OutlineUnified Dark Matter models
UDM weak lensing power spectraConclusions
Doctoral School in Science and High TechnologyCourse of Physics and Astrophysics
Weak lensing signal in Unified Dark Matter modelsarXiv:0902.4204 [astro-ph.CO]
Stefano Camera1,2
in collaboration with D. Bertacca, A. Diaferio, N. Bartolo and S. Matarrese
1Department of General Physics “Amedeo Avogadro”, University of Turin, Turin, Italy2National Institute of Nuclear Physics (INFN), Section of Turin, Turin, Italy
School of Astrophysics “Francesco Lucchin”Bertinoro, May 24-29, 2009
Stefano Camera Weak lensing signal in Unified Dark Matter models
OutlineUnified Dark Matter models
UDM weak lensing power spectraConclusions
Outline
1 Unified Dark Matter models
2 UDM weak lensing power spectraCMBBackground galaxies
3 Conclusions
Stefano Camera Weak lensing signal in Unified Dark Matter models
OutlineUnified Dark Matter models
UDM weak lensing power spectraConclusions
Outline
1 Unified Dark Matter models
2 UDM weak lensing power spectraCMBBackground galaxies
3 Conclusions
Stefano Camera Weak lensing signal in Unified Dark Matter models
OutlineUnified Dark Matter models
UDM weak lensing power spectraConclusions
Outline
1 Unified Dark Matter models
2 UDM weak lensing power spectraCMBBackground galaxies
3 Conclusions
Stefano Camera Weak lensing signal in Unified Dark Matter models
OutlineUnified Dark Matter models
UDM weak lensing power spectraConclusions
Unified Dark Matter models
UDM
Only one exotic component,a scalar field ϕ(t,x) that canmimic both DM and DE, i.e.
ρ [a(t)] = ρDM|z∝a−3
+
const.z|ρΛ
k−inflationa
expansion history, ISWeffect, halos of “UDM”b
UDM prediction of weak gravitational lensing by LSS
aArmendariz-Picon et al. (1999), Kamenshchik et al. (2001), Bilic et al. (2002), Scherrer (2004)
bBertacca & Bartolo (2007), Bertacca et al. (2008)
Stefano Camera Weak lensing signal in Unified Dark Matter models
OutlineUnified Dark Matter models
UDM weak lensing power spectraConclusions
Unified Dark Matter models
UDM
Only one exotic component,a scalar field ϕ(t,x) that canmimic both DM and DE, i.e.
ρ [a(t)] = ρDM|z∝a−3
+
const.z|ρΛ
k−inflationa
expansion history, ISWeffect, halos of “UDM”b
UDM prediction of weak gravitational lensing by LSS
aArmendariz-Picon et al. (1999), Kamenshchik et al. (2001), Bilic et al. (2002), Scherrer (2004)
bBertacca & Bartolo (2007), Bertacca et al. (2008)
Stefano Camera Weak lensing signal in Unified Dark Matter models
OutlineUnified Dark Matter models
UDM weak lensing power spectraConclusions
Unified Dark Matter models
UDM
Only one exotic component,a scalar field ϕ(t,x) that canmimic both DM and DE, i.e.
ρ [a(t)] = ρDM|z∝a−3
+
const.z|ρΛ
k−inflationa
expansion history, ISWeffect, halos of “UDM”b
UDM prediction of weak gravitational lensing by LSS
aArmendariz-Picon et al. (1999), Kamenshchik et al. (2001), Bilic et al. (2002), Scherrer (2004)
bBertacca & Bartolo (2007), Bertacca et al. (2008)
Stefano Camera Weak lensing signal in Unified Dark Matter models
OutlineUnified Dark Matter models
UDM weak lensing power spectraConclusions
ds2 ≡ gµνdxµdxν = a2(τ)ˆ−(1 + 2Φ)dτ2 + (1− 2Φ)d`2
˜equation for scalar perturbation in linear theory
v′′ − cs2∇2v − θ′′
θv = 0
v ∝ Φ
cs2 =
p,Xp,X+2Xp,XX
is the speed of sound of the scalar field
c∞ ≡ cs(a→∞)
Stefano Camera Weak lensing signal in Unified Dark Matter models
OutlineUnified Dark Matter models
UDM weak lensing power spectraConclusions
ds2 ≡ gµνdxµdxν = a2(τ)ˆ−(1 + 2Φ)dτ2 + (1− 2Φ)d`2
˜equation for scalar perturbation in linear theory
v′′ − cs2∇2v − θ′′
θv = 0
v ∝ Φ
cs2 = ΩΛc∞
2
ΩΛ+(1−c∞2)Ωma−3 is the speed of sound of the scalar field
c∞ ≡ cs(a→∞)
Stefano Camera Weak lensing signal in Unified Dark Matter models
OutlineUnified Dark Matter models
UDM weak lensing power spectraConclusions
(SC
et
al.
2009)
Gravitational potentials forΛCDM and UDM at differentscales and for different valuesof c∞ = 10−3, 10−2, 10−1.
Stefano Camera Weak lensing signal in Unified Dark Matter models
OutlineUnified Dark Matter models
UDM weak lensing power spectraConclusions
CMBBackground galaxies
Results
Convergence power spectrum
Cκκ(l) =l4
4
Z ∞0
dχW 2 (χ, n(χ))
χ6PΦ
„l
χ, χ
«
Assumptions
1 h = 0.72, Ωm = 0.26 and ΩΛ = 0.74
2 BBKS transfer function (Bardeen et al. 1986)
3 Peacock & Dodds (Peacock & Dodds 1996) linear to non-linear mapping
Stefano Camera Weak lensing signal in Unified Dark Matter models
OutlineUnified Dark Matter models
UDM weak lensing power spectraConclusions
CMBBackground galaxies
nCMB [χ(z)] = δD(χ(z)− χ(zrec))
(SC
et
al.
2009)
zp ≡ zrec = 1000
Weak lensing power spectral(l + 1)Cκκ(l)/(2π) of CMBlight for ΛCDM and UDM fordifferent values ofc∞
2 = 10−6, 10−5, 10−4.
Stefano Camera Weak lensing signal in Unified Dark Matter models
OutlineUnified Dark Matter models
UDM weak lensing power spectraConclusions
CMBBackground galaxies
The redshift distribution of sources is (Kaiser 1992)
ng [χ(z)] = βzα
z0α+1e−
„zz0
«βΓ
“α+1β
” dzdχ
(SC
et
al.
2009)
Redshift distribution ofgalaxies ng(z).
(SC
et
al.
2009)
Weight functions Wg(z) fordifferent ng(z) and zp.
Stefano Camera Weak lensing signal in Unified Dark Matter models
OutlineUnified Dark Matter models
UDM weak lensing power spectraConclusions
CMBBackground galaxies
(SC et al. 2009)
α = 1β = 4zp = 1
(SC et al. 2009)
α = 1β = 4zp = 2
(SC et al. 2009)
α = 1β = 4zp = 3
Weak lensing power spectra l(l + 1)Cκκ(l)/(2π) of background galaxy light forΛCDM and UDM for different values of c∞2 = 10−6, 10−5, 10−4.
Stefano Camera Weak lensing signal in Unified Dark Matter models
OutlineUnified Dark Matter models
UDM weak lensing power spectraConclusions
CMBBackground galaxies
(SC et al. 2009)
α = 1β = 4zp = 1
(SC et al. 2009)
α = −β = −zp = 1
(SC et al. 2009)
α = 2β = 1zp = 1
Weak lensing power spectra l(l + 1)Cκκ(l)/(2π) of background galaxy light forΛCDM and UDM for different values of c∞2 = 10−6, 10−5, 10−4.
Stefano Camera Weak lensing signal in Unified Dark Matter models
OutlineUnified Dark Matter models
UDM weak lensing power spectraConclusions
Conclusions
When the Jeans’ length of the Newtonian potential increases, Φk(a)starts to decay earlier in time (for a fixed scale), or yet at greater scales(for a fixed epoch).
This reflects on weak lensing by suppressing the convergence power spec-tra at high multipoles.
Moreover, we find that for low redshift sources the dependence of UDMweak lensing signal on the sound speed c∞ is much stronger.
Thanks!
Stefano Camera Weak lensing signal in Unified Dark Matter models
OutlineUnified Dark Matter models
UDM weak lensing power spectraConclusions
Conclusions
When the Jeans’ length of the Newtonian potential increases, Φk(a)starts to decay earlier in time (for a fixed scale), or yet at greater scales(for a fixed epoch).
This reflects on weak lensing by suppressing the convergence power spec-tra at high multipoles.
Moreover, we find that for low redshift sources the dependence of UDMweak lensing signal on the sound speed c∞ is much stronger.
Thanks!
Stefano Camera Weak lensing signal in Unified Dark Matter models
OutlineUnified Dark Matter models
UDM weak lensing power spectraConclusions
Conclusions
When the Jeans’ length of the Newtonian potential increases, Φk(a)starts to decay earlier in time (for a fixed scale), or yet at greater scales(for a fixed epoch).
This reflects on weak lensing by suppressing the convergence power spec-tra at high multipoles.
Moreover, we find that for low redshift sources the dependence of UDMweak lensing signal on the sound speed c∞ is much stronger.
Thanks!
Stefano Camera Weak lensing signal in Unified Dark Matter models
OutlineUnified Dark Matter models
UDM weak lensing power spectraConclusions
Conclusions
When the Jeans’ length of the Newtonian potential increases, Φk(a)starts to decay earlier in time (for a fixed scale), or yet at greater scales(for a fixed epoch).
This reflects on weak lensing by suppressing the convergence power spec-tra at high multipoles.
Moreover, we find that for low redshift sources the dependence of UDMweak lensing signal on the sound speed c∞ is much stronger.
Thanks!
Stefano Camera Weak lensing signal in Unified Dark Matter models
OutlineUnified Dark Matter models
UDM weak lensing power spectraConclusions
Results
Convergence power spectrum
Cκκ(l) =l4
4
Z ∞0
dχW 2 (χ, n(χ))
χ6PΦ
„l
χ, χ
«
W (χ, n(χ)) = −2χR∞χ
dχ′ χ′−χχ′ n(χ′) weight function of weak lensing
n [χ(z)] redshift distribution of sources
Assumptions
1 h = 0.72, Ωm = 0.26 and ΩΛ = 0.74
2 BBKS transfer function (Bardeen et al. 1986)
3 Peacock & Dodds (Peacock & Dodds 1996) linear to non-linear mapping
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Stefano Camera Weak lensing signal in Unified Dark Matter models
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