New Approach to Evolving Gravitational Waves in Loop Quantum Cosmology

Abstract

With the observational advance in recent years, primordial gravitational waves (GWs), known as the tensor-mode cosmic perturbations, in the Loop Quantum Cosmology (LQC) are becoming testable and thus require better framework through which to bridge between the observations and the theories. In this work we present a new formalism that employs the transfer functions to bring the GWs from any epoch, even before the quantum bounce, to a later time, including the present. The evolutionary epochs considered here include the possible deflation, quantum bounce, and inflation. This formalism enables us to predict more accurately the GW power spectrum today. With the ADM formalism for the LQC background dynamics, our approach is equivalent to the commonly used Bogoliubov transformations for evolving the primordial GWs, but more transparent for discussions and easier to calculate due to its nature of being linear algebra dealing with linear perturbations. We utilize this advantage to have resolved the IR suppression problem. We also propose the field-free approximation for the effective mass in the quantum bounce epoch to largely improve the accuracy in the predicted GW power spectrum. Our transfer-function formalism is general in dealing with any linear problems, and thus expected to be equally useful under other context with linearity.

arXiv comment17 pages, 9 figures

References in corpus (19)

• Quantum Nature of the Big Bang: Improved dynamics
• Absence of Singularity in Loop Quantum Cosmology
• Real Ashtekar Variables for Lorentzian Signature Space-times
• Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
• The Inverse Scale Factor in Isotropic Quantum Geometry
• Loop quantum gravity corrections to gravitational wave dispersion
• On the Hamiltonian Constraint of Loop Quantum Cosmology
• Inflation in loop quantum cosmology: Dynamics and spectrum of gravitational waves
• Hamiltonian cosmological perturbation theory with loop quantum gravity corrections
• Gravitational waves from the Big Bounce
• Formation and Evolution of Structure in Loop Cosmology
• Comparison of primordial tensor power spectra from the deformed algebra and dressed metric approaches in loop quantum cosmology
• Observing the Big Bounce with Tensor Modes in the Cosmic Microwave Background: Phenomenology and Fundamental LQC Parameters
• Tensor power spectrum with holonomy corrections in LQC
• Relic gravitons as the observable for Loop Quantum Cosmology
• Loop quantum cosmology with higher order holonomy corrections
• How loopy is the quantum bounce? A heuristic analysis of higher order holonomy corrections in LQC
• Cosmological inflation driven by holonomy corrections of loop quantum cosmology
• Perturbations in loop quantum cosmology

Cited by in corpus (1)

• Time Asymmetry of Cosmic Background Evolution in Loop Quantum Cosmology