RECONSTRUCTING THE INFLATION POTENTIAL - IN PRINCIPLE AND IN PRACTICE

Generalizing the original work by Hodges and Blumenthal, we outline a formalism which allows one, in principle, to reconstruct the potential of the inflaton field from knowledge of the tensor gravitational wave spectrum or the scalar density fluctuation spectrum, with special emp hasis on the importance of the tensor spectrum. We provide some illust rative examples of such reconstruction. We then discuss in some detail the question of whether one can use real observations to carry out th is procedure. We conclude that, in practice, a full reconstruction of the functional form of the potential will not be possible within the f oreseeable future. However, with a knowledge of the dark matter compon ents, it should soon be possible to combine intermediate-scale data wi th measurements of large-scale cosmic microwave background anisotropie s to yield useful information regarding the potential.