Tomographic Approach to Quantum Cosmology

C. Stornaiolo

Vladimir I. Man’ko, Giuseppe Marmo, C. Stornaiolo

V. I. Man`ko, Giuseppe Marmo, C. Stornaiolo

C. Stornaiolo

The importance of the tomographic approach is that either in quantum mechanics as in classical mechanics the state of a physical system is expressed with marginal probability functions called tomograms. The extension of this procedure to quantum cosmology is straightforward. But in this paper, instead of using the tomographic representation, we use tomograms to analyze the properties of the quantum and classical universes, starting from the wave functions in quantum cosmology and from the phase space distributions in classical cosmology. In this, there is a part where we resume the properties of the tomograms. Then, we apply them to study and discuss the properties of the initial conditions introduced by Hartle and Hawking, Vilenkin and Linde and finally we argue about their classical transition. According to the results of this paper it follows that the decay of the cosmological constant from the Planck scale to the present one could be responsible for the transition of the quantum universe to the classical one.

Jasel Berra–Montiel, Alberto Molgado

Salvatore Capozzıello, Vladimir I. Man’ko, G Marmo +1 more

Classical and quantum perturbations can be described in terms of marginal distribution functions in the framework of tomographic cosmology. In particular, the so-called Radon transformation and the mode-parametric quantum oscillator description can give rise to links between quantum and classical regimes. The approach results in a natural scheme to discuss the transition from quantum to classical perturbations and then it could be a workable scheme to connect primordial fluctuations with the large-scale structure observed today.