Nonlinear Evolution in Cold Dark Matter + Neutrino Cosmologies
Marilena LoVerde
C. N. Yang Institute for Theoretical Physics Stony Brook University
ML 1405.4855, 1602.08108 Hu, Chiang, Li, ML 1605.01412
Chiang, Li, Hu, ML 1609.01701 + in prep.
Nonlinear Evolution in Cold Dark Matter + Neutrino Cosmologies
Marilena LoVerde
C. N. Yang Institute for Theoretical Physics Stony Brook University
ML 1405.4855, 1602.08108 Hu, Chiang, Li, ML 1605.01412
Chiang, Li, Hu, ML 1609.01701 + in prep. Chi-Ting Chiang (YITP, Stony Brook) Wayne Hu (KICP, Chicago)
Yin Li (Berkeley & IPMU, U Tokyo)
What we know about the neutrino mass scale
𝜈i ≳ 0.05eV
neutrino mass
lower bounds on mass from oscillation data
𝜈j ≳ 0.01eV
What we know about the neutrino mass scale
𝜈i ≳ 0.05eV
(Troitsk experiment 2011)
neutrino mass
upper bound on mass m𝞶e ≲ 2eV
lower bounds on mass from oscillation data
𝜈j ≳ 0.01eV
What we know about the neutrino mass scale
𝜈i ≳ 0.05eV
(Troitsk experiment 2011)
neutrino mass
upper bound on mass m𝞶e ≲ 2eV
Cosmology
lower bounds on mass from oscillation data
Σ mν ≾ 0.49eV
upper bound on sum of masses
(CMB alone, Planck 2015)
Σ mν ≾ 0.17eV
(CMB + BAO, Planck 2015)
𝜈j ≳ 0.01eV
What we know about the neutrino mass scale
𝜈i ≳ 0.05eV
(Troitsk experiment 2011)
neutrino mass
upper bound on mass m𝞶e ≲ 2eV
future cosmology?!
Cosmology
lower bounds on mass from oscillation data
Σ mν ≾ 0.49eV
upper bound on sum of masses
(CMB alone, Planck 2015)
Σ mν ≾ 0.17eV
(CMB + BAO, Planck 2015)
𝜈j ≳ 0.01eV
(CMB S4, SO, DESI, Euclid, LSST, WFIRST. . .)
What neutrinos masses do to observables
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)
time
small-scale density perturbations don’t retain
neutrinos
𝝳𝞀c 𝞀c
cold dark matter and baryons density
perturbation growing
𝝳𝞀𝞶 𝞀𝞶
neutrino density perturbation
decaying
What neutrinos masses do to observables
large-scale density perturbations do
retain neutrinos
𝝳𝞀c 𝞀c cold dark
matter,
baryons and neutrinos
growing together
𝝳𝞀𝞶 𝞀𝞶
time
small-scale density perturbations don’t retain
neutrinos
What neutrinos masses do to observables
This scale-dependent growth is the effect that gives main cosmological constraints on neutrino mass
P(k) = ⟨δm(k)δm(k)⟩ where δm(k) = δρ—————ρmattermatter
Hu, Eisenstein, Tegmark 1998 Bond, Efstathiou, Silk 1980
Fourier mode k (h/Mpc)
small scales damped large-scales the same
Suppression in P(k) - variance of density fluctuations δneutrino
What neutrinos masses do to observables
This scale-dependent growth is the effect that gives main cosmological constraints on neutrino mass
Hu, Eisenstein, Tegmark 1998 Bond, Efstathiou, Silk 1980
What neutrinos masses do to observables
—> less gravitational lensing than a universe where all matter is
gravitationally clustered
—> lower amplitude galaxy clustering than a universe where all matter is
gravitationally clustered
Claim:
Small scale structure in regions (i) and (ii) will evolve differently. This gives new scale-
dependent signatures of massive neutrinos.
(i) super-Jeans scale over-density (ii) sub-Jeans scale overdensity
Claim:
Small scale structure in regions (i) and (ii) will evolve differently. This gives new scale-
dependent signatures of massive neutrinos.
δC
δν δC, δν
x.
. .. . x.
. .. .
δC(k >> kfs) δC(k << kfs)
(i) super-Jeans scale over-density (ii) sub-Jeans scale overdensity
Claim:
Small scale structure in regions (i) and (ii) will evolve differently. This gives new scale-
dependent signatures of massive neutrinos.
δC
δν δC, δν
x.
. .. . x.
. .. .
(i) super-Jeans scale over-density (ii) sub-Jeans scale overdensity
(e.g. eventual number of galaxies, amplitude of the small-scale power spectrum, etc will differ slightly in regions (i) and (ii))
δC
δν δC, δν
x.
. .. . x.
... .
(i) super-Jeans scale over-density (ii) sub-Jeans scale overdensity
Why?
evolution of 𝛅c(t)
t
δC(k >> kfs)
δC(k << kfs)
δC
δν δC, δν
x.
. .. . x.
... .
(i) super-Jeans scale over-density (ii) sub-Jeans scale overdensity
Why?
evolution of 𝛅c(t)
t
δC(k >> kfs)
δC(k << kfs)
local expansion aW = a(1 -𝛅c(t)/3)
t
δC(k >> kfs) δC(k << kfs)
δC
δν δC, δν
x.
. .. . x.
... .
(i) super-Jeans scale over-density (ii) sub-Jeans scale overdensity
Why?
evolution of 𝛅c(t)
t
δC(k >> kfs)
δC(k << kfs)
local expansion aW = a(1 -𝛅c(t)/3)
t
local growth of small-scale density perturbations
t
Ratio of fractional changes to (log of )
local expansion history for super/
sub Jeans regions
fν = 0.005
fν = 0.11
scale factor
Precisely:
Ratio of fractional changes to (log of )
local Hubble rate for super/sub Jeans
regions
Precisely:
scale factor
fν = 0.11
fν = 0.005
Predictions:
fractional neutrino energy density
~ squeezed-limit bispectrum
<𝝳(k___________s)𝝳(-ks -kL )𝝳(kL)>
P(kL)
The change in the growth rate in over/underdense regions is scale-dependent
wavenumber of long-wavelength mode kL
~ squeezed-limit bispectrum
<𝝳(k___________s)𝝳(-ks -kL )𝝳(kL)>
P(kL)
The change in the growth rate in over/underdense regions is scale-dependent
Predictions:
Predictions:
wavenumber k (Mpc-1)
scale-dependence of halo bias
b(k) = √Phh(k)/Pmm(k)
(Spherical Collapse in Separate Universe) The halo bias is scale-dependent
ML 2014
Test this with N-body simulations in regions with different background densities δc(k,a) with different k
Test this with N-body simulations in regions with different background densities δc(k,a) with different k
Account for δc(k,a) by feeding GADGET the a, H(a) that an observer in regions with δc(k,a) would see
Test this with N-body simulations in regions with different background densities δc(k,a) with different k
Account for δc(k,a) by feeding GADGET the a, H(a) that an observer in regions with δc(k,a) would see
McDonald 2001 Sirko 2005;
Gnedin & Kravtsov 2011
Baldauf, Seljak, Senatore, Zaldarriaga 2011, 2015 Li, Hu, Takada 2014, 2016
Chiang, Wagner, Schmidt, Komatsu 2014a, (+perm) 2014b
So-called “Separate Universe” approach, now extended to cosmologies beyond LCDM
Hu, Chiang, Li, ML 1605.01412 Chiang, Li, Hu, ML 1609.01701
wavenumber k
Results
wavenumber k
The change in small-scale growth of structure depends the on wavelength of the background over/under density
“Response” of growth to background over density
ks
Chiang, Li, Hu, ML in prep
wavenumber k
The change in small-scale growth of structure depends the on wavelength of the background over/under density
~ squeezed-limit bispectrum
<𝝳(k___________s)𝝳(-ks -kL )𝝳(kL)>
P(kL)
ks
Chiang, Li, Hu, ML in prep
wavenumber k
The change in the abundance of halos depends the on wavelength of the background over/under density
Chiang, Li, Hu, ML in prep
wavenumber k
The change in the abundance of halos depends the on wavelength of the background over/under density
Chiang, Li, Hu, ML in prep
this gives rise to a step feature in the halo bias
“step” in the bias
wavenumber k
The change in the abundance of halos depends the on wavelength of the background over/under density
Chiang, Li, Hu, ML in prep
this gives rise to a step feature in the halo bias
“step” in the bias
Summary
Nonlinear structure formation is complicated! But, can lead to new phenomena that may provide new insights into neutrinos and beyond
We have a new way to simply study a limited set of
observables in cosmologies with multiple fluids and non- gravitational forces, while still only doing CDM simulations (i.e. no new code to model additional fluid behavior)
The presence of a Jeans scale can lead to new
observables (scale dependent bias, scale-dependent squeezed bispectrum)