MAY 8, 2007
CCAPP, OSU
Voids of dark energy
Irit Maor
Case Western Reserve University
With Sourish Dutta
PRD 75, gr-qc/0612027
A very quick summary:
The universe is accelerating.
We do not know why.
[kinematics]
[dynamics]
Cosmological constant?
120 orders of magnitude!
w = ¡ 1:062+ 0:128
wmap3:
¡ 0:079
“wmap does not need quintessence ”
(Page)
Motivation for the cosmological
constant
Bludman, 0702085
But: “CMB needs something else”
Many degeneracies for w(z).
Maor et al, 0007297
Upadhye et al, 0411803
Which parameters?
Which priors?
Which data sets?
Liddle, 0401198
Maor et al, 0112526
Bridle et al, 0303180
Motivation for dynamical dark energy
w = w(z) 6
= ¡ 1

A mild generalization of the old standard cosmological
model.

Scalar fields are not a new concept, “inspired” by
fundamental theories.

Hopes for dynamical fine tuning.

Probably an ok description of more complicated scenarios.
..but:
tracker, k-essence, phantom, coupled, …your
favourite DDE model
fine tuning not solved!
Other alternatives
SN are wrong
Xtra dimensions ( effective w(z) or coupled
DDE)
your favourite theory of gravity ( same as above)
super horizon modes
The background:
BAO
Clusters
CMB
ISW
SN
SZ
WL
…
 #% for
w0
maybe #% for
dw
dz
Background measurements will have a very hard time
differentiating between CC and DDE.
All focus on w(z).
Null experiments, how far?
Looking for the dark stuff
Solar system
Extrapolation from the cosmic to the solar scale.
Clear signature of dark gravity!
Looking for the dark stuff
Perturbations
Does DDE cluster on scales less than ~100 Mpc?
(yes)
A thorough understanding of the behaviour of
perturbations is needed.
If it clusters, it is not the cosmological constant!!
Looking for the dark stuff
Non linear regime
how does the DDE behave?
model sensitivity vs generality?
In progress, with Dutta
Implications of inhomogeneities?
Large Scale, CMB
Weller and Lewis, 0307104
Smaller scale inhomogeneities
Takada, 0606533
Maor and Lahav, 0505308
Nunes et al, 0506043
Calculate, instead of parameterize, the
clustering properties of DDE.
L = LG + Lm + LÁ
LG
Standard
gravitational
action
Lm
Standard pressureless fluid
LÁ =
1
2
V (Á) =
m
H0
¼1
(@¹ Á) 2 ¡ V (Á)
1 m 2 Á2
2
Linear perturbation
½m (t; r ) ! ½m (t) + ±½(t; r )
Á(t; r ) ! Á(t) + ±Á(t; r )
V (Á + ±Á) = V (Á) + ±V (Á; ±Á)
ds2
=
dt 2
¡
a2 (t)
£
(1 + 2³ (t; r )) dr 2 + ((1 + 2Ã(t; r )) r 2 d
¤
2
(Synchronous gauge)
» ´ ³_+ 2Ã_
The equations


Zeroth order: standard FRW evolution of the
background.
First order: equations for the perturbation
variables, which after a Fourier transformation
are ODE’s.
Initial conditions



Matter: gaussian, with width well within the
horizon.
Scalar field: homogeneous IC, with no kinetic
energy (w=-1).
Metric: by the constraints equations.
Results are insensitive to IC
Results
Anti-correlation between matter and DE perturbations
Results
Amplitude grows fast!
Results
“cross-over”
Equation of State
w0 =
±w =
p0
½0
1
½0
=
¡
1
2
1
2
Á_2 ¡ V
Á_2 + V
¢
±p ¡ w0 ±½
w1 = w0 + ±w
Background EOS
Linear correction to
EOS
First order corrected
EOS
Equation of state
Spatial profile of the equation of state
Why a void?
Void formation
Energy density correction:
_ Á_
±½Á = m 2 Á±Á + Á±
PE correction < 0
KE correction quickly dominates
KE correction > 0
void
Á> 0
±Á < 0
Á_ < 0
±Á_ < 0
±K E > 0
±P E < 0
Acceleration slows, but doesn’t change sign.
Conclusions
DDE develops voids [ripples].
Our results are generic for slow-roll DDE.
Possible interesting dynamics in the non-linear regime.
Observables?