Gao, X (reprint author), Chinese Acad Sci, State Key Lab Theoret Phys, Inst Theoret Phys, Beijing 100190, Peoples R China.
; Li, Tianjun] Chinese Acad Sci, State Key Lab Theoret Phys, Inst Theoret Phys, Beijing 100190, Peoples R China
; [Gao, Xin
; Li, Tianjun] Chinese Acad Sci, Kavli Inst Theoret Phys China, Inst Theoret Phys, Beijing 100190, Peoples R China
; [Gao, Xin] Virginia Tech, Dept Phys, Blacksburg, VA 24061 USA
; [Li, Tianjun] Univ Elect Sci & Technol China, Sch Phys Elect, Chengdu 610054, Peoples R China
; [Shukla, Pramod] Univ Turin, Dipartimento Fis, I-10125 Turin, Italy
; [Shukla, Pramod] Ist Nazl Fis Nucl, Sez Torino, I-10125 Turin, Italy
Using delta N formalism in the context of a generic multi-field inflation driven on a non-flat field space background, we revisit the analytic expressions of the various cosmological observables such as scalar tensor power spectra, scalar/tensor spectral tilts, non-Gaussianity parameters, tensor-to-scalar ratio, and the various runnings of these observables. In our backward formalism approach, the subsequent expressions of observables automatically include the terms beyond the leading order slow-roll expansion correcting many of the expression at subleading order. To connect our analysis properly with the earlier results, we rederive the (well) known (single field) expressions in the limiting cases of our generic formulae. Further, in the light of PLANCK results, we examine for the compatibility of the consistency relations within the slow-roll regime of a two-field roulette poly-instanton inflation realized in the context, of large volume scenarios.