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/

Global: Zendy Plus annual

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

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Linear cosmological perturbation theory is pivotal to a theoreticalunderstanding of current cosmological experimental data provided e.g. by cosmicmicrowave anisotropy probes. A key issue in that theory is to extract the gaugeinvariant degrees of freedom which allow unambiguous comparison between theoryand experiment. When one goes beyond first (linear) order, the task of writingthe Einstein equations expanded to n'th order in terms of quantities that aregauge invariant up to terms of higher orders becomes highly non-trivial andcumbersome. This fact has prevented progress for instance on the issue of thestability of linear perturbation theory and is a subject of current debate inthe literature. In this series of papers we circumvent these difficulties bypassing to a manifestly gauge invariant framework. In other words, we onlyperturb gauge invariant, i.e. measurable quantities, rather than gauge variantones. Thus, gauge invariance is preserved non perturbatively while we constructthe perturbation theory for the equations of motion for the gauge invariantobservables to all orders. In this first paper we develop the general frameworkwhich is based on a seminal paper due to Brown and Kuchar as well as therealtional formalism due to Rovelli. In the second, companion, paper we applyour general theory to FRW cosmologies and derive the deviations from thestandard treatment in linear order. As it turns out, these deviations arenegligible in the late universe, thus our theory is in agreement with thestandard treatment. However, the real strength of our formalism is that itadmits a straightforward and unambiguous, gauge invariant generalisation tohigher orders. This will also allow us to settle the stability issue in afuture publication.

Manifestly Gauge-Invariant General Relativistic Perturbation Theory: I. Foundations