The First Acoustics Peak CMBR and Cosmic Total Density

Abstract

Boomerang measured the first peak in CMBR to be at location of $l_D=196\pm 6$, which excites our strong interesting in it. A widely cited formula is $l_D\simeq 200Ω_T^{-0.50}$ to estimate the cosmic total density. Weinberg shows it is not correct and should be $l_D\propto Ω_T^{-1.58}$ near the interest point $(Ω_m,Ω_Λ)=(0.3,0.7)$. We show further that it should be $l_D\propto Ω_T^{-1.43}Ω_m^{-0.147}$ or $Ω_T^{-1.92}Ω_Λ^{0.343}$ near the same point in the more veracious sense if we consider the effect from the sound horizon. We draw a contour graph for the peak location, show that the recent data favor to a closed universe with about $Ω_T\simeq 1.03$. If we insist on obtaining a flat universe, a point $(0.36,0.64)$, i.e., more matter and less vacuum energy, is still possible, which has a more right-side first peak $l_D=208$ in CMBR and a smaller acceleration parameter $-q_0=0.10$ for the $z=0.4$ redshift SNIa.