neutrinos in large-scale structurecosmo2014.uchicago.edu/depot/talk-loverde-marilena.pdfc...

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


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



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


Neutrinos in Cosmology

Neutrinos in cosmology

T𝜸 = T𝝼 ∝ 1/a

neutrinos in equilibrium

with photons e+, e-

T𝝼 ∝ 1/a neutrinos decoupledT𝝼 ∝ 1/a


T𝜸 = T𝝼 ∝ 1/a


with photons e+, e-


T𝜸 ≈ T𝝼114

1/3

n1𝝼 ~ T𝞶3

relativistic, in thermal equilibrium at early times


T𝜸 = T𝝼 ∝ 1/a


with photons e+, e-


T𝜸 ≈ T𝝼114

1/3

n1𝝼 ~ T𝞶3


energy density dominated by mass at late times

𝞀𝝼 ~ ∑ m𝝼i n1𝝼 i


T𝜸 = T𝝼 ∝ 1/a


with photons e+, e-


T𝜸 ≈ T𝝼114

1/3

n1𝝼 ~ T𝞶3


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


(clump easily) (don’t clump easily)



(clump easily) (don’t clump easily)

baryons and cold dark matter

neutrinos (or other exotic light dark

matter)


time

small-scale density perturbations don’t retain

neutrinos


𝝳𝞀c𝞀c

cold dark matter and baryons density

perturbation growing

𝝳𝞀𝞶𝞀𝞶

neutrino density perturbation

decaying

time


neutrinos large-scale density perturbations do retain neutrinos


𝝳𝞀c𝞀c

cold dark matter,

baryons and neutrinos growing together

𝝳𝞀𝞶𝞀𝞶

time




Growth of matter perturbations is scale-

dependent

time



Relevant scale: !

Typical distance a neutrino can travel in a Hubble time

λfs ~ u𝞶/H



dependent

time



“free-streaming scale”


Relevant scale: !

Typical distance a neutrino can travel in a Hubble time

λfs ~ u𝞶/H


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


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_


fluctuations is independent of their wavelength

incr

easin

g time

(k, zfinal) ∝ D(zfinal) (k, zinitial)𝝳𝞀𝞀_ 𝝳𝞀

𝞀_


halos can’t tell the wavelength of the background matter density perturbation



incr

easin

g time



the effect of on the halo field (the linear bias) is independent of k𝝳𝞀𝞀_



incr

easin

g time



the effect of on the halo field (the linear bias) is independent of k𝝳𝞀𝞀_

massive neutrinos break this halo bias can depend on k


incr

easin

g time


neutrinoscold dark matter

WANT: estimate of k-dependence of the halo bias caused by massive

neutrinos

incr

easin

g time



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;)



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

neutrinos in large-scale structurecosmo2014.uchicago.edu/depot/talk-loverde-marilena.pdfc...

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