New Study of Cosmological Model with Cosmological Constant

Einstein’s field equations with variable cosmological constant is considered in the presence of a perfect fluid for a Bianchi type-I universe by assuming that the cosmological term is proportional to the square of the Hubble parameter. The variation law for vacuum density was recently proposed by many researchers on the basis of quantum field estimation in a curved expanding background. The cosmological term tends asymptotically to a genuine cosmological constant and the model tends to a de-sitter universe. Here we wish to desire some results by using a slightly different method from that of fore researchers and obtain that the present universe is accelerating with a large fraction of cosmological density in the form of a cosmological term.