New Approaches to Modeling Nonlinear Structure Formation

New Approaches to Modeling Nonlinear Structure Formation

Nuala McCullaghJohns Hopkins University

Cosmology on the BeachCabo San Lucas, Mexico

January 13, 2014

In collaboration with:Alex Szalay and Mark Neyrinck

Outline

• Introduction• Modeling the correlation function• Beyond Gaussianity: log transform• Conclusions

z=0

z=1100

Modeling 2-point statistics: Linear Theory

Linear Theory:

Correlation Function:

Power Spectrum:

Overdensity:

Linear power spectrum

Linear correlation function

Modeling 2-point statistics: Systematics

π [M

pc/h

]

σ [Mpc/h]0 20-20

020

-20

Hawkins et al. (2002), astro-ph/02123752dFGRS: β=0.49±0.09

Nonlinearity

Redshift-space distortions

Galaxy bias

Image: Max Tegmark

Modeling 2-point statistics: SPTStandard Perturbation Theory: perturbative solution to the fluid equations in Fourier space:

Figure: Carlson, White, Padmanabhan, arXiv:0905.0497 (2009)

Linear2nd order3rd order

Modeling 2-point statistics: New Approach

• Structure of the Fourier space kernels suggests that in configuration space, the result may be simpler

• Terms beyond 2nd order may be simplified in configuration space compared to Fourier space

• Configuration space can be more easily extended to redshift space

Modeling 2-point statistics: New Approach

1st order Lagrangian perturbation theory (Zel’dovich approximation):

1LPT:

Poisson:

Expansion of the density in terms of linear quantities:

Modeling 2-point statistics: New Approach

Nonlinear correlation function:

McCullagh & Szalay. ApJ, 752, 21 (2012)

First nonlinear contribution to the correlation function in terms of initial quantities:

Where:

77 Indra simulationsT. Budavári, S. Cole, D. Crankshaw, L. Dobos, B. Falck, A. Jenkins, G. Lemson, M. Neyrinck, A. Szalay, and J. Wang

z=1.08 z=0.41

z=0.06 z=0.00

Line

of si

ght

Linear Nonlinear, z=0

Modeling 2-point statistics: New Approach

Zel’dovich model extended to redshift space:

Beyond Gaussianity: Log transform

A=log(1+δ(x))

McCullagh, Neyrinck, Szapudi, & Szalay. ApJL, 763, L14 (2013)

δ

log(1+δ)

Beyond Gaussianity: Log transformLinear Theory: 106.4 Mpc/hZel’dovich density: 105.8 Mpc/h -0.6 Mpc/hZel’dovich log-density: 106.1 Mpc/h -0.3 Mpc/h

McCullagh, Neyrinck, Szapudi, & Szalay. ApJL, 763, L14 (2013)

Conclusions & Future Directions• Extracting cosmological information from large-scale

structure requires accurate modeling of systematics• Modeling statistics in configuration space simplifies

higher-order corrections and extension to redshift space– Our approach should be extended to higher orders in LPT for

greater accuracy• Log-transform restores information to the 2-point

statistics– Possible improvements to BAO, redshift-space distortions, and

small-scale power spectrum– Must be demonstrated in real data in presence of discreteness

Thank you!