Coupling between the structures and h d the dkdark sector · SDSS ~106 600Mpc~2 billion lyr 5....
Transcript of Coupling between the structures and h d the dkdark sector · SDSS ~106 600Mpc~2 billion lyr 5....
Chaire Galaxies et Cosmologie
Coupling between the structures d h d kand the dark sector
Françoise Combes
Relation large-scale structures– dark energy
The Universe: homogeneous and isotrope at the beginningLarge-scale structures today are highly contrastedEffect on space-time dynamics? « back-reaction »Average density to compute the metricAverage density to compute the metricNon commutativity, Einstein equations are non-linear
Galaxy clusters as cosmological testsIn addition to BAO, and gravitational lensesS d d l d diStandard ruler and distance measurementUniversal baryon fraction
Growth rate of structures, affected by the progressive domination of dark energyp g gyTest of modified gravity
The Copernic PrincipleHypothesis, quasi philosophical, that our Universe ishomogeneous and isotropeg p
One of the bestconfirmation: the diffusemicro-wave background
~10-5
Large-scale structures of the local Universe
4Nearby clusters and superclusters
SDSSSDSS
~106
5600Mpc~2 billion lyr
Density of structures in the UniverseSolar system 10-12 g/cm3
Milky Way 10-24 g/cm3
Local Group 10-28 g/cm3
G l l t 10 29 / 3Galaxy cluster 10-29 g/cm3
Supercluster 10-30 g/cm3Supercluster 10 g/cm
Density of photons (3K) 10-34 g/cm3
Density of baryons (b) 5 10-31 g/cm3
Critical density (=1) 10-29 g/cm3
6 ~1030 on Earth!
Smoothing of inhomogeneities
The smoothing of inhomogeneities modifies considerably the structure of Ei i i hi h liEinstein equations, which are non-linearThe two operations do not commuteSolve the equations then smooth ≠ smooth then solve the equations
GTG 8Solve the equations then smooth, ≠ smooth then solve the equations
The inhomogeneities introduce then a reaction with respect smoothing,e o oge e es oduce e a eac o w espec s oo g,a term of “back-reaction” in the right-hand side of the equationThere is no reason for the effective tensor energy-momentum Twith the back-reaction, to satisfy the usual conditions P>-/3,even though the original T satisfied themThe smoothing is useful to avoid singularitiesThe smoothing is useful to avoid singularities.The back-reaction term could lead to an accelerated expansionEven from a fluid with positive or null pressurep p
Acceleration due to inhomogeneitiesAcceleration due to inhomogeneitiesHomogeneous model Inhomogeneous model
3
h
V
3h ha V
Hh h hH a a
h i x ?h iH H
May be, or may-be not!
The principle of inhomogeneitiesThe principle of inhomogeneities•Friedmann–Lemaître–Robertson–WalkerInhomogeneous model
FLRW, ,G x t G t G x t
Inhomogeneous model
FLRW00 00 00
, ,
, 8 ,G t G x t GT x t
Homogeneous flat model,Ei i d Si P 0
2
008 3
3 8a G G
G
Einstein-deSitter P~0
003 8a G
d i / ( )< > domain = -4G/3 (eff + 3Peff)
Kolb, et al 2006, 2011Buchert, 2000, 05, 07
Average at large-scaleAverage at large-scale
1/3 3a V V V d x h
• Average over a large volume VD:
0 D D D DD
a V V V d x h • Corresponding Hubble constant :
13
DD D
D
aHa
4Da G
• Equations of effective evolution:
RQ Diff t f eff eff
2
4 33
8
D
D
a G pa
G
eff 16 163
D DD
RQG GRQ
Different from l’equation ofstate
eff8
3D
D
a Ga
eff33
16 16D D
RQpG G
p w
• Backreaction: 22 223 2D DD D
Q
Advantages of inhomogeneitiesAdvantages of inhomogeneities• No need to add a 5th force!
•No need to modify gravity, keep general relativityd f di i•No need of extra dimensions
•Explains why dark energy is becoming significant only now•(5Gyr ago), while the contrast in structures develops with time• Negligible at T~400 000 yrs
•Magic? However we still need a proof that / is sufficient•Modifies the zero mode and the scale factor•Modifies the zero mode, and the scale factor
Perturbations larger than the horizonPerturbations larger than the horizon• The largest observable perturbation has the scale of Hubble radius
todaytoday
Hubble Radius (5Gpc)z= 2 1018 4000 0 5
10-32s 40 103yr 5 109yrz 2 10 4000 0.5
Lesgourgues 2006
10-32s
Toy model from Nambu-Tanimoto (2005)• The basis: flat universe LTB Lemaître-Tolman-Bondi, solution of
Einstein equationsq• Contains a region of positive curvature (c), and one negative• When the dense region collapses, then on average the expansion g p , g p
of the ensemble accelerates
LDeceleration
r0
open
closed
open
t/(oL3)closed
Acceleration Also Mansouri 2005, Alnes et al 2006
Estimation of Green & WaldG = 8G/c4 T
• Green & Wald, 2011, 13, 16: introduction of a computation methodWi h h h (0)
G 8G/c T
• With hypotheses: g = g(0) + << 1, but not the derivatives g(0) is not solution of Einstein
eq ations C r at re of g at scale of H bble radi sequations -- Curvature of g at scale of Hubble radius
I h iti L << R(H bbl )Inhomogeneities on L << R(Hubble)Average over the scales L << D << R b k ti i ti f th d f 1% back reaction: variations of the order of 1%Always positive, traceless tensor
Justification: the perturbations are not far from Newtonian (v non l ti i ti ) ith li ti t bl k h lrelativistic), with linear equations, except near black holes
True for Einstein, bit not for f(R)
But a smooth background metric…Estimation without approximation ( expansion shear)
Shows a term with a non-zero traceShows a term with a non zero trace
The equations are undetermined. What is the dependence on time q pof QD?
Could QD become large enough to accelerate the expansion? P bl th ll f t t f tiProblems as soon as the collapse of structures form caustics
Voids are important and must be taken into account
Buchert et al 2015, Kolb et al 2016
Computations from Bardeen et al (2007)Even in the toy model from Nambu-Tanimoto (2005)The density contrast give rise to causticsAll the mass is found in a shell (LTB non valid)All the mass is found in a shell (LTB non valid)Less deceleration, but no acceleration of expansion
S scaleCurvature
S scalefactor
R/SR/S
RayonThe average has no longer any senseNewtonian approx is valid, relativistic effects negligible
Rayon
In summary The perturbations beyond horizon provide no acceleration
The inhomogeneities at small scale could “renormalise” the large The inhomogeneities at small scale could renormalise the large scale acceleration on average (+3P <0)
The smoothing of perturbations below horizon raises problems, and should be done properly
In a frame comoving with the matter flow unless unreliableresults
An effect which should be quantified, even it cannot explain the dark energydark energy
The debate keeps open !The debate keeps open !
Clarkson et al 2011
Some tests are possibleM f di tMeasure of distances
Curvature of geodesics ExpansionCurvature and distance coupled in standard, not in LTBAlso k independent of zTests on the BAO ruler, Supernovae, SDSS surveys
Measure of redshift evolution(Uzan et al 2008 Liske et al 2008)
dz/dt
(Uzan et al 2008, Liske et al 2008)
Or else w(z) requires also H’(z)Or else w(z), requires also H (z)
Simulations 20 yrs of observationsof 10 QSO with ELT, H=8km/s
z
Baryonic acoustic peak Power
Waves detected todayIn the distribution of baryonsy
50 000 galaxies in SDSS
Separation
Eisenstein et al 2005
19
A simple perturbation
Creates a depression
Sound wave at c /√3 Sound Horizonat recombination
R 150MpcR~150Mpc
Gala iesGalaxies
In the over-densites
20Acoustic waves Daniel Eisenstein
Multiple perturbationsSignal reduced by therandom phasesMultiple wavesl 1% in the P(k)
Power
Daniel Eisenstein
21Separation
Expected oscillationsExpected oscillations
Not in phaseNot in phaseat small scales(velocities)( )
And 2x wavelength
Hütsi 2005Hütsi 2005
22M. White 2007
BAO: baryonic oscillationsy
Radial BAO: dr = (c/H)dz
cz/H
Radial BAO: dr (c/H)dzIn the plane of the sky: dr = DAd
Observer
D
Better than the CMB3D instead of 2D!
D
c z/H = D Alcock & Paczynski (1979)T t f th l i l t t
P ibilit t
Test of the cosmological constant
Can test the bias b
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Possibility to determine H(z)
Can test the bias bOr = m
5/9/b
Power spectrum of matter fluctuations
Linear power spectrum
S l f h i P(k)Scale of the maximum P(k)= horizon size at the epoch ofmatter-radiation
Large scales Small
matter-radiation equivalence
50 000 yrs after the Big-Bang
f 1/3f m = 1/3
m = 3 7evm 3.7ev
The relativistic neutrinos
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Reduce small-scale structures
Voids dominate the UniverseGalaxy clusters, 3- 15 Mpc, + network of filaments and surfaces like “walls” surrounding voidsg
The Universe is dominated by voids (60–80%) in volume, with a di t ib ti d h t i ti l (40% f th t t l l )distribution and a characteristic scale (40% of the total volume)
Voids ~40 Mpc density contrast of ~ -0 94Voids 40 Mpc, density contrast of 0.94
The statistic homogeneity scale is of 100 -150 MpcAt larger scales, the contrast < 0.4
Th i iti l t b ti lifi d b tiThe initial perturbations are amplified by acoustic wavesThe statistic homogeneity scale is near that of BAO
BAO can be considered in the linear regime
Tests of backreaction modelsBelow this scale, there can exist differential expansionsdue to inhomogeneities
Towards LeoVelocity of Local Group vs CMB = 645 km/sVsun LG 318km/s
Towards aquariusVsun-LG= 318km/sDipole of 3.31 mK
Determination of peculiar velocitiesDetermination of peculiar velocitiesVpec= cz –H0 r
Local cosmic flowsPeculiar velocities: to reach the underlying potential Vpec= cz –H0 rb, DM,
Distance indicators Tully-Fisher Tip of Red Giant branch Fl t ti f f Fluctuations of surfacebrightness Fundamental plane Fundamental plane Cepheids
The origin of the dipoleNot yet completely elucidated
Lavaux et al 2010
In which direction?
A di h id d
Dipole CMB
According to the consideredvolumes
Lavaux et al 2010
Dipole CMB
Unknown still remain
Flat Universe, k= 0m = 0.3, CDM
Obs m=0.15-0.2
Lavaux et al 2008
The dipole does not converge
2MASS galaxies in NIR, depths ofmin and max 7 and 400 Mpcp(Virgo 17Mpc, Hydra 47 Mpc,Leo > 120 Mpc)
The data analysisThe data analysisYields a value of m = 0.20m
= m0.55/b = 0.38
Bilicki et al 2011M03: Maller et al 2003E06 Erdogdu et al 2006
Simulations of the local UniverseTh b SNI i ld diff t l f HThe nearby SNIa yield a different value of H0They follow the dipole, and therefore are biased +Divergent velocities around Virgo boost H0 H0=1 76 km/s/MpcDivergent velocities around Virgo, boost H0 H0 1.76 km/s/Mpc
Hess & Kitaura 2016
Residual cosmic flow ~200km/sIn spite of the increase of the galaxy number, the residual velocityis still unexplained
Springob et al 2016Blue, green, redIncreasing volume
We live at the border of a superclusterIt contains the clusters of Virgo, Hydra-Centaurus, Pavo-IndusLaniakea in the process of dilution, dispersion (160Mpc, 1017M)
ShapleyComa
Perseus-Pisces
35Tully et al 2014
Rees-SciamaRees Sciamaeffect
The late ISW effect (in the local Universe), when it becomes
li i ll d R S inon-linear is called Rees-Sciama
In presence of the super-clusters and voids see their density contrastIn presence of , the super-clusters and voids see their density contrastdecreasingThe microwave photons get out of super-clusters bluer (morep g p (energetic) and the contrary in voids
T if h ff i l h li h lTo quantify the effect, one must simulate the light travelin the non-linear relativistic regime
ray-tracing algorithm
Relativistic simulations of differential expansionRelativistic simulations of differential expansionThe effect of inhomogeneities is simulated exactly, without the g y,smoothing approximationImpossible to account for observations, without a non-kinematicalffeffect
(1+z)obs= (1+z)expHo(1+z)pech d i li l i i i ll dWhat does not enter in peculiar velocities vpec, is called
non-kinematic effect
The underlying expansion is supposed to come from the isotropiclocal model, with an average FLRW metric, gThe CMB dipole corresponds to T/T =1.23 10-3, of the same orderOf magnitude than =v/c = 2.1 10-3, but there are residuals
Bolejko et al 2016
Simulations with the Szekeres modelThe effect of inhomogeneities (local void Great attractor) is simulatedThe effect of inhomogeneities (local void, Great attractor) is simulatedexactly, by numerically solving Einstein equationsOn the photon path effect of anisotropies on the expansionp p p p
Bolejko et al 2016Dipole Quadrupole8/h Mpc
8/h Mpc
DATA
LTB
Simulationsof BAO
Springel et al 2005
Power spectrumDM and galaxiesin the BAO regionin the BAO region(after division bythe linear CDMspectrum)
Blue: all pointsBlack: average
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State of BAO measuresWith SDSS galaxies, 8500°2, 0.2 < z < 0.7, sound horizon rdH=96.8 + 3.4 km/s/Mpc Distances/rd compatible with CDM
H from the separation
and
Anderson et al 2014
BAO with the Ly forestIonised gas absorbants in cosmic filamentsin front of remote quasars 137 000 quasars 2.1 < z < 3.5S d h i 2 34 dSound horizon at z=2.34 : rdDA/rd 7% smallerDH/rd 7% largerDH/rd 7% largerthan CDM
Significant to 2.5
Z=2.91
Delubac et al 2015
Test of modified gravity models
Yamamoto et al 2006
42
Dvali-Gabadadze-Porrati « DGP model »
Gravitational lenses
The distance as a function of redshift depends on
Growth of structures, depends on
43Schneider 2003
Reduces the number of galaxiesgAmplification of background sourcesBy increasing their radius Conservation of surface brightnessBy increasing their radius, Conservation of surface brightnessReduction of the source density
Discrepant recent results?Hildebrandt et al 2016 KIDS: 450°2 weak gravitational lensing
15 millionsof galaxies
Discordantwith Planck-2015
Comparison of several data sets
Galaxy clusters and dark energyClusters provide different and complementary tests
On distances, fgas ~fbar is supposed universal (17%)
O h h f d k h iOn the growth of structures: dark energy has an actionopposing gravity, and limits their formationStudy as a function of zStudy as a function of z
The rate of growth probesg pmodified gravity models, at very large scales
Vikhlinin 2008
Self-similar distribution
At the centre, this is no longer, gtrue, because of cooling flowphenomena
Chandra
Morandi & Sun 2016
Constance of baryons/total ratioMgas mass of X-ray gas Mt t total mass of the galaxy cluster
gasgas M
Mf Mtot total mass of the galaxy cluster
The hot gas represents the bulk of baryons gasgal fhf 5.019.0tot
g M
The baryon fraction in clusters = universal baryon fraction
bb b is the bias factor, bbf f +f m b
fgas(1 0.19h0.5),
accounts for gas ejected at the
m
bbaryon bf
fgas+fgal=
formation epoch of the clusterDistances measured for 0.06<z<1.2 320 clusters
5.1
mod )()(
)19.01()(
zdzd
hbzf
A
refAb
gas
Mgas dA(z)2.5
Mtot dA(z) V2 R
test combined with +HST+BBNS priors
)()19.01( dh Am
Test of galaxy clustersX-ray emission of 320 galaxy clusters0.056 < z < 1.24, kT> 3 keV with the X-ray satellite Chandra
Clusters are self-similarEspecailly in outer parts
E ti f t t fEquation of state of dark energy P= w
w= -1.010±0.030
Compatible with a cosmological constant
Morandi & Sun 2016
Coma clusterX-rays, optical,
XMM‐Newton= X
X rays, optical, Sunyaev-Zeldovich
ff t (SZ)effect (SZ)
Telescope CFHT= optical
H diffHot diffuse gas107K, 13%
Galaxies: 2%
Dark matter: 85%
Two tracers of the hot gasBremstrahlung radiation
Total SZ flux, proportional to Mgas/DA(z)2
SZ effect detected by PlanckIntensity I
SPT 244 SZ d d (1 1’) Tdlny e
SPT 244 SZ detected (1.1’)ACT 91 detected (1.4’)
Planck 1653 sources (5’)1200 galaxy clusters
frequency
g y
2
ref
obsref
yydd
Advantages of clustersg
• Standard ruler, measure of distances with X and SZ: precision semilar to SNIa and BAO with some advantages
Simple physics, models and simulations The X-ray emission improves in S/N fgas : extra constraint on Ωm
fgas + CMB raise up degeneraciesg
Low systematic dispersion in fgas(z) X+SZ independent of bias and of hydrostatic equilibrium
Resistance to the gravityResistance to the gravityDark energy reduces the number and the mass of clusters
w
Vikhlinin et al 09Vikhlinin et al 09
Growth of Growth of structures
Number of clusters as a function of redshift
Test of equation ofstate of dark energy
P wP=w
ww
m
Summary
Could large-scale structures contribute to dark energy? Atwhich scale does isotropy dominate?which scale does isotropy dominate?and « back-reaction » become negligible?
Several complementaty tests of dark energy BAOW k l iWeak lensingGalaxy clustersAs standard ruler and measure of distanceAs standard ruler and measure of distanceAnd using the universal baryon fraction
Growth rate of structures, perturbed by the progressive domination of dark energy, tests of modified
itgravity