Slides in PDF format - hep

dark energy
phenomenology
Martin Kunz
University of Sussex
mainly with Luca Amendola and Domenico Sapone

Outline
• State of the nation: w(z)
– And ask questions at any time
– Please slow me down if needed!!
• Why go beyond w?
– Because we need to / we do it already
– Because we learn more
• The future
• Conclusions

how much vacuum energy?
Let us count the energy density in the
universe:
(Ω X
=ρ X
/ρ c
=8πGρ X
/(3H 02
))
- radiation: CMB-temp ⇒ Ω γ
≈ 5x10 -5
too small to matter…
combine SN-Ia and CMB distance
measurements:
- matter: Ω m
≈ 0.3
(whereof baryons ≈ 0.05! [BBN/CMB])
-cosmological const.: Ω Λ
≈ 0.7
(and space is close to flat)

what is the problem with Λ?
log ρ
radiation (~1/a 4 )
matter
(~1/a 3 )
Let’s guess the size of the
contribution by Λ:
• QM contribution ~ k 4 .
• Planck cutoff: Λ ≈ 10 76 GeV 4
• measured: Λ ≈ 10 -47 GeV 4
• worst prediction ever?
cosmological
constant (~constant)
log a
imagination
dominated
radiation
dominated
matter
dominated
Lambda
dominated
p=wρ

homogeneous dark energy
Assume that the universe is perfectly homogeneous and isotropic
(and flat): FLRW metric
T µν
must be:
ds 2 = dt 2 - a(t) 2 dr 2
Einstein:
H 2 =
probed by
distance
measurements
matter: p = 0 -> ρ ~ a -3
radiation: p = ρ/3 -> ρ ~ a -4
dark energy: p = ? (< -ρ/3)
(define w = p/ρ)
-> the only thing to measure
is w(z) or H(z) / a(t)

distances in the universe
( 1+z = a 0
/a )
standard ruler
(CMB peak, BAO, …)
D
standard candle
(supernova)
r
r

(current) quintessence results
WMAP-3yr + SNLS-1yr limits:
• scalar field model
[ c s2
=1, σ=0]
• regularised transition of w=-1
• uses “kink” model for w(z)
• cosmological constant fits well
• strong constraints only at low-z
• dark energy becomes subdominant
in the past
excluded
95% confidence
region
MK & D. Sapone, PRD 74, 123503 (2006)
B.A. Bassett, P.S. Corasaniti & MK, ApJL 617, L1 (2004)
P.S. Corasaniti, MK, D. Parkinson, E.J. Copeland & B.A. Bassett, PRD 70, 083006 (2004);
MK, P.S. Corasaniti, D. Parkinson & E.J. Copeland, PRD 70, 041301R (2004);
B.A. Bassett, MK, D. Parkinson & C. Ungarelli, PRD 68, 043504 (2003);
B.A. Bassett, MK, J. Silk & C. Ungarelli, MNRAS 336, 1217 (2002) + diverse proceedings

Short summary
• Flat LCDM good fit to data
• -0.7

measuring dark things
Einstein:
(in cosmology)
(determined by the
metric)
geometry
stuff
(what is it?)
your favourite theory
something
Cosmologists observe the
geometry of space time
something
else
This depends on the total
energy momentum tensor
That is what we measure!

In our minds, dark matter and
dark energy are neatly
separated concepts.
hot
cold
But in reality we can only observed their
combined effect.
If we can adjust the temperature and
flow of the hot water, we can vary the
flow of the cold water without changing
the total flow or the total temperature.

What do you think?
Do we understand the dark energy?
YES
NO
Do you believe that in a flat universe Ω m
≈ 0.2 - 0.4?
YES
NO

The true value of Ω m
is…

the dark degeneracy
How well do we know Ω m
in general (flat) DE models?
Different question: given H(z), what is w(z)?
We get a solution for any Ω m
!
impossible to measure simultaneously w(z) and Ω m
only total dark energy-momentum tensor is measurable
good test for generality of a parametrisation…

perturbations are important!
Only a cosmological constant has no perturbations
c s2
=0
c s2
=1
Λ
c s2
=1
(c s
2
> 1 , X = (∇φ) 2 , also DBI, f(R)? )
M.Kunz, astro-ph/0702615, arXiv:0710.5712

Where are we (going)?
• Whether we can measure Ω m
depends
decisively on the DE perturbations
• So what defines the properties of the DE
perturbations?
• Are modified gravity models different?
• Notice a very strong degeneracy between
smooth DE and curvature: what is Ω K
?
(exercise: can you break this degeneracy?)

measuring the dark side
small perturbations: extended metric
φ, ψ gravitational potentials δρ and V perturbations of T µν
Einstein eqs.
fluid properties
measure total w, δp, σ !
δp = c s
2
δρ in DE rest frame
σ (anisotropic stress, φ =ψ for σ=0)
(and compare with predictions)
(alternatively, measure φ and ψ: weak lensing (WL) measures φ+ψ,
while peculiar velocities / redshift space distortions measure ψ alone)

equations
metric:
conservation equations (for each fluid independently)
(vars: δ=δρ/ρ, V ~ divergence of velocity field, δp , σ anisotropic stress)
Einstein equations (common, may be modified if not GR)
(Bardeen 1980)

What do you think?
Can we distinguish dark energy from
modified gravity and rule out GR
by measuring the growth-rate?
YES
NO
it depends

dark gravity vs dark energy
• DGP: brane-world model
without dark energy
• scalar field: high sound speed
prevents DE clustering
• the perturbations in the dark
energy can perturb the dark
matter
• and mimic models of modified
gravity
• σ = 0 kills DGP, S/T, f(R)
• σ ≠ 0 kills scalar field DE
-> we can test such models!
-> but we cannot rule out GR
dark matter pert. growth rate δ m
/a
σ
δp
scalar field
DGP
MK & D. Sapone, PRL 98, 121301 (2007)

The general argument
modified “Einstein” eq: X µν
= -8πGT µν
(e.g. projection to 3+1D from higher-D scenario)
Y µν
can be seen as an effective DE energy-momentum
tensor.
Is it conserved?
Yes, since T µν
is conserved, and since G µν
obeys the Bianchi
identities!
There is also no place “to hide”, since T µν
is also derived
from a general symmetric tensor.

ug or feature?
• bug:
– cannot directly test GR
• feature:
– strong clues in result + need theory anyway
– clear target for what should be measured
– independent of whether MG or DE is
realised
it’s a feature!

dark energy phenomenology
• Perturbations are an essential part of many
cosmological measurements
• If we “ignore” them, we are effectively just
choosing something without being aware of it
• Results do strongly depend on that choice
• Observationally, they can be characterised by two
(possibly effective) additional functions,
independently of the mechanism that generates
the accelerated expansion
• Models make specific predictions for the
perturbations – much more so than for w(z)!

How can we measure it?
• w(z) from SN-Ia, BAO directly (and contained in
most other probes)
• Curvature from radial & transverse BAO
• In addition 5 quantities, e.g. φ, ψ, bias, δ m
, V m
• Could even skip DM, we cannot see it (yet)
• Need 3 probes (since 2 cons eq for DM)
• e.g. 3 power spectra: lensing, galaxy, velocity
• Lensing probes φ + ψ
• Velocity probes ψ (z-space distortions?)
• And galaxy P(k) then gives bias (reqd for z-dist)
→ Euclid / JDEM can do it all!

weak lensing forecasts [DUNE]
different nonlinear
mappings
lensing potential:
not just φ!
don’t
forget!
4πGa 2 ρ m
∆ m
but ∆ m
is also affected directly! [with γ=γ(Q,η)]
quintessence
DGP
Σ = Q (1+η/2) ~ 1+O(0.1)
• these are very optimistic plots
• weak lensing has uncertain systematics
• and requires linear -> non-linear mapping
• very powerful if it works!
L. Amendola, MK and D. Sapone, JCAP 04, 013 (2008)

future experiments
• CMB: parameters, ISW; Planck, ground (SZ/B-pol)
• SN-Ia: w(z); lots (FEADEP*, ground † )
– low-z : normalisation, probe of local universe
– perturbations, “luminosity tomography”
– theoretical & statistical advances (reduce dispersion)
• BAO: w(z); SDSS, WFMOS, photo † , FEADEP, Ly-α (z ≤ 3)
– complementary to SN-Ia (mostly linear physics, different)
– can in principle measure evolution of curvature
• weak lensing: φ+ψ [not DM!]; FEADEP, ground †
• galaxy surveys: growth rate, φ; SDSS, WFMOS, FEADEP
• peculiar velocities: ψ; redshift space distortions?
• LHC / dark matter searches: pin down DM, theory
†
e.g. FMOS, DES, darkCAM, Pan-STARRS [~2009] / LSST, SKA [2014+]
* Future European American Dark Energy Probe [~2017+]

final summary
• still no really good theoretical model …
Λ fits all obs.
• cosmology can (and will!) measure just a few
functions, e.g. w(z), φ(k,z), ψ(k,z)
• good (clear target for observations) and bad (no
unique identification of physical mechanism)
• requires multiple probes, e.g. weak lensing +
galaxy surveys + supernovae
• control of systematics will be crucial as effects
are very small!
• but the data is only just beginning to pour in!