Isometries and primordial fluctuations

Abstract

Inflation has become a basic paradigm of modern physical cosmology. One of the most widely used description of such an accelerating expanding universe is that of the de Sitter space (dS). We explicitly derive the exact form of the dS isometries by considering an embedding in a higher dimensional Minkowski spacetime; these are spatial translations and rotations and spacetime dilations and boosts. For the boost in particular, we obtain its finite form, while in the literature we could find only its infinitesimal form. We then proceed to consider these same isometries in the context of quasi-de Sitter space via the slow roll formalism, where the dilations and boosts are broken. Furthermore, we discuss some insights these isometries provide, such as the dS/CFT duality and the consistency relation for inflaton correlators, which can be applied even outside of dS.