Loop cosmological dynamics and dualities with Randall-Sundrum braneworlds

TL;DR

This paper explores how loop quantum cosmology modifies the Friedmann equation similarly to Randall-Sundrum braneworlds, revealing new scalar field dynamics, super-inflation phases, and dualities between different cosmological regimes.

Contribution

It demonstrates the existence of super-inflation independent of inverse scale factor effects and establishes dual relationships between loop quantum cosmology and Randall-Sundrum models.

Findings

Identification of super-inflation phase in loop quantum cosmology.

Scalar field mimics phantom dynamics during super-inflation.

Duality between loop quantum cosmology and Randall-Sundrum scaling solutions.

Abstract

The discrete quantum geometric effects play an important role in dynamical evolution in the loop quantum cosmology. These effects which are significant at the high energies lead to the quadratic energy density modifications to the Friedmann equation, as in the Randall-Sundrum braneworld scenarios but with a negative sign. We investigate the scalar field dynamics in this scenario and show the existence of a phase of super-inflation independent of the inverse scale factor modifications as found earlier. In this regime the scalar field mimics the dynamics of a phantom field and vice versa. We also find various symmetries between the expanding phase, the contracting phase and the phantom phase in the loop quantum cosmology. We then construct the scaling solutions in the loop quantum cosmology and show their dual relationship with those of the Randall-Sundrum cosmology.