleration? (phase transition, decay, (p)reheating ...)
oscillatory
ϕ ∼M
U (ϕ) ∼ m2
possible, but not necessary
z < 0.2
Thursday, August 11, 2011
motivation
• see “Simple exercises to flatten your potential” (Dong et. al, context: inflation)
• explicit models: eg axion monodromy quintessence (Trivedi et. al)
• why not? extremely rich phenomenology
observationally constrainable
Thursday, August 11, 2011
quintessence potential
U(ϕ) =m2M2
2
(ϕ/M)2
1 + (ϕ/M)2(1−α)
ϕ ∼M
U(ϕ) ∝ ϕ2α
U (ϕ) ∼ m2
Thursday, August 11, 2011
a worked exampleα ≈ 0
M ≈ 10−3mpl
m ≈ 103H0
ρ ∼ m2M
2 ∼ m2plH
20
ϕ ∼M
U(ϕ) ∝ ϕ2α
U (ϕ) ∼ m2
Thursday, August 11, 2011
aosc
0.0 0.2 0.4 0.6 0.8 1.050510152025
a
Mfield evolution
slow roll
oscillatory
ϕ ∼M
U (ϕ) ∼ m2
Thursday, August 11, 2011
equation of stateslow roll
oscillatory
ϕ ∼M
U (ϕ) ∼ m2
0.0 0.2 0.4 0.6 0.8 1.01.00.50.00.51.0
a
w
Thursday, August 11, 2011
expansion history
aosc
0.0 0.2 0.4 0.6 0.8 1.0
3
2
1
0
a
DD
comoving distance deviation
also see: Mortenson, Hu & Huterer on hiding rapid transitions in expansion history
Thursday, August 11, 2011
include expansion
δϕk ≈δϕk(ti)a3/2(t)
exp
dtµk(t)
=δϕk(ai)
a3/2exp
d ln a
µk(a)H(a)
(µk) H
∂2t δϕk + 3H∂tδϕk +
k
2
a2+ U
(ϕ)
δϕk = 0
Thursday, August 11, 2011
related interpretations
• imaginary sound speed at low wave-numbers only Johnson & Kamionkowski
• resonant particle production Traschen & Brandenberger, Linde, Kofman& Starobinski
Thursday, August 11, 2011
resonant growth: important
• growth on limited range of scales (sub-horizon)
• growth rate can be much faster than H
Thursday, August 11, 2011
include gravity
Note: dark matter perturbations included via constraints
ds2 = −(1 + 2Φ)dt2 + a2(1− 2Ψ)dx2
Φk = Ψk
δϕk + 3H ˙δϕk +k
2
a2+ U
(ϕ)
δϕk = −2U(ϕ)Ψk + 4ϕΨk
Ψk + 4HΨk +1
m2pl
U(ϕ)Ψk =1
2m2pl
ϕ ˙δϕk − U
(ϕ)δϕk
no anisotropic stress
Thursday, August 11, 2011
initial conditions (during matter domination)
b
0.0 0.2 0.4 0.6 0.8 1.0
1
2
3
4
a
ka
a
aosc anl0.0 0.2 0.4 0.6 0.8 1.0
10
104
107
1010
a
∆ka
δϕk =ck
k3H
[cos(2kH + ∆k) + 2kH sin(2kH + ∆k)]− 2Ψk
U(ϕ)H2
1k
2H
1− 7
k2H
+35
2k4H
δϕk ∝ a2
Ψk ≈ const
Thursday, August 11, 2011
quintessence +gravitational potentiala
aosc anl0.0 0.2 0.4 0.6 0.8 1.0
10
104
107
1010
a
∆ka
b
0.0 0.2 0.4 0.6 0.8 1.0
1
2
3
4
a
ka
Thursday, August 11, 2011
limits of linear analysis
δϕ21/2L = [∆δϕ(k, a)]k∼L−1
a
0.002 0.005 0.01 0.02 0.05 0.1
108
106
104
0.01
1
k Mpc1
∆kM
r.m.s amplitude of quintessence fluctuations
Thursday, August 11, 2011
∆δϕ(k, anl) ∼ ϕosc(anl).
b
0.90 0.91 0.92 0.93 0.94 0.95 0.96 0.970
5
10
15
a
Condition for nonlinearity
limits of linear analysis
Thursday, August 11, 2011
potential power spectrum
initial condition consistent with LCDM at early times (CAMB/CMBFast)
a
0.002 0.005 0.010 0.020 0.050 0.100
1013
1012
1011
1010
109
k Mpc1
2 k
Gravitational potential power spectrum
initial conditions
LCDM today
our model today
Thursday, August 11, 2011
matter power spectrum
b
0.002 0.005 0.010 0.020 0.050 0.100
51010
1109
5109
1108
5108
k Mpc1
P dmkM
pc3
WIMP overdensity power spectrum
Thursday, August 11, 2011
dark matter (WIMP) growth
c
0.0 0.2 0.4 0.6 0.8 1.0010203040506070
a
∆ dma
δdm + 2H δdm = −k2
a2Ψk + 3
2HΨk + Ψk
.
δdm = − a3
3H20Ωdm
6H
2 − ϕ2
m2pl
+ 2k
2
a2
Ψk + 6HΨk +
ϕ
m2pl
˙δϕk +1
m2pl
U(ϕ)δϕk
aosc anl
Thursday, August 11, 2011
important
a
0.002 0.005 0.010 0.020 0.050 0.100
1013
1012
1011
1010
109
k Mpc1
2 k
Gravitational potential power spectrum
b
0.002 0.005 0.010 0.020 0.050 0.100
51010
1109
5109
1108
5108
k Mpc1P dmkM
pc3
WIMP overdensity power spectrum
Thursday, August 11, 2011
a
0.002 0.005 0.010 0.020 0.050 0.100
1013
1012
1011
1010
109
k Mpc1
2 k
Gravitational potential power spectrum
one important scale
galaxies and dark matter respond more slowly
oscillatory
U (ϕ) ∼ m2
after fixing expansion history
k ∼ 0.05m
Thursday, August 11, 2011
observational signature!
• extra power in potential (see it in lensing)
• rapid change in potential (see in ISW)
• not so in the matter power spectrum (see in galaxy power spectrum)
Thursday, August 11, 2011
weak lensing
10.05.02.0 20.03.0 30.015.07.01 107
2 107
5 107
1 106
2 106
5 106
1 105
l
CΚl
Convergence Power Spectrum
recent growth implies large angles
l ∼ θ−1 ∼ kresDA
assumed LCDM expansion history
b
10.05.02.0 3.0 15.07.0
1.0
1.1
1.2
1.3
1.4
1.5
l
CΚ lC lΚ
CDM
Ratio of convergence power spectra
Thursday, August 11, 2011
integrated sachs-wolfeb
0.0 0.2 0.4 0.6 0.8 1.0
1
2
3
4
a
ka
anlaosc
∆ISWl (k) =
anl
ai
da jl(kχa)[∂a(Ψk + Φk)]
≈ 2
j
jl(kχaj )∆Ψk(aj)
∆l(k) = ∆SWl (k) + ∆ISW
l (k)
Cl =
d ln k k3∆2l (k)
Thursday, August 11, 2011
integrated Sachs-Wolfe
10.05.02.0 3.0 15.07.01.0
5.0
2.0
3.0
1.5
lC lC lC
DM
CMB angular Power Spectrum
assumed LCDM expansion history
WMAP 7 yr
Thursday, August 11, 2011
choice of params.• change time of transition aosc
• change m to change number of oscillations
• M (linked to m) determines rate of growth
• change slope of potential (not easy)
oscillatory
U (ϕ) ∼ m2
ϕ ∼M
aosc
Thursday, August 11, 2011
rich nonlinear phenomenology
nonlinear fragmentation!
(-- additional ISW --)
MA 2010MA, Finkel, Easther 2010MA, Easther, Finkel, Flauger, Hertzberg 2011
Also see McDonald&Broadhead, Hindmarsh & Salmi, Gleiser et. al ...
Qualitative
Thursday, August 11, 2011
lumps?
(1) oscillatory (2) spatially localized (3) very long lived
Bogolubsky & Makhankov 1976, Gleiser 1994, Copeland et al. 1995, ...
ϕfor some range of
V (ϕ)− 12m2ϕ2 < 0
necessary:
satisfied if α < 1
oscillon
!
Thursday, August 11, 2011
nonlinear simulations
• include nonlinear dark matter clustering
• include nonlinear quintessence pert.
• much easier to do, canonical scalar field, no modified gravity!
Andrey Kratsov
Thursday, August 11, 2011
• parameter “sweep”
• coupling to other SM fields and consequences
• other phase transitions
• large angular scale inhomogeneities, implications ?
additional ISW, lensing, non-gaussianity?
Thursday, August 11, 2011
motivation: 2
• scale dependent potential growth
simple, no gravity modification
no Chameleons or Vainshtein
• difference in lensing and matter spectrum
• No effective anisotropic stress (linear)
• Growth rate (from matter) and expansion history not enough
Thursday, August 11, 2011
summaryscale-dependent growth gravitational
potential growth, dark clumps
oscillatory
ϕ ∼M
U (ϕ) ∼ m2
resonant growth
constrain via (i) lensing (ii) integrated Sachs-Wolfe
An example with scale dependent potential growth + difference in matter and gravitational power spectrum without modified gravity/non-canonical kinetic terms
Thursday, August 11, 2011