Lagrangian Perturbation Theory: Applications in Cosmology
Lagrangian Perturbation Theory
:
3
rd
order solutions for general dark energy models
Seokcheon Lee (
이석천
)
Korea Institute for Advanced Study
(
고등과학원
)
Feb. 12
th
. 2014
based on : arXiv/1401.2226
Outline
•
Why do we need LPT?
•
Analytic Perturbation Theories
–
Standard Perturbation Theory (SPT)
–
Lagrangian Perturbation Theory (LPT)
•
Application
–
Matter power spectrum
–
Two point correlation function
•
Third order solutions for general DE models
•
Future works
Why do we need LPT?
•
Upcoming large-scale surveys
(
LSST & Euclid
)
requires
huge number of mock catalogs
to
estimate covariance matrix
•
N-body simulations
:
accurate,
numerically expensive
•
Semi-analytic methods
(
PThalos, PINOCCHIO,
COLAR
) :
fast
,
inaccurate
: using LPT to
displace particles at large scales
Analytic Perturbation Theories
Standard Perturbation Theory (SPT)
•
Both
background evolution
and
perturbed
quantities
are required to study
Large scale
structure (LSS)
•
Linear theory
well describes
LSS
in linear
regime
SPT II
•
There’s no reason to stop at linear order
•
Problems :
convergences
of an expansion
are not clear,
diverge
at large k (cannot do
FT), confined in
real space
Lagrangian Perturbation Theory
(LPT)
•
In LPT, a fundamental variable to represent
perturbation is a displacement field, S
•
First order LPT : Zel’dovich approximation
•
Initial conditions for N-body simulations are
open generated using ZA or 2
nd
order LPT
•
LPT can overcome problems of SPT
LPT II
•
Drawbacks
of LPT
–
Successful at high redshifts but poor results
at late times due to shell crossing
–
Power in small scales is suppressed
–
Multiple streams through same Eulerian
position
–
Before shell crossing, the system described
by a velocity field
Applications
•
Predictions for cosmological dependence
(including
Ω
m
,
ω
, etc) on
–
(quasi-linear) power spectrum
–
Weak lensing
–
Bispectrum
–
Halo bias
–
Two point correlation function (BAO)
Third order solutions
: for general dark energy models
•
Goal
–
So far one uses
EdS universe approximation
for the time dependence part of solutions
–
Thus, one investigates 2pt CF or PS for
Λ
CDM
model
with this assumption
–
This is
self inconsistent
and can’t be used for the
cosmological model different from
Λ
CDM
–
One needs to improve this in order to predict
DE dependence on those observable
1
st
order solution
2
nd
order solution
3
rd
order solutions : Fa
3
rd
order solutions : Fb
Future works
•
Adopt the correct higher order solutions
to power spectrum (in progress)
•
Using these solutions in the 2pt
correlation function to forecast BAO
signals (in progress)
•
Also check the prediction for WL
Lagrangian Perturbation Theory (LPT) offers solutions for general dark energy models and is crucial for upcoming large-scale surveys. It provides a method to displace particles at large scales efficiently. While Standard Perturbation Theory (SPT) is limited at linear order, LPT overcomes its drawbacks and offers better results at high redshifts. LPT finds applications in predicting cosmological dependencies, weak lensing, bispectrum analysis, halo bias, and the two-point correlation function, among others.
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Presentation Transcript
Lagrangian Perturbation Theory : 3rdorder solutions for general dark energy models Seokcheon Lee ( ) Korea Institute for Advanced Study ( ) Feb. 12th. 2014 based on : arXiv/1401.2226
Outline Why do we need LPT? Analytic Perturbation Theories Standard Perturbation Theory (SPT) LagrangianPerturbation Theory (LPT) Application Matter power spectrum Two point correlation function Third order solutions for general DE models Future works
Why do we need LPT? Upcoming large-scale surveys (LSST & Euclid) requires huge number of mock catalogs to estimate covariance matrix N-body simulations : accurate, numerically expensive Semi-analytic methods (PThalos, PINOCCHIO, COLAR) : fast, inaccurate : using LPT to displace particles at large scales
Analytic Perturbation Theories Standard Perturbation Theory (SPT) Both background evolution and perturbed quantities are required to study Large scale structure (LSS) Linear theory well describes LSS in linear regime
SPT II There s no reason to stop at linear order Problems : convergences of an expansion are not clear, diverge at large k (cannot do FT), confined in real space
Lagrangian Perturbation Theory (LPT) In LPT, a fundamental variable to represent perturbation is a displacement field, S First order LPT : Zel dovich approximation Initial conditions for N-body simulations are open generated using ZA or 2ndorder LPT LPT can overcome problems of SPT
LPT II Drawbacks of LPT Successful at high redshifts but poor results at late times due to shell crossing Power in small scales is suppressed Multiple streams through same Eulerian position Before shell crossing, the system described by a velocity field
Applications Predictions for cosmological dependence (including m , , etc) on (quasi-linear) power spectrum Weak lensing Bispectrum Halo bias Two point correlation function (BAO)
Third order solutions : for general dark energy models Goal So far one uses EdS universe approximation for the time dependence part of solutions Thus, one investigates 2pt CF or PS for CDM model with this assumption This is self inconsistent and can t be used for the cosmological model different from CDM One needs to improve this in order to predict DE dependence on those observable
Future works Adopt the correct higher order solutions to power spectrum (in progress) Using these solutions in the 2pt correlation function to forecast BAO signals (in progress) Also check the prediction for WL
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