Starobinsky Model in Schroedinger Description

TL;DR

This paper reformulates the Starobinsky inflationary model's quantum cosmology using a Schrödinger equation with time, revealing initial conditions linked to wormholes and Hawking-like states, thus offering a new perspective on quantum initial conditions.

Contribution

It reduces the Wheeler-DeWitt equation of the Starobinsky model to a Schrödinger form with time, incorporating initial conditions influenced by wormholes and Hawking states.

Findings

Schrödinger equation with time derived from Wheeler-DeWitt equation

Gaussian ansatz leads to Hawking-type initial conditions

Wormholes induce randomness in initial quantum states

Abstract

In the Starobinsky inflationary model inflation is driven by quantum corrections to the vacuum Einstein equation. We reduce the Wheeler-DeWitt equation corresponding to the Starobinsky model to a Schroedinger form containing time. The Schroedinger equation is solved with a Gaussian ansatz. Using the prescription for the normalization constant of the wavefunction given in our previous work, we show that the Gaussian ansatz demands Hawking type initial conditions for the wavefunction of the universe. The wormholes induce randomness in initial states suggesting a basis for time-contained description of the Wheeler-DeWitt equation.