Recently, cosmic voids have been recognized as a powerful cosmological probe. A number of studies have focused on the effects of the gravitational lensing by voids on the temperature (and in some cases polarization) anisotropy of the Cosmic Microwave Background (CMB) background at relatively large to medium scales, l ~ 1000. Many of these studies attempt to explain the unusually large cold spot in CMB temperature maps and dynamical evidence of dark energy via detections of late-time integrated Sachs Wolfe (ISW) effect. Here, the effects of lensing by voids on the CMB temperature anisotropy at small scales, up to l = 3000, will be investigated. This work is carried out in the light of the benefits of adding large catalogues of cosmic voids, to be identified by future large galaxy surveys such as EUCLID and LSST, to the analysis of CMB data such as those from Planck mission. Our numerical simulation utilizes two methods, namely, the small-de ectionangle approximation and full ray-tracing analysis. Using the fitted void density profiles and radius (RV ) distribution available in the literature from N-body simulations, we simulated the secondary temperature anisotropy (lensing) of CMB photons induced by voids along a line of sight from redshift 0 to 2. Each line of sight contains approximately 1000 voids of effective radius RV;eff = 35 h-1Mpc with randomly distributed radial and projected positions. Both methods are used to generate temperature maps. The two methods will be compared for their accuracy and effciency in the implementation of theoretical modeling.

ABSTRACT
1. INTRODUCTION
2. THEORY
    2.1. CMB Flat Sky Approximation
    2.2. Void Profile
3. METHOD
    3.1. Lensing Potential Calculation
4. RESULTS AND DISCUSSION
REFERENCES

• Anut Sangka(School of Physics, Institute of Science,Suranaree University of Technology, Nakhon Ratchasima)
• Utane Sawangwit(National Astronomical Research Institute of Thailand)
• Nuanwan Sanguansak(School of Physics, Institute of Science,Suranaree University of Technology/National Astronomical Research Institute of Thailand)