Cosmic Clocks

Abstract

In a perturbed Universe, comoving tracers on a two-dimensional surface of constant observed redshift are at different proper time since the Big Bang. For tracers whose age is known independently, one can measure these perturbations of the proper time. Examples of such sources include cosmic events which only happen during a short period of cosmic history, as well as evolving standard candles and standard rulers. In this paper we derive a general gauge-invariant linear expression for this perturbation in terms of space-time perturbations. As an example, we show that the observed temperature perturbations of the cosmic microwave background (CMB) on large scales are exactly given by these proper time perturbations. Together with the six ruler perturbations derived in Schmidt and Jeong (2012), this completes the set of independent observables which can be measured with standard rulers and candles.

10 pages, 2 figures

References in corpus (3)

• New Perspective on Galaxy Clustering as a Cosmological Probe: General Relativistic Effects
• The Observed Squeezed Limit of Cosmological Three-Point Functions
• Superhorizon Perturbations and the Cosmic Microwave Background

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• N-body methods for relativistic cosmology
• Observed galaxy number counts on the lightcone up to second order: II. Derivation
• How Gaussian can our Universe be?
• Large-Scale Structure Observables in General Relativity
• Imprints of Oscillatory Bispectra on Galaxy Clustering
• Gauge-Invariance and Infrared Divergences in the Luminosity Distance
• The Limited Accuracy of Linearized Gravity
• Unified Treatment of the Luminosity Distance in Cosmology
• Spectral distortion anisotropies from single-field inflation
• Non-linear relativistic contributions to the cosmological weak-lensing convergence
• Large-scale imprint of relativistic effects in the cosmic magnification
• Covariant Decomposition of The Non-Linear Galaxy Number Counts and Their Monopole
• Long gradient mode and large-scale structure observables
• Incompatibility of Standard Galaxy Bias Models in General Relativity
• Non-linear power spectra in the synchronous gauge
• Observable Gravitational Wave Strain at Second Order
• The gauge invariant cosmological Jacobi map from weak lensing at leading order