Tunneling in Quantum Cosmology and Holographic SYM theory

TL;DR

This paper investigates the early universe's quantum tunneling processes influenced by a cosmological constant and SYM fields, using holographic methods and comparing Wheeler-DeWitt and path-integral approaches.

Contribution

It introduces a holographic calculation of the SYM energy-momentum tensor and compares two quantum cosmology methods for early universe evolution.

Findings

Inflationary solutions emerge at late times for positive cosmological constant.

Quantum effects significantly alter early universe dynamics when SYM radiation is included.

Comparison of Wheeler-DeWitt and path-integral methods provides insights into quantum cosmology approaches.

Abstract

We study the time evolution of early universe which is developed by a cosmological constant $\Lambda_4$ and supersymmetric Yang-Mills (SYM) fields in the Friedmann-Robertson-Walker (FRW) space-time. The renormalized vacuum expectation value of energy-momentum tensor of the SYM theory is obtained in a holographic way. It includes a radiation of the SYM field, parametrized as $C$. The evolution is controlled by this radiation $C$ and the cosmological constant $\Lambda_4$. For positive $\Lambda_4$, an inflationary solution is obtained at late time. When $C$ is added, the quantum mechanical situation at early time is fairly changed. Here we perform the early time analysis in terms of two different approaches, (i) the Wheeler-DeWitt equation and (ii) Lorentzian path-integral with the Picard-Lefschetz method by introducing an effective action. The results of two methods are compared.