New Approaches to Modeling Nonlinear Structure Formation Nuala McCullagh Johns Hopkins University Cosmology on the Beach Cabo 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 [Mpc/h] σ [Mpc/h] Hawkins et al. (2002), astro-ph/ dFGRS: β=0.49±0.09 Nonlinearity Redshift-space distortions Galaxy bias Image: Max Tegmark

Modeling 2-point statistics: SPT Standard Perturbation Theory: perturbative solution to the fluid equations in Fourier space: Figure: Carlson, White, Padmanabhan, arXiv: (2009) Linear 2 nd order 3 rd 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 2 nd 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 1 st 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 simulations T. 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=0.06z=0.00

Line of sight LinearNonlinear, 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 transform Linear Theory:106.4 Mpc/h Zel’dovich density: Mpc/h-0.6 Mpc/h Zel’dovich log-density: 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!