Neutrinos in Large-scale structureMarilena LoVerde
University of Chicago ( Fall 2015 —> Yang Institute for Theoretical Physics, Stony Brook University)
Neutrinos in Large-scale structureMarilena LoVerde
University of Chicago ( Fall 2015 —> Yang Institute for Theoretical Physics, Stony Brook University)
ML and Zaldarriaga 1310.6459ML 1405.4855ML 1404:4858
ML in prep.
Outline
Neutrinos in Cosmology
Scale-dependent structure growth from massive neutrinos
Scale-dependent halo bias from massive neutrinos
Observational Consequences
Neutrinos
Neutrinos!𝝼electron
𝝼muon
𝝼tau
𝝼1
𝝼3
𝝼2
flavor eigenstates mass eigenstates
Pontecorvo 1957, 1958, 1967; Maki, Nakagawa, Sakata 1962
Neutrinos!𝝼electron
𝝼muon
𝝼tau
𝝼1
𝝼3
𝝼2
flavor eigenstates mass eigenstates
m22 - m12 = (7.5 ± 0.2) 10-5 eV2
|m32 - m22| = (2.32 ) 10-3 eV2+ 0.12- 0.08
(solar neutrino oscillations)
(atmospheric neutrino oscillations)
oscillation data gives mass splittings
Pontecorvo 1957, 1958, 1967; Maki, Nakagawa, Sakata 1962
Neutrinos!𝝼electron
𝝼muon
𝝼tau
but the absolute masses are unknown!
flavor eigenstates
mas
s
?𝜈1 ≈ 0eV𝜈2 ≈ 0.009eV𝜈3 ≈ 0.049eV
𝜈3 ≈ 0eV
𝜈2 ≈ 0.049eV𝜈1 ≈ 0.047eV
𝜈1 ≈ 𝜈2 ≈ 𝜈3
``Normal” ``Inverted” ``Degenerate”
𝝼1
𝝼3
𝝼2
mass eigenstates
Pontecorvo 1957, 1958, 1967; Maki, Nakagawa, Sakata 1962
Neutrinos in Cosmology
Neutrinos in cosmology
T𝜸 = T𝝼 ∝ 1/a
neutrinos in equilibrium
with photons e+, e-
T𝝼 ∝ 1/a neutrinos decoupledT𝝼 ∝ 1/a
Neutrinos in cosmology
T𝜸 = T𝝼 ∝ 1/a
neutrinos in equilibrium
with photons e+, e-
T𝝼 ∝ 1/a neutrinos decoupledT𝝼 ∝ 1/a
T𝜸 ≈ T𝝼114
1/3
n1𝝼 ~ T𝞶3
relativistic, in thermal equilibrium at early times
Neutrinos in cosmology
T𝜸 = T𝝼 ∝ 1/a
neutrinos in equilibrium
with photons e+, e-
T𝝼 ∝ 1/a neutrinos decoupledT𝝼 ∝ 1/a
T𝜸 ≈ T𝝼114
1/3
n1𝝼 ~ T𝞶3
relativistic, in thermal equilibrium at early times
energy density dominated by mass at late times
𝞀𝝼 ~ ∑ m𝝼i n1𝝼 i
Neutrinos in cosmology
T𝜸 = T𝝼 ∝ 1/a
neutrinos in equilibrium
with photons e+, e-
T𝝼 ∝ 1/a neutrinos decoupledT𝝼 ∝ 1/a
T𝜸 ≈ T𝝼114
1/3
n1𝝼 ~ T𝞶3
relativistic, in thermal equilibrium at early times
energy density dominated by mass at late times
𝞀𝝼 ~ ∑ m𝝼i n1𝝼 i
n1𝝼 is known, so a measurement of 𝞀𝝼 gives ∑ m𝝼
Neutrinos in Large-scale structure
(Kravtsov)time
The gravitational evolution of large-scale structure is different for fast and slow moving particles
Massive neutrinos and linear structure growth
The gravitational evolution of large-scale structure is different for fast and slow moving particles
(clump easily) (don’t clump easily)
Massive neutrinos and linear structure growth
The gravitational evolution of large-scale structure is different for fast and slow moving particles
(clump easily) (don’t clump easily)
baryons and cold dark matter
neutrinos (or other exotic light dark
matter)
Massive neutrinos and linear structure growth
time
small-scale density perturbations don’t retain
neutrinos
Massive neutrinos and linear structure growth
𝝳𝞀c𝞀c
cold dark matter and baryons density
perturbation growing
𝝳𝞀𝞶𝞀𝞶
neutrino density perturbation
decaying
time
small-scale density perturbations don’t retain
neutrinos large-scale density perturbations do retain neutrinos
Massive neutrinos and linear structure growth
𝝳𝞀c𝞀c
cold dark matter,
baryons and neutrinos growing together
𝝳𝞀𝞶𝞀𝞶
time
small-scale density perturbations don’t retain
neutrinos large-scale density perturbations do retain neutrinos
Massive neutrinos and linear structure growth
Growth of matter perturbations is scale-
dependent
time
small-scale density perturbations don’t retain
neutrinos large-scale density perturbations do retain neutrinos
Relevant scale: !
Typical distance a neutrino can travel in a Hubble time
λfs ~ u𝞶/H
Massive neutrinos and linear structure growth
Growth of matter perturbations is scale-
dependent
time
small-scale density perturbations don’t retain
neutrinos large-scale density perturbations do retain neutrinos
“free-streaming scale”
Massive neutrinos and linear structure growth
Relevant scale: !
Typical distance a neutrino can travel in a Hubble time
λfs ~ u𝞶/H
Growth of matter perturbations is scale-
dependent
larger scales
large compared to λfree streaming Δ
P mm(k
)/P m
m(k
)
wave number k (1/Mpc)
change in typical amplitude of 𝝳m(k) from m𝞶= 0
Ade et al 2013Planck Data
Prob
abilit
y
∑i m𝞶i (eV)0.0 0.4 0.8 1.2 1.6 2.0
0.2
0.4
0.6
0.8
1.0
Scale-dependent growth
cosmological constraints!
Hu, Eisenstein, Tegmark 1998Bond, Efstathiou, Silk 1980
The scale-dependent growth of density
perturbations causes halo bias to be scale
dependent
Scale-dependent bias:halos are biased
tracers of the matter density field
halos are biased tracers of the matter
density field
the number density of halos is modulated by long-wavelength fluctuations in the matter density field
Scale-dependent bias:
halos are biased tracers of the matter
density field
the number density of halos is modulated by long-wavelength fluctuations in the matter density field
≣ b𝝳n n
𝝳𝞀 𝞀
long-wavelength
b is the halo bias
Scale-dependent bias:
In a universe with CDM only, the linear evolution of matter fluctuations is independent of their wavelength
incr
easin
g time
(k, zfinal) ∝ D(zfinal) (k, zinitial)𝝳𝞀𝞀_ 𝝳𝞀
𝞀_
Scale-dependent bias:
fluctuations is independent of their wavelength
incr
easin
g time
(k, zfinal) ∝ D(zfinal) (k, zinitial)𝝳𝞀𝞀_ 𝝳𝞀
𝞀_
In a universe with CDM only, the linear evolution of matter fluctuations is independent of their wavelength
halos can’t tell the wavelength of the background matter density perturbation
Scale-dependent bias:
fluctuations is independent of their wavelength
incr
easin
g time
In a universe with CDM only, the linear evolution of matter fluctuations is independent of their wavelength
halos can’t tell the wavelength of the background matter density perturbation
the effect of on the halo field (the linear bias) is independent of k𝝳𝞀𝞀_
Scale-dependent bias:
fluctuations is independent of their wavelength
incr
easin
g time
In a universe with CDM only, the linear evolution of matter fluctuations is independent of their wavelength
halos can’t tell the wavelength of the background matter density perturbation
the effect of on the halo field (the linear bias) is independent of k𝝳𝞀𝞀_
massive neutrinos break this halo bias can depend on k
Scale-dependent bias:
incr
easin
g time
Scale-dependent bias:
neutrinoscold dark matter
WANT: estimate of k-dependence of the halo bias caused by massive
neutrinos
incr
easin
g time
Scale-dependent bias:
neutrinoscold dark matter
WANT: estimate of k-dependence of the halo bias caused by massive
neutrinos
incr
easin
g time
( see also Hui & Parfrey 2008; Parfrey, Hui, Sheth 2011;)
Scale-dependent bias:
neutrinoscold dark matter
Prescription for calculating the halo
bias in a universe with massive neutrinos
Prescription for calculating the halo bias
Gunn & Gott 1972Press & Schechter 1974
initial proto-halo distributioninitial density field
late time halo distribution
≣ b𝝳n n
𝝳𝞀 𝞀
long-wavelength
(ML 2014)
Prescription for calculating the halo bias
Gunn & Gott 1972Press & Schechter 1974
initial proto-halo distributioninitial density field
≣ b𝝳n n
𝝳𝞀 𝞀
long-wavelength
(ML 2014)
want this!
late time halo distribution
Numerical estimates for scale-dependent halo bias
Numerical results for halo bias
𝝳n(k)/n = b(k) 𝝳matter(k) scale-dependent change to final bias
wavenumber k (Mpc-1)frac
tion
al c
hang
e in E
uler
ian
halo b
ias
(ML 2014)
(Use Bhattacharya et al 2011 for
n(M| 𝝳crit)
b(k)
= √
P hh(k
)/P m
m(k
)
ampl
itude
of
feat
ure
in
the
halo b
ias
Numerical results for halo bias
𝝳n(k)/n = b(k) 𝝳matter(k) scale-dependent change to final bias
(ML 2014)
(Use Bhattacharya et al 2011 for
n(M| 𝝳crit)
Observational consequences of scale-
dependent bias?
Observational consequences of scale dependent bias?
suppression in galaxy power spectrum less than in matter power spectrum
k (wave number )
(incorrectly) assuming constant bias
(ML 2014)
But the scale-dependent halo bias is itself an observable!
frac
tion
al c
hang
e in E
uler
ian
halo b
ias
k (wave number)
ratio
of b
ias
fact
ors
for
two
gala
xy
popu
lation
s b 2
(k)/
b 1(k
)
σb1/b2 ~ √n1Pg2g2 1___
(ML in prep.)
The scale-dependent halo bias is an observable!
σb1/b2 ~ √Nℓn1Cg2g2
1____
(ML in prep.)
The scale-dependent halo bias is an observable!
ratio
of b
ias
fact
ors
for
two
gala
xy
popu
lation
s
ℓ (multipole moment)
Accuracy of these predictions?
Simulations with massive neutrinos?
Viel, Haehnelt, Springel 2010; Marulli, Carbone, Viel, Moscardini, Cimatti 2011; Agarwal & Feldman 2011; Brandbyge, Hannestad, Haugboelle, Wong 2012; Upadhye, Biswas, Pope, Heitmann, Habib 2013: Villaescusa-Navarro, Bird, Pena-Garay, Viel 2013;
N-body simulations are the community standard for cold dark matter structure.
(i) Tricky. very few exist, very new (ii) Want a model that provides insight into the physical processes responsible for new effects (iii) Don’t want to rerun for every possible neutrino mass hierarchy scenario (iv) It will be great to make comparisons in the future!
(ML 2014)
0.01 0.1
1.6
1.8
2.0
2.2
k @hMpc-1DbHkL
M > 2â1013 Müz = 0
Phh ê PmmPhh ê Pcc
0.01 0.1
1.6
1.8
2.0
2.2
k @hMpc-1D
bHkL
M > 2â1013 Müz = 0
Pmh ê PmmPch ê Pcc
0.01 0.1
2.2
2.4
2.6
2.8
3.0
3.2
3.4
k @hMpc-1D
bHkL
M > 2â1013 Müz = 0.5
0.01 0.1
2.2
2.4
2.6
2.8
3.0
3.2
3.4
k @hMpc-1DbHkL
M > 2â1013 Müz = 0.5
Figure 6. Halo bias as a function of scale determined from the simulation Set A for halos with M >2⇥1013 h�1 M�. Left panels show the measurements of linear bias b(hh)c (continuous curves) and b(hh)m (dashed
curves) from the halo power spectrum Phh(k). Right panels show b(hc)c (continuous curves) and b(hm)m (dashed
curves) respectively from the Phc and Phm cross-power spectra. Top left panels correspond to z = 0, bottompanels to z = 0.5. The continuous and dotted horizontal lines show the constant bias values determined frommeasurements of bc and bm, respectively, at k = 0.07hMpc�1, shown in turn as a vertical gray line in allpanels. Error bars show the uncertainty on mean over the eight realizations.
curves) defined in eqs. (5.3) and (5.5) in terms of cross-power spectra. Top row shows the results atz = 0, bottom row at z = 0.5. To guide the eye, the continuous and dashed horizontal lines show thevalues of b
c
(k) and b
m
(k) at k = 0.07hMpc�1 (shown as a vertical line): below this value of k, thebias is observed to be constant for most measurements. This value also defines the bias values we usefor the study of bias as a function of ⌫ later in figure 9.
The fixed mass threshold clearly results in di↵erent bias values for the three models. This is aconsequence of the fact that the same mass threshold corresponds to quite di↵erent number counts
– 12 –
wavenumber k (h/Mpc)
halo b
ias
b(k)
massless 𝝼
three 0.1eV 𝝼
three 0.2eV 𝝼
simulations from Castorina et al 2013
Scale-dependent bias from massive neutrinos
comparison with sims looks reasonable!
wavenumber k (h/Mpc)
halo b
ias
b(k)
my calculations
three 0.2eV 𝝼
three 0.1eV 𝝼
massless 𝝼
ConclusionsCosmology provides interesting information about neutrino physics!
Scale-dependent halo bias is a new signal of massive neutrinos in large-scale structure
Scale-dependent halo bias is a new systematic for massive neutrinos in large-scale structure