investigating dark energy and gravitation at...

Investigating Dark Energy and Gravitation at

cosmological scales with EUCLID

Alain Blanchard

LaThuile, March 26th, 2015

Alain Blanchard Investigating dark gravity with EUCLID

Λ CDM modelremarkable success

Successes of Λ CDM model




SnIa




SnIa

BAO




SnIa

BAO

CMB


Precision cosmology area


Tightening down Dark Energy properties

Tools



Tools

Laboratory experiments.



Tools

Laboratory experiments. limited



Tools


Solar system test.



Tools


Solar system test. ...



Tools



Galactic level.



Tools



Galactic level. NL ...



Tools




Cosmological scales:



Tools




Cosmological scales:Let’s go for it!


Basics of EUCLID


Basics of EUCLID: bureaucracy...


Basics of EUCLID

Goals


Basics of EUCLID

Goals

Provide astrophysical data (z ≤∼ 2) for investigating Dark Energy:


Basics of EUCLID

Goals


Weak lensing.


Basics of EUCLID

Goals


Weak lensing.

Galaxy clustering & Redshift distorsion.


Basics of EUCLID

Goals


Weak lensing.


Secondary probes

Clusters.


Basics of EUCLID

Goals


Weak lensing.


Secondary probes

Clusters.

CBM/X cross correlations.


Basics of EUCLID

Goals


Weak lensing.


Secondary probes

Clusters.


Strong lensing.


Basics of EUCLID

Goals


Weak lensing.


Secondary probes

Clusters.


Strong lensing.

Legacy Science

Primeval Universe.


Basics of EUCLID

Goals


Weak lensing.


Secondary probes

Clusters.


Strong lensing.

Legacy Science

Primeval Universe.

Galaxy/AGN evolution.


Basics of EUCLID

Goals


Weak lensing.


Secondary probes

Clusters.


Strong lensing.

Legacy Science

Primeval Universe.


Local Universe


Basics of EUCLID

Goals


Weak lensing.


Secondary probes

Clusters.


Strong lensing.

Legacy Science

Primeval Universe.


Local Universe

Milky Way,


Basics of EUCLID

Goals


Weak lensing.


Secondary probes

Clusters.


Strong lensing.

Legacy Science

Primeval Universe.


Local Universe

Milky Way, Exo-Planets,


Basics of EUCLID

Goals


Weak lensing.


Secondary probes

Clusters.


Strong lensing.

Legacy Science

Primeval Universe.


Local Universe

Milky Way, Exo-Planets, SNe & Transients


Basics of EUCLID: Science Working Groups (SWG)

Weak lensing (H.Hoekstra, T.Kitching, K.Benabed).




Galaxy clustering (L.Guzzo, W.Percival, Y.Wang).





Clusters (L.Moscardini, J.Weller, J.Bartlett).






CBM/X cross correlations (N.Ahanim, C.Baccigaluppi.







Strong lensing (M.Meneghetti, J.-P. Kneib, R. Gavazzi).








Theory (L.Amendola, M.Kunz, M.Viel).









Cosmological simulations (P.Fosalba, R.Teyssier).










Primeval Universe (J.-G. Cuby, J Fynbo).











Galaxy/AGN evolution (J.Brichmann, D.Elbaz, A.Cimati).












Local Universe (B.Poggianti, C. Conselice)













Milky Way (E.Tolstoy, A. Ferguson)














Exo-Planets (J.-P. Beaulieu, M. Zapatero-Osorio, E.Kerins)














Exo-Planets (J.-P. Beaulieu, M. Zapatero-Osorio, E.Kerins)

SNe & Transients (I.Hook, C.Tao, E.Cappellaro).


Astrophysical point of view

Testing cosmology at the background level




D(z) =1.

H0Ω1/2K

SK

(

H0Ω1/2K

∫ z

0

dz

H(z)

)




D(z) =1.

H0Ω1/2K

SK

(

H0Ω1/2K

∫ z

0

dz

H(z)

)

SNIa, CMB, tranversal BAO




D(z) =1.

H0Ω1/2K

SK

(

H0Ω1/2K

∫ z

0

dz

H(z)

)


H(z)




D(z) =1.

H0Ω1/2K

SK

(

H0Ω1/2K

∫ z

0

dz

H(z)

)


H(z)longitudinal BAO, z , t(z)




D(z) =1.

H0Ω1/2K

SK

(

H0Ω1/2K

∫ z

0

dz

H(z)

)



Testing cosmology at the (linear) perturbation level




D(z) =1.

H0Ω1/2K

SK

(

H0Ω1/2K

∫ z

0

dz

H(z)

)




G (z)δ(z) = G (z)δ0 growth factor




D(z) =1.

H0Ω1/2K

SK

(

H0Ω1/2K

∫ z

0

dz

H(z)

)




G (z)δ(z) = G (z)δ0 growth factordln(G)dln(a) ∼ Ωγ

m(a)




D(z) =1.

H0Ω1/2K

SK

(

H0Ω1/2K

∫ z

0

dz

H(z)

)





m(a)

γ is the growth index (γ ∼ 0.55 in ΛCDM)




D(z) =1.

H0Ω1/2K

SK

(

H0Ω1/2K

∫ z

0

dz

H(z)

)





m(a)

γ is the growth index (γ ∼ 0.55 in ΛCDM)Weak Lensing,




D(z) =1.

H0Ω1/2K

SK

(

H0Ω1/2K

∫ z

0

dz

H(z)

)





m(a)

γ is the growth index (γ ∼ 0.55 in ΛCDM)Weak Lensing, RSD, Clusters


Fiducial model of dark energy

Quintessence : scalar field with minimal couplings and canonicalkinetic energy.




S =

∫

d4x√

g

[

R

16πG− 1

2gµνgµν∂µφ∂νφ− V (φ) + Lm

]




S =

∫

d4x√

g

[

R

16πG− 1


]

Equation of state parameter:

w =P

ρ=

1/2φ2 − V (φ)

1/2φ2 + V (φ)




S =

∫

d4x√

g

[

R

16πG− 1


]


w =P

ρ=

1/2φ2 − V (φ)

1/2φ2 + V (φ)

CPL parametrization: w(z) = wp + (1 − a)wa




S =

∫

d4x√

g

[

R

16πG− 1


]


w =P

ρ=

1/2φ2 − V (φ)

1/2φ2 + V (φ)


growth index:

γ = 0.55 + 0.05[1 + w(z = 1)](fitted)




S =

∫

d4x√

g

[

R

16πG− 1


]


w =P

ρ=

1/2φ2 − V (φ)

1/2φ2 + V (φ)


growth index:

γ = 0.55 + 0.05[1 + w(z = 1)](fitted)

Quintessence has γ ∼ 0.55 “ standard dark energy model”


Where we go:


Where we go:

R ∝ −(ρ+ 3P)R


The Curvature–Newtonian Potential diagram.

Psaltis 2008.


Further reading

Euclid Definition Study Report mission

R. Laureijs et al., Euclid red book : arXiv:1110.3193


Further reading

Euclid Definition Study Report mission

R. Laureijs et al., Euclid red book : arXiv:1110.3193

Cosmology and fundamental physics with the Euclid satellite.

L. Amendola et al., Living Reviews in Relativity 16, 6 (2013).


Perturbation dynamics

Scalar Perturbations (Newtonnian gauge)

ds2 = a2(t)[−(1 + 2Ψ)dt2 + (1 − 2Φ)dx idxi ]




ds2 = a2(t)[−(1 + 2Ψ)dt2 + (1 − 2Φ)dx idxi ]

Sub-horizon dynamics

−k2Φ = 4πGQ(a, k)a2ρm∆m




ds2 = a2(t)[−(1 + 2Ψ)dt2 + (1 − 2Φ)dx idxi ]



Ψ− Φ relation:Φ = η(a, k)Ψ




ds2 = a2(t)[−(1 + 2Ψ)dt2 + (1 − 2Φ)dx idxi ]



Ψ− Φ relation:Φ = η(a, k)Ψ

For a given DE/MG theory, Q, η can be computed and equationsfor perturbations can be solved.


From redshift survey



Pg (k)



Pg (k) then to PDM(k)



Access to ΦAlain Blanchard Investigating dark gravity with EUCLID

From weak lensing


From weak lensing

Dark matter tomography


From weak lensing


From weak lensing

Access to ψ +Φ


Models of dark energy and modified gravity



Beyond standard DE model



Beyond standard DE model: differences between DE and MG is lessclear: a modification to Einstein’s equation can be interpreted asstandard Einstein gravity with a modified “matter” source (⊃scalars, vectors and tensors).




Terminology :




Terminology :

Standard dark energy: standard gravity, canonical kineticenergy, minimal couplings, sound speed = c.




Terminology :


Clustering dark energy: k-essence




Terminology :


Clustering dark energy: k-essence

Explicit modified gravity models: F (R), Scalar-tensor theories(F (φ)R), Gauss-Bonnet...



Coupled dark energy models




S =

∫

d4x√

g

[

R

16πG− 1

2gµνgµν∂µφ∂νφ− V (φ) + m(φ)ψψ + Lm(ψ)

]




S =

∫

d4x√

g

[

R

16πG− 1


]

coupling can be with baryons, neutrinos, dark matter...




S =

∫

d4x√

g

[

R

16πG− 1


]

coupling can be with baryons, neutrinos, dark matter...writing m(φ) = m exp(−β(φ)φ) then :

G = G (1 + 2β2(φ)



Classifying theories:




Identify a limited number of parameters that can be determinedfrom observations and which are meaningful in the “space oftheories”





Parametrized Post Friedmann (PPF) formalism






Effective Field Theories (EFT)






Effective Field Theories (EFT)

...


One more comment...Friedmann-Lemaître equation:

(

R

R

)2

=8πGρm

3+

8πGρDE

3− kc2

R2



(

R

R

)2

=8πGρm

3+

8πGρDE

3− kc2

R2

The split between ρm and ρDE is not (gravitationally) testable(Kunz 2009)



(

R

R

)2

=8πGρm

3+

8πGρDE

3− kc2

R2

The split between ρm and ρDE is not (gravitationally) testable(Kunz 2009)Just use it as a parametrization.


Precision cosmology area: curvature


A Cosmological Test of GR at the background levelDynamic

One can derive dynamical equation for a(t) from Newtonianconsideration




Newtonian dynamic:

a2 + K =8πG

3

∑

ρa2.

(see Mukhanov’s book)




Newtonian dynamic:

a2 + K =8πG

3

∑

ρa2.

(see Mukhanov’s book)

General Relativity

K = c2

soΩk = 1.−

∑

Ωcontents


Testing GR at cosmological scales



so testing:

Ωk = 1.−∑

Ωcontents

is testing GR on large scale at the background level



so testing:

Ωk = 1.−∑

Ωcontents


So we can define :

Ωkgeo = − k

(a0H0)2

andΩkdyn = 1.−

∑

Ωcontents



so testing:

Ωk = 1.−∑

Ωcontents


So we can define :

Ωkgeo = − k

(a0H0)2

andΩkdyn = 1.−

∑

Ωcontents

and use SNIa, CMB, BAO to constrain these quantities.Yves Zolnierowski & AB, arXiv:1503.00111


With w = −1

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04

Ωkgeo

Ωk d

yn


With w free

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04Ωkgeo

Ωk d

yn


With w free

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

-2.5 -2 -1.5 -1 -0.5 0 0.5

Ωk d

yn

w


Conclusion

Euclid will allow to test gravity at

cosmological scale in many ways


Conclusion



This can/should be complemented by

other data from cosmological relevance

(CMB, H0, z , t(z), ...)


Conclusion





(CMB, H0, z , t(z), ...)

First results at Moriond 2021 (TBC)


Conclusion





(CMB, H0, z , t(z), ...)

First results at Moriond 2021 (TBC)

Thank You


investigating dark energy and gravitation at...

Documents