Year-end Sale % OFF 
Abstract
We consider a recent approach to the construction of gauge-invariant relational observables in gravity in the context of cosmological perturbation theory. These observables are constructed using a field-dependent coordinate system, which we take to be geodesic lightcone coordinates. We show that the observables are gauge-independent in the fully non-linear theory, and that they have the expected form when one adopts the geodesic lightcone gauge for the metric. We give explicit expressions for the Sasaki-Mukhanov variable at linear order, and the Hubble rate — as measured both by geodesic observers and by observers co-moving with the inflaton — to second order. Moreover, we show that the well-known linearised equations of motion for the Sasaki-Mukhanov variable and the scalar constraint variables follow from the gauge-invariant Einstein's equations.
Highlights
These additional dust fields, change the physics of the system, i. e., modify the dynamics of gauge-invariant observables such as the Bardeen potentials [21] and the Sasaki
The idea is to construct them as solutions of scalar differential equations on the perturbed spacetime that are trivially satisfied by the background coordinates. This method is suited to the construction of invariant observables in perturbative gravity over highly symmetric backgrounds, such as the ones needed in cosmology
There are examples of coordinate systems adapted to measurements on the lightcone, such as the optical coordinates [34], the observational coordinates [35,36,37], and coordinates based on the past lightcone of geodesic observers, such as the proposal of Ref. [38] and the geodesic lightcone (GLC) coordinates [39]
Summary
We consider a spacetime with coordinates xμ and metric gμν, and assume that the metric can be written as a background metric gμν and perturbations: gμν ≡ gμν + κgμ(1ν). The invariant covariant derivative operator ∇μ allows us to perform calculations directly in the field-dependent coordinate system X (μ), rather than performing them first in the background coordinates and transforming the result using Eq (2.7) to produce a gaugeinvariant expression. This will considerably shorten some of the computations presented in
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
