The Consistent Result of Cosmological Constant From Quantum Cosmology and Inflation with Born-Infeld Scalar Field

TL;DR

This paper explores quantum cosmology with Born-Infeld scalar fields, revealing how the cosmological constant relates to wave functions and inflation parameters, and predicts potential observable tensor perturbations.

Contribution

It introduces a novel analysis of the cosmological constant in quantum cosmology with Born-Infeld scalar fields, linking it to inflationary tensor perturbations and observational prospects.

Findings

Hartle-Hawking wave function predicts $\

Vilenkin wave function suggests a larger cosmological constant.

Tensor perturbation amplitude could be detectable in future experiments.

Abstract

The Quantum cosmology with Born-Infeld(B-I) type scalar field is considered. In the extreme limits of small cosmological scale factor the wave function of the universe can also be obtained by applying the methods developed by Hartle-Hawking(H-H) and Vilenkin. H-H wave function predicts that most Probable cosmological constant $\Lambda$ equals to $\frac{1}{\eta}$($\frac{1}{2\eta}$ equals to the maximum of the kinetic energy of scalar field). It is different from the original results($\Lambda=0$) in cosmological constant obtained by Hartle-Hawking. The Vilenkin wave function predicts a nucleating unverse with largest possible cosmological constant and it is larger than $1/\eta$. The conclusions have been nicely to reconcile with cosmic inflation. We investigate the inflation model with B-I type scalar field, and find that $\eta$ depends on the amplitude of tensor perturbation $\delta_h$, with the form $\frac{1}{\eta}\simeq \frac{m^2}{12\pi[(\frac{9\delta_{\Phi}^2}{N \delta_h^2})^2-1]}.$ The vacuum energy in inflation epoch depends on the tensor-to-scalar ratio $\frac{\delta_h}{\delta_{\Phi}}$. The amplitude of the tensor perturbation ${\delta_{h}}$ can, in principle, be large enough to be discovered. However, it is only on the border of detectability in future experiments. If it has been observed in future, this is very interesting to determine the vacuum energy in inflation epoch.