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Recent astrophysical data indicate that our universe might currently be in a de Sitter (dS) phase. The importance of dS space has been primarily ignited by the study of the inflationary model of the universe and the quantum gravity. As we know Einsteins theory of gravitation (with a nonzero cosmological constant) can be interpreted as a theory of a metric field; that is, a symmetric tensor field of rank2 on a fixed de Sitter background. It has been shown the massless spin2 FierzPauli wave equation (or the linearized Einstein equation) is not conformally invariant. This result is in contrary with what we used to expect from massless theories. In this thesis we obtain conformally invariant wave equation for the massless spin2 in the dS space. This study is motivated by the belief that conformal invariance may be the key to a future theory of quantum gravity.
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