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!