Planetary Perturbation with cosmological Constant

A contribution of quantum vacuum to the energy momentum tensor is inevitably experienced in the present universe. One requires the presence of non-zero cosmological constant (Λ) to make the various observations consistent. A case of Λ in the Schwarzschild de Sitter space-time shows that precession of perihelion orbit provides a sensative solar test for non-zero Λ. Application of the relations involving Λ to the planetery perturbation indicates the values near to the present bound on Λ. Also suggested are some relations in vacuum dominated flat universe with a positive Λ. The cosmological constant[1-3] has been an outstanding problem in various microscopic theories of particle physics and gravity for the past several decades, ever since Einstein introduced it in the field equations to avoid an expanding universe. The standard model of cosmology based on the ideas arising from particle physics involves the following trilogy of ideas: (i) Ω=1, (ii) Λ = 0 and (iii) Ωmatter < ∼ 0.9[4]. But, in reference to the large scale structure measurements, the density of the matter insufficient to result in a flat universe(Ω = 1) suggests a non-zero Λ. Now one would prefer either (1) Ω 6= 1, Λ = 0, Ωmatter ≈ 0.2− 0.4 or (2) Ω ≡ 1, Λ 6= 0, Ωmatter ≈ 0.2− 0.4. A small non-vanishing Λ is also required to make the two independent observations: the Hubble constant,Ho which explains the expansion rate of the present universe, and the present age of the universe (to) consistent each other[5]. This has forced us critically re-examine the simplest and most appealing cosmological modela flat universe with Λ = 0[4]. A flat universe with Ωm ≡ 0.3 and Ωm +ΩΛ = 1 is most preferable and Λ = 0 flat universe is almost ruled out[4,5]. Indeed, Λ follows from the dynamical