%0 Journal Article
%T The Turning Point for the Recent Acceleration of the Universe with a Cosmological Constant
%A Zhang T. X.
%J Progress in Physics
%D 2012
%I HEXIS (Arizona)
%X The turning point and acceleration expansion of the universe are investigated according to the standard cosmological theory with a non-zero cosmological constant. Choosing the Hubble constant H0, the radius of the present universe R0, and the density parameter in matter ¦¸M,0 as three independent parameters, we have analytically examined the other properties of the universe such as the density parameter in dark energy, the cosmological constant, the mass of the universe, the turning point redshift, the age of the present universe, and the time-dependent radius, expansion rate, velocity, and acceleration parameter of the universe. It is shown that the turning point redshift is only dependent of the density parameter in matter, not explicitly on the Hubble constant and the radius of the present universe. The universe turned its expansion from past deceleration to recent acceleration at the moment when its size was about 3/5 of the present size if the density parameter in matter is about 0.3 (or the turning point redshift is 0.67). The expansion rate is very large in the early period and decreases with time to approach the Hubble constant at the present time. The expansion velocity exceeds the light speed in the early period. It decreases to the minimum at the turning point and then increases with time. The minimum and present expansion velocities are determined with the independent parameters. The solution of time-dependent radius shows the universe expands all the time. The universe with a larger present radius, smaller Hubble constant, and/or smallerdensity parameter in matter is elder. The universe with smaller density parameter in matter accelerates recently in a larger rate but less than unity
%K acceleration expansion
%K standard cosmological theory
%K redshift
%U http://www.ptep-online.com/index_files/2012/PP-29-02.PDF