Astronomy and Astrophysics – Astrophysics
Scientific paper
2000-08-24
Astrophys.J. 546 (2001) 620-634
Astronomy and Astrophysics
Astrophysics
Accepted by ApJ. Received June 14, Accepted August 24. 24 pages including 9 figures
Scientific paper
10.1086/318305
We present quantitative investigations of the weak lensing effect on the two-point correlation functions of local maxima (hotspots), $\xipk(\theta)$, in the cosmic microwave background (CMB) maps. The lensing effect depends on the projected mass fluctuations between today and the redshift $z_{\rm rec}\approx1100$. If adopting the Gaussian assumption for the primordial temperature fluctuations field, the peak statistics can provide an additional information about the intrinsic distribution of hotspots that those pairs have some characteristic separation angles. The weak lensing then redistributes hotspots in the observed CMB maps from the intrinsic distribution and consequently imprints non-Gaussian signatures onto $\xipk(\theta)$. Especially, since the intrinsic $\xipk(\theta)$ has a pronounced depression feature around the angular scale of $\theta\approx 70'$ for a flat universe, the weak lensing induces a large smoothing at the scale. We show that the lensing signature therefore has an advantage to effectively probe mass fluctuations with large wavelength modes around $\lambda\approx 50 h^{-1}{\rm Mpc}$. To reveal the detectability, we performed numerical experiments with specifications of {\em MAP} and {\em Planck Surveyor} including the instrumental effects of beam smoothing and detector noise. It is then found that our method can successfully provide constraints on amplitude of the mass fluctuations and cosmological parameters in a flat universe with and without cosmological constant, provided that we use maps with 65% sky coverage expected from Planck.
Futamase Toshifumi
Takada Masahiro
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