Gauge-invariant cosmological perturbation theory for collisionless matter: Application to the Einstein-Liouville system

1996 ◽  
Vol 28 (11) ◽  
pp. 1335-1359 ◽  
Author(s):  
Zbigniew Banach ◽  
Slawomir Piekarski
Keyword(s):  
Perturbation Theory ◽  
Cosmological Perturbation ◽  
Gauge Invariant ◽  
Cosmological 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 Second-Order Gauge-Invariant Cosmological Perturbation Theory: Current Status

2010 ◽  
Vol 2010 ◽  
pp. 1-26 ◽  
Author(s):  
Kouji Nakamura
Keyword(s):  
Perturbation Theory ◽  
Scalar Field ◽  
Second Order ◽  
Current Status ◽  
Cosmological Perturbation ◽  
Gauge Invariant ◽  
Cosmological Perturbation Theory ◽  
Theoretical Predictions ◽  
Recent Developments ◽  
The Universe

The current status of the recent developments of the second-order gauge-invariant cosmological perturbation theory is reviewed. To show the essence of this perturbation theory, we concentrate only on the universe filled with a single scalar field. Through this paper, we point out the problems which should be clarified for the further theoretical sophistication of this perturbation theory. We also expect that this theoretical sophistication will be also useful to discuss the theoretical predictions of non-Gaussianity in CMB and comparison with observations.

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