We extend our earlier work of boson star (BS) rotation after incorporating the cosmological constant and coupling term of the curvature of the Universe with the field of boson star. Due to the cosmological constant and coupling term in the Lagrangian density of the boson star, the oscillation amplitudes of the boson star are modified for the entire study and the amplitudes are found to increase from the result obtained earlier. The introduction of cosmological constant and coupling of curvature prove the hypothetical assumption of the existence of the bosonstar.