Constraints on the Dark Side

of the UniverseAlessandro Melchiorri

Fogli et al., Phys. Rev. D 75, 053001 (2007)

04.073.0

A model without cosmological constant isnow ruled out at more than 18 sigma!

Friedmann Cosmological Model works only if:

Why so small ? Why now ?

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.

WMAP Cosmological Parameters, Spergel et al., 2007

1.01w

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

Giannantonio et al, ‘06

Current Observational status

Corasaniti, Giannantonio, AM, Phys.Rev. D71 (2005) 123521

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)

M

DE

0Let’s assume:

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.):

A direct proof for dark energy ?

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)

Fogli et al., Phys. Rev. D 75, 053001 (2007)

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

Miniboone results, April 2007 “excludes” LSND

April 2007MINIBOONE RULES OUT LSND:

WE “KNEW” IT !!!

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)

Indication for N>3 from Cosmology ?

Mangano, Melchiorri, Mena, Miele, Slosar JCAP03(2007)006

Systematics in the data ?

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

If you fix Q=5 for 2df and SLOAN you get different results:

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

Mangano, Melchiorri, Mena, Miele, Slosar JCAP03(2007)006

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

Vernizzi, Melchiorri, Phys.Rev. D63 (2001) 063501

Looking at the distant past…