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Ignacy SawickiAIMS
arXiv:1305.008, 1210.0439 (PRD) + 1208.4855 (JCAP)Together with: L. Amendola, M. Kunz, M. Motta, I.Saltas.
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The Bygone Era of Easy Choices
ฮ
Dark Energy
โข ๐ค = โ1
โข ๐ค โ โ1
โModified gravityโ
โข ๐ค =/โ โ1โข ๐s
2 = 1โข ๐ โ 1
k-essenceโข ๐ค =/โ โ1โข ๐s
2 โ 1โข ๐ = 1
15 November 2013 AIMS, Muizenberg
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Managing the Model Bestiary
Slow-Rolling ๐๐ โช ๐๐ฟ๐ฏ
๐
Fast-Rolling ๐๐ โผ ๐๐ฟ๐ฏ
๐
Acceleration effectively from ฮ
๐s2 = 1
Non-minimal coupling gives fifth force
Chameleon screening & Compton scale
(coupled) Quintessence, ๐ ๐น , Brans-Dicke
Acceleration from kinetic condensate
Can describe hydrodynamics (incl. imperfect corrections)
Realistically should be nearly shift-symmetric
Non-trivial acoustic metric
Screening through Vainsteinmechanism
k-essence, KGB, galileons, shift-symmetric Horndeski
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What you get depends on what you put in
PlanckAde et al. (2013)
SDSS-III DR9Anderson et al. (2012)
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In this talkโฆ
What properties can we actually observe without having assumed a model first? Only ๐ป(๐ง) not ๐ค Only potentials ฮฆ, ฮจ, not e.g. DM growth rate
Can we measure properties of DE in a model-independent way? Not all, but can form null tests from data which can eliminate
model classes
Fundamental reason: dark degeneracy between dark matter and dark energy All cosmological probes are only sensitive to geodesics
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15 November 2013 AIMS, Muizenberg
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Our Limited Eyes
Galaxies P(k): BAO/RSD
Galaxy Shapes:Lensing
Supernovae:๐L
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The Best-Case Scenario
as little as feasibleAssume
โข FRW + (scalar) linear perturbations
โข Matter & light move on geodesics of some metric
โข Linear density bias ๐ฟgal = ๐(๐, ๐)๐ฟmโข (Equivalence principle/Universality of couplings)
build Super-EuclidInfinite โฌ$ยฃยฅ
โข Desired precision for position and redshift
โข SNe
โข lensing
โข counting galaxies
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LSS: Galaxy Power Spectrum
Baryon Acoustic Oscillations is a fixed ruler
use to measure distance if same physical size
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SDSS III, Anderson et al. (2012)
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Background
โข ๐ป0๐ท ๐ง =1
โฮฉ๐0sinh โฮฉ๐0
๐ป0d๐ง
๐ป(๐ง)
SNe, โฅ BAO, CMB peak
โข ๐ป ๐ง =ฮ๐ง
๐ ๐งโฅ BAO
โข Observables are ๐ป(๐ง)/๐ป0, ฮฉ๐0โข Not๐ค ๐ง or ฮฉm
In principle
15 November 2013 AIMS, Muizenberg
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Dark Degeneracy
In principle no way of measuring split between DE and DM
Only choice of parameterisation breaks degeneracy
e.g. constant ๐ค
Kunz (2007)
ฮฉ๐ = 1 โ๐ป02
๐ป2ฮฉ๐0๐
โ2 + ฮฉm0๐โ3
Anderson et al. (2012)
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Natural EoS for Quintessence
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Huterer and Peiris (2006)
๐ค = ๐ค0 + ๐ค๐ 1 โ ๐ ?
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Perturbations
Want to measure ๐บeffand ๐ to determine DE model
Can we actually do this?
Remember: ๐บeff and ๐hide dynamics No reason for them to be
simple
3 ฮฆโฒ โฮจ + ๐2ฮฆ =3
2ฮฉm๐ฟm +
๐
๐๐๐ฟ๐น๐ฟ
ฮฆ+ฮจ = ๐น๐ = ๐ฮฉ๐๐ฟ๐
๐2ฮจ = โ3
2๐ฎ๐๐๐ ๐, ๐ ฮฉm๐ฟm
ฮฆ+ฮจ = 1 โ ๐ผ(๐, ๐) ฮจ
d๐ 2 = โ 1 + 2ฮจ d๐ก2 + ๐2 1 + 2ฮฆ d๐๐
๐ฟmโฒโฒ + 2 +
๐ปโฒ
๐ป๐ฟmโฒ โ
3
2๐ฎ๐๐๐ ๐, ๐ ๐น๐ฆ = 0
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Is dark energy smooth?
โข ๐ = 1
โข ๐บeff = 1
ฮ: of course
โข ๐s2 = 1
โข ๐ = 1
โข ๐บeff โ 1 +๐ผ
๐s2๐2
Quintessence: more or less
โข ๐s2 = 1
โข ๐ =1
2
โข ๐บeff =4
3
๐(๐ ): not at all
๐ฟ๐๐ = โ1
3๐ฟ๐m
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LSS: Measure Galaxy Shapes
Weak lensing Gravity from DM and DE
changes path of light, distorting galaxy shapes
Can invert this shear to measure the gravitational potential
๐ฟ = ๐2 ฮฆโฮจ
Measure distribution of potential not of DM
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LSS: Measure Galaxy Shapes
Weak lensing Gravity from DM and DE
changes path of light, distorting galaxy shapes
Can invert this shear to measure the gravitational potential
๐ฟ = ๐2 ฮฆโฮจ
Measure distribution of potential not of DM
15 November 2013 AIMS, Muizenberg
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LSS: Galaxy Power Spectrum
Amplitude: related to dark matter through bias๐ฟgal = ๐ ๐, ๐ง ๐ฟm ๐ can only be measured
when you know what DE is
๐8 is not an observable
15 November 2013 AIMS, Muizenberg
SDSS III, Anderson et al. (2012)
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LSS: Redshift-Space Distortions Real Space
Redshift Space
Measure peculiar velocity of galaxies, ๐gal
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Hawkins et al (2002)
๐ฟgal๐ง ๐, ๐ง, cos2๐ผ = ๐ฟgal ๐, ๐ง โ cos2๐ผ
๐gal ๐, ๐ง
๐ป
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How are RSD (ab)used?
BOSS DR9 + WiggleZ, SDSS LRG, 2dFRGS Samushia et al. (2012)
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โข Only measuring velocities of galaxiesโฆ everything else is our interpretation
โข Non-linearity important at early times. How do you set the initial conditions?
Continuity for DM
๐ฟmโฒ + ๐m โ 0
โข If ๐m = ๐gal then can measure
dark matter growth rate
๐ฟmโฒ โก ๐๐ฟm = ๐๐8
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From acceleration measure force
๐ฟgal๐ง ๐, ๐ง, cos2๐ผ = ๐ฟgal ๐, ๐ง โ cos2๐ผ
๐gal ๐, ๐ง
๐ป
Galaxies move on geodesics
(๐2๐gal)โฒ =๐2
๐ปฮจ
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๐2ฮจ = โ๐ โฒ โ ๐ 2 +๐ปโฒ
๐ป
๐ด(๐, ๐ง) ๐ (๐, ๐ง)
๐2 ฮฆโฮจ = ๐ฟ
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Reconstruction of Metric
Ratios of potentials always observable
We measure power spectra of potentials, not dark matter
โฮฆ
ฮจ= ๐
ฮจโฒ
ฮจ= 1 + ฮ
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What about ๐บeff?
Dark degeneracy strikes back
No way of measuring ๐บeff without a model
Would somehow need to weigh DM and separated from DE
๐บeffโฒ
๐บeff+ ๐บeff
ฮฉm0 1 + ๐
๐ฟ/๐ = ฮ
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So what?
Full constraints on particular models of course are perfectly fine Expensive and non-generic: how to anoint the particular
model? Initial conditions?
In practice, we use parameterisations which represent parts of model space Are they consistent? Do they say anything about my model? Do they allow us to unambiguously see the things my
model canโt do?
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The model space
If ๐ small, then nothing new
Quintessence๐ ๐ Brans-Dicke
If ๐ large, then any term can be important
The background is a path across the 4D operator space
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โ โผ ๐พ ๐,๐ + ๐บ3 ๐, ๐ โง ๐ +
+๐บ4 ๐, ๐ ๐ป๐๐ป๐๐2+ ๐บ5 ๐, ๐ ๐ป๐๐ป๐๐
3+ grav
Horndeski (1974)Nicolis, Ratazzi, Tricherini (2009
Deffayet, Gao, Steer, Zahariade (2011)
โ โ ๐ + ๐ ๐ + ๐(๐)๐
2๐ โก ๐๐๐2
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What can we actually say?
On FRW, get corrections to perfect fluid that go as ๐2
๐๐๐๐= ๐๐๐
perf+ ๐ 3๐
2๐๐ + ๐ 4๐
2๐๐
Alternative: e.g. braneworld models: corrections go as ๐ Lorentz-violating: higher powers of ๐
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๐2(๐) = d๐ก๐3๐ perf ๐ก ๐ชperf ๐ก, ๐2 + ๐ 3 ๐ก ๐ช3 ๐ก, ๐2 +
+๐ 4 ๐ก ๐ช4 ๐ก, ๐2 + ๐ 5(๐ก)๐ช5(๐ก, ๐2)
Measure DE properties fromscale dependence
on the realised background
Amin, Wagoner, Blandford (2007)
๐บeff ๐, ๐บeffJeans
Blas, Sibiryakov (2011)
Creminelli, Luty, Nicolis, Senatore (2006)IS, Saltas, Amendola, Kunz (2012)
Gleyzes, Piazza, Vernizzi (2013)
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Is it any scalar at all?
๐ฟ๐00 โ ๐ฟ๐, ๐ฟ๐, ๐ฟm ๐ฟ๐๐
0 โ ๐ฟ๐, ๐น๐, ๐m ๐ฟ๐๐๐ โ ๐น๐
๐ฟ๐๐๐ โ ๐ฟ๐ , ๐ฟ๐, ๐น๐ ๐ฟ๐ = EoM
ฮฆโฒโฒ
ฮจ+ ๐ผ1
ฮฆโฒ
ฮจ+ ๐ผ2
ฮจโฒ
ฮจ+ ๐ผ3 + ๐ผ4๐
2ฮฆ
ฮจ+ ๐ผ5 + ๐ผ6๐
2 ฮจ = ฮฉm๐ผ7๐m
ฮ(๐, ๐ง) ๐ โฒ/๐
Fix ๐ผ๐(๐ง)
๐(๐, ๐ง)
2 October2013 NYU Abu Dhabi
๐(๐ ): one param ๐C(๐ง)
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The Takeaway
In principle, we can reconstruct the evolution of the metric We cannot get the split between DE and DM without assuming
some class of models
Generically, DE models predict a change in the power law for ฮจ as a function of scale Different frameworks give you different scale dependence: could
potentially eliminate scalars completely
If I told you today that the background was inconsistent with ๐ค = โ1, what have you learned? If that happens, weโll have to be more sophisticated about
interpreting the data
15 November 2013 AIMS, Muizenberg