Galaxy bias and gauges at second order in General Relativity
Daniele Bertacca (Western Cape U. & AIfA Bonn), Nicola Bartolo (Padua, U. & INFN, Padua), Marco Bruni (Portsmouth U., ICG), Kazuya Koyama, (Portsmouth U., ICG), Roy Maartens (Western Cape U. & Portsmouth U., ICG),, Sabino Matarrese (Padua U. & INFN, Padua & GSSI, Aquila)
TL;DR
This paper examines gauge choices in second-order relativistic density perturbations, highlighting the unique suitability of the comoving-synchronous gauge for describing matter overdensities and Lagrangian bias.
Contribution
It clarifies misconceptions and establishes the comoving-synchronous gauge as the appropriate choice for second-order matter overdensity analysis in General Relativity.
Findings
The comoving-synchronous gauge uniquely corresponds to the Lagrangian frame.
This gauge is most suitable for describing second-order matter overdensity.
It resolves misconceptions in recent literature regarding gauge choices.
Abstract
We discuss the question of gauge choice when analysing relativistic density perturbations at second order. We compare Newtonian and General Relativistic approaches. Some misconceptions in the recent literature are addressed. We show that the comoving-synchronous gauge is the unique gauge in General Relativity that corresponds to the Lagrangian frame and is entirely appropriate to describe the matter overdensity at second order. The comoving-synchronous gauge is the simplest gauge in which to describe Lagrangian bias at second order.
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