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A Large Sky Simulation of the Gravitational Lensing of the Cosmic

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A Large Sky Simulation of the Gravitational Lensing of the Cosmic Draft version November 2, 2018 Preprint typeset using LATEX style emulateapj v. 08/22/09 A LARGE SKY SIMULATION OF THE GRAVITATIONAL LENSING OF THE COSMIC MICROWAVE BACKGROUND Sudeep Das & Paul Bode Princeton University Observatory Peyton Hall, Ivy Lane, Princeton, NJ 08544 USA Draft version November 2, 2018 ABSTRACT Large scale structure deflects cosmic microwave background (CMB) photons. Since large angular scales in the large scale structure contribute significantly to the gravitational lensing effect, a realistic simulation of CMB lensing requires a sufficiently large sky area. We describe simulations that include these effects, and present both effective and multiple plane ray-tracing versions of the algorithm, which employs spherical harmonic space and does not use the flat sky approximation. We simulate lensed CMB maps with an angular resolution of 0.′9. The angular power spectrum of the simulated sky agrees well with analytical predictions. Maps∼ generated in this manner are a useful tool for the analysis and interpretation of upcoming CMB experiments such as PLANCK and ACT. Subject headings: cosmic microwave background — gravitational lensing — large-scale structure of universe — methods: N-body simulations — methods: numerical 1. INTRODUCTION gular size produce small-scale distortions in the CMB, While the current generation of CMB experiments have thereby transferring power from large scales in the CMB had a significant impact on cosmology by helping to es- to the higher multipoles. Also, although the primordial tablish a standard paradigm for cosmology (Spergel et al. CMB can be safely assumed to be a Gaussian random 2003, 2007), the upcoming generation of CMB experi- field (Komatsu et al. 2003), and the large scale lensing ments still has the potential to provide novel new in- potential can also be well approximated by a Gaussian sights into cosmology. PLANCK1 and ground based ex- random field, the lensed CMB— being a reprocessing periments, such as the Atacama Cosmology Telescope of one Gaussian random field by another— is itself not (ACT)2, will be mapping the CMB sky with significantly Gaussian. The effect of lensing on the power spectrum higher angular resolution than ever before. Secondary of the CMB is important enough that it should be taken anisotropies on small angular scales encode important in- into account while deriving parameter constraints with formation about the late time interaction of CMB pho- future higher resolution experiments. But what is even tons with structure in the Universe. One of the most more interesting is that the non-Gaussianity in the lensed basic of these interactions is the gravitational effect of CMB field should enable us to extract information about the large scale structure potentials deflecting the paths the projected large scale structure potential, and thereby of the photons, an effect justifiably referred to as the constrain the late time evolution of the Universe and Gravitational Lensing of the CMB. Dark Energy properties. Therein lies the main moti- The effect of gravitational lensing can be thought of as vation of studying this effect in utmost detail. Progress a remapping of the unlensed CMB field by a line-of-sight in this area has been slow. Measurements of the CMB averaged deflection field (for a recent review, see Lewis precise enough to enable a detection of weak lensing were & Challinor 2006). Therefore, lensing does not change not available in the pre-WMAP era. Also, picking out the one-point properties of the CMB. However, it does non-Gaussian signatures in the measured CMB sky by arXiv:0711.3793v3 [astro-ph] 25 Apr 2008 modify the two and higher-point statistics, and gener- itself is extremely difficult, due to confusion from sys- ates non-Gaussianity (Seljak 1996; Zaldarriaga & Seljak tematics, foregrounds, and limited angular resolution. 1999; Zaldarriaga 2000). Although the typical deflection Rather than looking at signatures of lensing only in the suffered by a CMB photon during its cosmic journey is CMB, one can also measure to what extent the deflection about three arcminutes, the deflections themselves are field estimated from the CMB correlates with tracers of coherent over several degrees, which is comparable to the the large scale structure which contributed to the lensing. typical size of the acoustic features on the CMB. Thus It is easily realized that this approach is powerful (Peiris lensing causes coherent distortions of the hot and cold & Spergel 2000) because many of the systematics disap- spots on the CMB, and thereby broadens their size dis- pear upon cross-correlating data sets. This approach was tribution. This leads to redistribution of power among taken in recent years by Hirata et al. (2004) and Smith the acoustic scales in the CMB, and shows up in the et al. (2007), using WMAP 1-year and 3-year data re- two-point statistics as a smoothing of the acoustic peaks. spectively. The former work looked at the cross correla- At smaller scales, where the primordial CMB is well ap- tion with SDSS luminous red galaxies (LRG), while the proximated by a local gradient, deflectors of small an- latter used the NRAO-VLA Sky Survey (NVSS) radio sources as their large scale structure tracers. As the lens- Electronic address: [email protected],[email protected] efficiency for the CMB is highest between redshifts of 1 http://www.rssd.esa.int/index.php?project=Planck one and four, higher redshift tracers should show greater 2 http://www.physics.princeton.edu/act cross correlation signal, which makes the NVSS radio 2 Das & Bode sources better tracers for such study; Smith et al. (2007) acoustic peaks of the CMB occurs via coupling of modes report a 3.4σ detection. An independent analysis by Hi- in the CMB with these large coherent modes in the de- rata et al. (2008) looking for this effect in the WMAP flection field. A large sky allows for several such modes 3-year data in cross correlation with SDSS LRG+QSO to be realized. It is estimated that a small (flat) sky sim- and NVSS sources find this signal at the 2.5σ level. With ulation that misses these modes would typically under- these pioneering efforts and with higher resolution CMB estimate the lensing effect by about 10% in the acoustic data from experiments such as ACT, PLANCK and the regime, and more in the damping tail (Hu 2000). Sec- South Pole Telescope (SPT)3 on the horizon, we are en- ond, one of the major goals of simulations such as this is tering an era where robust detection and characterization to produce mock observations for upcoming CMB exper- of this effect will become a reality. Also, with upcom- iments. PLANCK is an all-sky experiment, and many of ing and proposed large scale structure projects (LSST4, the future CMB experiments (including ACT and SPT) SNAP5, ADEPT6, DESTINY7, etc.) there will in future will observe relatively large patches of the sky. There- be many more datasets to cross-correlate with the CMB. fore, simulating CMB fields on a large area of the sky One of the immediate results of such cross-correlation is a necessity. This method fully takes into account the studies will be a measurement of the bias of the tracer curvature of the sky. Although presented here for a polar population. Because such cross correlations tie together cap like area, it can be trivially extended to the full sky. early universe physics from the CMB and late time evolu- The value of a simulation as described here is multi- tion from large scale structure, they will also be sensitive faceted, particularly in the development of algorithms for to Dark Energy parameters (Hu et al. 2006) and neutrino detection and characterization of the CMB lensing effect properties (Smith et al. 2006a; Lesgourgues et al. 2006), for a specific experiment. Since each experiment has a and can potentially break several parameter degenera- unique scanning mode, beam pattern, area coverage, and cies in the primordial CMB (M. Santolini, S. Das and foregrounds, operations and optimizations performed on D. N. Spergel, in preparation). Combination of galaxy the data to extract the lensing information will have to or cluster lensing of the CMB with shear measurements be tailored to the specific experiment. A large-sky lensed from weak lensing of galaxies can also provide impor- CMB map acting as an input for a telescope simula- tant constraints on the geometry of the Universe (S. Das tor provides the flexibility of exploring various observing and D. N. Spergel, in prep; Hu et al. 2007). Again, strategies, and also allows for superposition of known with high enough precision of CMB data, it is possi- foregrounds. Another important aspect of this simula- ble to estimate, using quadratic (Okamoto & Hu 2003) tion is that the halos identified in the large scale struc- or maximum likelihood (Hirata & Seljak 2003) estima- ture simulation can be populated with different tracers tors, the deflection field that caused the lensing. Such of interest. Also, other signals, such as the Thermal and estimates can be turned into strong constraints of the Kinetic Sunyaev Zel’dovich effects and weak lensing of power spectrum of the projected lensing potential (Hu galaxies by large scale structure, can be simulated using & Okamoto 2002), which is also sensitive to the details the same large scale structure. This opens up the possi- of growth of structure. The estimated potential from bility of studying the cross-correlation of the CMB lens- the lensed CMB alone, or the potential estimated from ing signal with various indicators of mass, and thereby weak lensing surveys (Marian & Bernstein 2007), can be predicting the level of scientific impact that a specific also used to significantly de-lens the CMB. This is par- combination of experiments can have.
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