Cosmic Clocks

TL;DR

This paper derives a gauge-invariant expression for proper time perturbations in a perturbed universe, linking them to observable phenomena like CMB temperature fluctuations and expanding the set of measurable cosmological observables.

Contribution

It provides a general linear gauge-invariant formula for proper time perturbations and relates these to observable CMB temperature fluctuations, completing the set of standard ruler and candle observables.

Findings

Proper time perturbations match large-scale CMB temperature fluctuations.

The derived formula is gauge-invariant and applicable to various cosmological sources.

Completes the set of independent observables for standard rulers and candles.

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.