Cosmological Dependence of
Matter Power Spectrum Response
Xiaoqi Yu
Backgrounds
➔Cosmologists are interested in finding out the
fundamental physics laws that govern the birth
and evolution of the universe.
➔Large Scale Structure: what can we learn about
the physics on the smallest scale from the
physics on the largest scale?
➔Observational data == evidence. Simulations ==
Experiments
➔In term of energy density, 70% dark energy and
25% of dark matter
Motivations
➔Large Scale Structure (LSS) of the universe
contains cosmological information
➔Higher Order Statistics of the LSS are necessary,
but they are computationally and analytically
difficult to compute
➔Power spectrum responses are used to approach
higher order statistics in previous studies.
However, the cosmological dependence of the
responses had never been studied.
Cosmological Information in the
Large Scale Structure
The local overdensity
The Nth moment of
overdensity distribution
2nd Order
Cosmological Information in the
Large Scale Structure
The local overdensity
The Nth moment of
overdensity distribution
3rd Order
Cosmological Information in the
Large Scale Structure
The local overdensity
The Nth moment of
overdensity distribution
higher Orders
Motivations
➔Large Scale Structure (LSS) of the matter field
contains cosmological information
➔Higher Order Statistics of the LSS are necessary,
but they are numerically and analytically
difficult to compute
➔Power spectrum responses are used to approach
higher order statistics in previous studies.
However, the cosmological dependence of the
responses had never been studied.
The Second
Order Statistics
The 2-point correlation
function
The Power Spectrum
The Growth of Structure
in Linear Regime
The Power Spectrum Depends on
Cosmology
The Second
Order Statistics
The 2-point correlation
function
The Power Spectrum
The Growth of Structure
in Linear Regime
The Power Spectrum deviate from
Linear Prediction on small scales
→We need Higher Order Statistics
The Higher Order Statistics are
difficult to compute
Patches of Universe under Long
Wavelength Perturbation
The Matter Power Spectrum Response:
Three contributions to the response:
Reference density,
Dilation effect
Physical Response
Specifically For the First Order
Response
Reference Density
Dilation Effect
Physical
Response
The Physical Response
(measured using the Separate Universe Simulation -- the power spectrum of
local patch under long-wavelength perturbation is equivalent to power spectrum
in a separate universe with modified cosmological parameters)
Motivations
➔Large Scale Structure (LSS) of the matter field
contains cosmological information
➔Higher Order Statistics of the LSS are necessary,
but they are computationally and analytically
difficult to compute
➔Power spectrum responses are used to approach
for higher order statistics in previous studies.
However, the cosmological dependence of the
response had never been studied.
Bispectrum at Squeezed Limit
k
k’
q
Simulation Setup
➔5 realizations for each set of cosmology of
particles in box of 300 Mpc/h.
➔Planck’s values are set for the fiducial cosmology:
➔For all cosmologies, the amplitude of the long
wavelength perturbation is taken to be .
➔and are chosen to investigate the
cosmological dependence of the responses.
Measured First
Order Growth Only
response for
cosmologies with
matter density
parameters
.
Finding: the first
order responses
depends on the
cosmological
parameter
Predicted G_1 for
cosmologies with
different matter
density parameter
using linear
Interpolation.
On scale of k=1
h/Mpc, the first
order response
varies by 3%
within planck’s
2sigma bounds at
redshift z=0.5.
Take-Aways
➔Responses are useful in approaching higher order
statistics of the Large Scale Structure, which contains
cosmological information.
➔The dependence of the first order response on matter
density can be a concern when taking the response
approach for higher order statistics of the Large Scale
Structure.
➔Thorough study is needed to narrow down the
statistical uncertainty in the response measurements.
Similar approach can be taken to find the
cosmological dependence of responses on other
parameters.
Acknowledgement
➔Dr. Alexandre Barreira and Dr. Fabian Schmidt for
advising.
➔Rechenzentrum Garching for providing the
computational resource
➔The EuroScholars program, and Ms. Barbara
Habermann for facilitating with accommodation and
cultural events.
➔Faculties and Friends at Max Planck Institute for
Astrophysics and Ludwig Maximilian University
Munich.
