English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

The dressed metric and the hybrid approach to perturbations are the two mainapproaches to capture the effects of quantum geometry in the primordial powerspectrum in loop quantum cosmology. Both consider Fock quantized perturbationsover a loop quantized background and result in very similar predictions exceptfor the modes which exit the horizon in the effective spacetime in the Planckregime. Understanding precise relationship between both approaches has so farremained obscured due to differences in construction and technical assumptions.We explore this issue at the classical and effective spacetime level for linearperturbations, ignoring backreaction, which is the level at which practicalcomputations of the power spectrum in both of the approaches have so far beenperformed. We first show that at the classical level both the approaches leadto the same Hamiltonian up to the second order in perturbations and result inthe same classical mass functions in the Mukhanov-Sasaki equation on thephysical solutions. At the effective spacetime level, the difference inphenomenological predictions between the two approaches in the Planck regimecan be traced to whether one uses the Mukhanov-Sasaki variable $Q_{\vec k}$(the dressed metric approach) or its rescaled version $\nu_{\vec k}=aQ_{\veck}$ (the hybrid approach) to write the Hamiltonian of the perturbations, andassociated polymerization ambiguities. It turns out that if in the dressedmetric approach one chooses to work with $\nu_{\vec{k}}$, the effective massfunction can be written exactly as in the hybrid approach, thus leading toidentical phenomenological predictions in all regimes. Our results explicitlyshow that the dressed metric and the hybrid approaches for linearperturbations, at a practical computational level, can be seen as two sides ofthe same coin.

On a close relationship between the dressed metric and the hybrid approach to perturbations in effective loop quantum cosmology