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The Cosmological Perturbed Lightcone Gauge

Center for Space Research, North-West University, Potchefstroom 2531, South Africa
Universe 2018, 4(10), 108; https://doi.org/10.3390/universe4100108
Received: 7 September 2018 / Revised: 27 September 2018 / Accepted: 28 September 2018 / Published: 16 October 2018
The lightcone gauge is a set of what are called the observational coordinates adapted to our past lightcone. We develop this gauge by producing a perturbed spacetime metric that describes the geometry of our past lightcone where observations are usually obtained. We connect the produced observational metric to the perturbed Friedmann-Lemaître-Robertson-Walker (FLRW) metric in the standard general gauge or what is the so-called 1+3 gauge. We derive the relations between these perturbations of spacetime in the observational coordinates and those perturbations in the standard metric approach, as well as the dynamical equations for the perturbations in observational coordinates. We also calculate the observables in the lightcone gauge and re-derive them in terms of Bardeen potentials to first order. A verification is made of the observables in the perturbed lightcone gauge with those in the standard gauge. The advantage of the method developed is that the observable relations are simpler than in the standard formalism, and they are expressed in terms of the metric components which in principle are measurable. We use the perturbed lightcone gauge in galaxy surveys and the calculations of galaxy number density contrast. The significance of the new gauge is that by considering the null-like light propagations the calculations are much simpler due to the non-consideration of the angular deviations. View Full-Text
Keywords: general relativity; past lightcone gauge; direct observational approach; cosmological observables; galaxy surveys; galaxy number count; density contrast; overdensity; cosmological perturbations general relativity; past lightcone gauge; direct observational approach; cosmological observables; galaxy surveys; galaxy number count; density contrast; overdensity; cosmological perturbations
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Elmardi, M. The Cosmological Perturbed Lightcone Gauge. Universe 2018, 4, 108.

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