Inflation in unimodular loop quantum cosmology

Abstract

We study inflation in the setting of unimodular loop quantum cosmology, where time evolution is defined in unimodular time rather than with respect to a free, massless scalar field as is standard in loop quantum cosmology. The unimodular setting leads to a natural Schrödinger time evolution in a time coordinate with clear geometric meaning, defined independently of any particular matter content; an inflaton can be included but is not needed as a clock. We review the unimodular version of loop quantum cosmology and comment on possible connections to full (unimodular) loop quantum gravity. Then, focusing on semiclassical effective equations, we derive analytical solutions in simple cases such as a constant potential, emphasising the use of a unimodular time coordinate. We also discuss numerical solutions for phenomenologically interesting cases such as a quadratic potential and Starobinsky inflation, comparing different possible choices of initial conditions. In particular, we show that choosing an $\hat{I}\pm$-attractor potential allows for models of a bounce either dominated by kinetic or potential energy, which are compatible with observations while potentially including observable imprints of the quantum-gravity regime.

34 pages, 10 figures (with 30 figure files); Python code included as ancillary files

Topics & keywords