constraints on the dark side of the universe alessandro melchiorri
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04.073.0
A model without cosmological constant isnow ruled out at more than 18 sigma!
Friedmann Cosmological Model works only if:
COSMOLOGICAL COSTANT vs “Something else”
const
p 0
X (z)X (0)exp 3 dz'1 w(z')
1 z'0
z
pX w(z)X
X 0
Vs.
Dark Energy Parametrizations(Just a Few…)
0)( waw
)1()( 10 awwaw
qs
q
qs
q
awaw
aawwaw
0110)(
)1(300
0
)1()(
aww
waw
Wanilla Parametrization
CPL Parametrization
Hannestad Mortsell Parametrization
Unified Models: Chaplygin
When did Cosmic acceleration start?
)(
)()(
eq
eqMeqX
zt
zz
In cosmology we can define two very important epochs:
)(
0)()(2
acc
accacc
zt
zaH
azq
Redshift and Time ofMatter-Dark energy equality
Redshift and Time ofonset of cosmic acceleration
1)1(2 3/1 eqacc zz
Those two epochs can be different, for the case of acosmological constant we have:
But we may have a different relation for different darkEnergy models…
Melchiorri, Pagano, Pandolfi, PRD, 2007
CosmologicalConstant
)1()( 10 awwaw
qs
q
qs
q
awaw
aawwaw
0110)(
0)( waw
Melchiorri, Pagano, Pandolfi, PRD, 2007
When cosmological data are combined, the redshift ofThe onset of cosmic acceleration is consistent between the different parametrization of w.
AM, Luca Pagano, Stefania Pandolfi arXiv:0706.131Phys. Rev. D 76, 041301 (2007)
When did Cosmic acceleration start?
Results are reasonably consistent between datasets (tension between 2dF and SDSS) and DEparametrizations.Age constraints change a lot if youinclude extra hot dark matter orCurvature.
Bayesian Model Selection
E PD | H P
D |,H P
,H
Likelihood Prior
Jeffrey(1961):
1 ln(E) 2.5 Substantial
2.5 ln(E) 5 Strong
5 ln(E) Decisive
Current cosmological data are in agreement with more complicatedDark energy parametrizations, but do we need more parameters ?More complicated models should give better fits to the data.In model selection we have to pay the larger number of parameters(see e.g. Mukherjee et al., 2006):
Evidence
P. Serra, A. Heavens,A. MelchiorriAstro-ph/0701338MNRAS, 379, 1,1692007
More Parameters
Current data:“Substantial” Evidencefor a cosmologicalconstant…
Integrated Sachs-Wolfe effect
while most cmb anisotropies arise on the last scattering surface, some may be induced by passing through a time varying gravitational potential:
dT
T2
linear regime – integrated Sachs-Wolfe (ISW)
non-linear regime – Rees-Sciama effect
when does the linear potential change?
22 4 aG Poisson’s equation
• constant during matter domination• decays after curvature or dark energy come to dominate (z~1)
induces an additional, uncorrelated layer of large scale anisotropies
two independent maps
Integrated Sachs-Wolfe mapMostly large angular features
Early time map (z > 4)Mostly from last scattering surface
Observed map is total of these, and has features of both (3 degree resolution)
compare with large scale structure
potential depth changes as cmb photons pass through
time dependent gravitational potential
observer
density of galaxies traces the potential depth
ISW fluctuations are correlated with the galaxy distribution!
since the decay happens slowly, we need to see galaxies at high redshifts (z~1)
active galaxies (quasars, radio, or hard x-ray sources) possibility of accidental correlations means full sky needed
A Test for departure from Einstein General Relativity with Cosmological Constant
])21()21()[( 2222 xddtads
)1(
2
,22 12)( kGak
Consider the FRW perturbed metric in conformal gauge:
For standard LCDM (no radiation) we have:
Newtonian Potential:Strenght of gravity
Longitudinal Potential:Amount of curvature producedper unit rest mass
Modification to General Relativity may lead to a different relation:
Degeneracy with anisotropic stresses from relativistic fluids:
Caldwell, Cooray, AM, Phys. Rev. D 76, 023507 (2007)
Caldwell, Cooray, AM, Phys. Rev. D 76, 023507 (2007):
But we get more information from ISW-Galaxy cross correlation:Correlation could be negative !
,))2(( dT
T
ISW
1.02.0
From ISW datawe get (at 95%c.l.):
Can we constrain H(z) directly ?Investigated by Sandage 1961, Loeb proposed the use of
Lyman-alpha in 1998 (see Corasaniti, Huterer,AM, Phys. Rev. D 75, 062001 (2007) )
(assuming CODEX-likeExperiment see Pasquini, Molaro et al. 2006)
s
s
z
zEtH
c
v
1100 2/12)1(33 )1()1()1( zzzzE K
wXM
ELT: Extreme Large Telescope42m telescope (in 10 years time)+ CODEX Spectrograph (see Pasquini et al., 2005)
Can we constrain H(z) directly ?
SL test is definitly for “patient”Cosmologists !Not competitive with WL and SN-IaFor constant w.It may shed light on non-standardModels as DE/DM Interaction
Bounds on for increasingly rich data sets (assuming 3 Active Neutrino model):
Fogli et al., Phys. Rev. D 75, 053001 (2007)
Axel De La Macorra, Alessandro Melchiorri, Paolo Serra, Rachel Bean Astroparticle Physics 27 (2007) 406-410
Massive Neutrino affect the constraints on w
Steen Hannestad Phys. Rev. Lett. 95 (2005) 221301
Moreover, controversial results from LSND seems to suggest a 4thsterile neutrino (not favoured by oscillation experiments.NO ALLOWED REGIONS EXIST FOR LOW m2. (Pierce & Murayama, hep-ph/0302131; Giunti hep-ph/0302173)
???4N
What about a fourth massive sterile neutrino ?
CMB+2df+Sloan+Ly-
ms<0.23 eV at95% c.l.
Dodelson,Melchiorri,Slosar,Phys.Rev.Lett. 97 (2006) 04301
s 0.0106ms
eV
0.01063m
eV
Butts on the line"The implications were staggering," says Scott Dodelson at Fermilab.
"Cosmologically, we decided there should not be a sterile neutrino, so to some extent, our butts were on the line."
New Scientist, April 2007, (immediately after MiniBOONE press release)
Can the suggestion of N>3 be due to systematics in SLOAN ? Hamann et al.
Suggested a wrong assumption on how non-linearities are treated (Q parameter).
)(1
1 22 kP
Ak
QkbP LinNL
6.4
4.1
Q
AFrom Numerical simulations:Quite Robust
For 2df-GRS but it depends on galaxy typeAnd modelling
But if you vary QThe difference isStill there…
2dfGRS Red galaxies areIn agreementWith SLOAN
…but LRG galaxiesAre in agremeentWith 2df!
The Q formuladoes’nt work…
Sanchez, ColeArxiv:07081517
Age of the Universe
Gyrs23.084.138.91
04
100
rm aa
adaHt
CMB data are able to tightly constrain the age of the Universe (see e.g. Ferreras, AM, Silk, 2002). For WMAP+all and LCDM:
Spergel et al., 2007
Direct and “modelindependent”age aestimateshave much largererror bars !Not so goodfor constrainingDE
Gyrs3.083.13 (if w is included)
Age of the Universe
effrel N
…however the WMAP constrain is model dependent. Key parameter: energy density in relativistic particles.
Gyrs8.13 3.22.30
t
Error barson agea factor 10larger whenExtra Relativisticparticles are Included.
F. De Bernardis, A. Melchiorri, L. Verde, R. Jimenez, 2007
F. De Bernardis, A. Melchiorri, L. Verde, R. Jimenez, 2007
Independent age aestimates are important.Using Simon, Verde, Jimenez aestimates plus WMAPall we get:
1.17.3 effN
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