scholarly journals Second order gauge invariant perturbation theory and conserved charges in cosmological Einstein gravity

2019 ◽  
Keyword(s):  
Perturbation Theory ◽  
Einstein Gravity ◽  
Second Order ◽  
Gauge Invariant ◽  
Conserved Charges ◽  
Invariant Perturbation Theory

scholarly journals Gauge invariant perturbation theory via homotopy transfer

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Christoph Chiaffrino ◽  
Olaf Hohm ◽  
Allison F. Pinto
Keyword(s):  
Perturbation Theory ◽  
Lie Algebras ◽  
Closed String ◽  
Cosmological Perturbation ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Cosmological Perturbation Theory ◽  
Invariant Perturbation Theory ◽  
General Gauge ◽  
Algorithmic Procedure

Abstract We show that the perturbative expansion of general gauge theories can be expressed in terms of gauge invariant variables to all orders in perturbations. In this we generalize techniques developed in gauge invariant cosmological perturbation theory, using Bardeen variables, by interpreting the passing over to gauge invariant fields as a homotopy transfer of the strongly homotopy Lie algebras encoding the gauge theory. This is illustrated for Yang-Mills theory, gravity on flat and cosmological backgrounds and for the massless sector of closed string theory. The perturbation lemma yields an algorithmic procedure to determine the higher corrections of the gauge invariant variables and the action in terms of these.

scholarly journals GAUGE-INVARIANT VARIABLES IN GENERAL-RELATIVISTIC PERTURBATIONS: GLOBALIZATION AND ZERO-MODE PROBLEM

2012 ◽  
Vol 21 (11) ◽  
pp. 1242004 ◽  
Author(s):  
KOUJI NAKAMURA
Keyword(s):  
Perturbation Theory ◽  
Zero Mode ◽  
Higher Order ◽  
Gauge Invariant ◽  
General Relativistic ◽  
Essential Problem ◽  
Invariant Perturbation Theory

An outline of a proof of the local decomposition of linear metric perturbations into gauge-invariant and gauge-variant parts on an arbitrary background spacetime is briefly explained. We explicitly construct the gauge-invariant and gauge-variant parts of the linear metric perturbations based on some assumptions. We also point out the zero-mode problem is an essential problem to globalize of this decomposition of linear metric perturbations. The resolution of this zero-mode problem implies the possibility of the development of the higher-order gauge-invariant perturbation theory on an arbitrary background spacetime in a global sense.

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