Resonances in the early Universe

TL;DR

This paper investigates quantum cosmology with a FLRW model featuring a double barrier potential, revealing resonance phenomena that influence the universe's initial conditions through tunneling probabilities.

Contribution

It introduces a quantum cosmology model with a parameter-dependent effective potential and demonstrates the occurrence of resonances affecting tunneling probabilities.

Findings

Resonances significantly affect tunneling probabilities in the model.

The effective potential depends on parameters A, B, and σ, shaping the tunneling behavior.

Resonance peaks suggest preferred initial conditions for the universe.

Abstract

In the present paper, we study a Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) quantum cosmology model with positively curved spatial sections. The matter content of the model is given by a radiation fluid, a Chaplygin gas, and an ad hoc potential. After writing the Hamiltonian of the model, we notice that the effective potential ($V_{eff}$) depends on three parameters: $A$ and $B$ associated with the Chaplygin gas, and $\sigma$ associated with the ad hoc potential. Depending on the values of these parameters $V_{eff}$ becomes a double barrier potential. We quantize the model and obtain the Wheeler-DeWitt equation. We solve that equation using the WKB approximation and compute the corresponding probability ($TP_{WKB}$) that the wavefunction of the universe tunnels through the double barrier potential $V_{eff}$. We study how $TP_{WKB}$ behaves as a function of the parameters $A$, $B$, $\sigma$ and the radiation energy $E$. We notice a significant occurrence of resonances in $TP_{WKB}$ when varying it as a function of $E$ or $\sigma$. It is a very interesting phenomenon because it may cause the universe to be born with selected values of $E$ or $\sigma$.