Cosmology and Nongalactic Astrophysics · arXiv:1305.1299 v1 · submitted 6 May 2013
Cosmic Clocks
The paper says
“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.”
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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.
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abstract compiled · 2026-09-23 · no language-model review
How the main claim is stated: asserted 1.00
What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.81 · mentions code or data availability 0.02
The abstract, sentence by sentence
This table labels the abstract only (arXiv listing abstract v1). The number is the probability the classifier gave the label.
| Sentence | Role | The authors' own work | States the main conclusion | Strength |
|---|---|---|---|---|
| In a perturbed Universe, comoving tracers on a two-dimensional surface of constant observed redshift are at different proper time since the Big Bang. | background 0.98 | 0.11 | 0.08 | asserted 1.00 |
| For tracers whose age is known independently, one can measure these perturbations of the proper time. | background 0.49 | 0.10 | 0.05 | asserted 0.74 |
| 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. | background 0.80 | 0.08 | 0.03 | asserted 0.93 |
| In this paper we derive a general gauge-invariant linear expression for this perturbation in terms of space-time perturbations. | contribution 0.93 | 0.96 | 0.37 | asserted 1.00 |
| 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. | result 0.97 | 0.86 | 0.26 | asserted 1.00 |
| 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. | interpretation 0.80 | 0.51 | 0.21 | asserted 1.00 |
What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00
What was examined, and what was not
Sources read
- arXiv listing abstract v1
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- C citations
- R cross-paper relations
How the labels were made
Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,915 input tokens, $0.0002 reported.
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Cited by 10 Pith papers
Reviewed papers on Pith that cite this one. The full citation record
- Observed galaxy number counts on the lightcone up to second order: II. Derivation astro-ph.CO · Jun 2014
- The Cosmological Perturbation Theory on the Geodesic Light-Cone background gr-qc · Sep 2020
- How Gaussian can our Universe be? hep-th · Nov 2016
- On Separate Universes astro-ph.CO · Apr 2015
- Observed galaxy number counts on the lightcone up to second order: I. Main result astro-ph.CO · May 2014
- Large-Scale Structure and Gravitational Waves III: Tidal Effects astro-ph.CO · Dec 2013
- The Observed Squeezed Limit of Cosmological Three-Point Functions astro-ph.CO · May 2013
- Cosmic Rulers astro-ph.CO · Apr 2012
- Imprints of Oscillatory Bispectra on Galaxy Clustering astro-ph.CO · Apr 2018
- Cosmological Parameter Estimation with Large Scale Structure Observations astro-ph.CO · Aug 2013
How the literature uses it
15 arXiv papers cite this in 34 sentences
Papers citing it · 22 sentences without a confident label
Builds on it 1 paper
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First, we apply the cosmic ruler framework of Refs. [ref] to the galaxy number counts, and find a covariant decomposition for the observed galaxy density contrast $$ into an expression involving relatively simple, individually observable quantities, each of which has a clear physical meaning on its own.
Covariant Decomposition of The Non-Linear Galaxy Number Counts and Their Monopole · Introduction · 0.99
Uses its method or tool 3 papers
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However, these “projection effects” are independent of the dynamics, and can be computed separately, for example with the so-called ruler perturbations of [ref] (see also [ref] for similar approaches).] In Conformal Fermi Coordinates $(t_F,x⃗_F = q⃗)$, where $t_F$ is the proper time and $q⃗$ is the Lagrangian coordinate of comoving observers with the matter fluid, this “separate universe picture” is manifest, and we can define the Eulerian [equation] as the derivative of the proper density of halos of a given mass, averaged in the CFC patch, with respect to the contribution of the local curvature to the energy density.
Imprints of Oscillatory Bispectra on Galaxy Clustering · Bias as dependence from local curvature · 0.93
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In order to obtain $Δlna^(1)_o$ and $Δlna^(2)_o/2$ we can follow the prescription used in [ref] (which computes $a_o$ only at first order).
Observed galaxy number counts on the lightcone up to second order: II. Derivation · The observed redshift · 0.81
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They can be easily computed at linear order with the so-called ruler perturbations of [ref] (see also [ref] for similar approaches).
How Gaussian can our Universe be? · Connection to observations · 0.93
Compares with it 2 papers
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Furthermore, the expression [ref] of the $𝒯$-ruler reduces to [equation] These expressions recover those presented in [ref] , which emphasises that the two possible conventions for the $𝒞$ and $ℳ$ rulers presented in Section [ref] agree in this limit.
Covariant Decomposition of The Non-Linear Galaxy Number Counts and Their Monopole · Angular Power Spectrum in Einstein-de-Sitter Background · 0.96
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This can be easily seen by noticing that the first equation of Eqs [ref] combined within the first equation of Eqs. [ref] precisely returns Eq. (13) of [ref] .
The Cosmological Perturbation Theory on the Geodesic Light-Cone background · Gauge invariant observables in the geodesic light-cone perturbations · 0.89
Cites it as support 2 papers
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We note that the correct gauge-invariant calculation $δ𝒟_L= δ𝒟_L^std+δ𝒟_L^δτ_o$ has been presented [ref] with the coordinate lapse $δτ_o$ properly considered.
Gauge-Invariance and Infrared Divergences in the Luminosity Distance · Gauge-invariance of the Luminosity distance in an inhomogeneous universe · 0.97
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The $𝒯$-ruler is also gauge-invariant as demonstrated in [ref] .
Covariant Decomposition of The Non-Linear Galaxy Number Counts and Their Monopole · Gauge-invariance of $𝒞$ · 0.98
Cites it as background 3 papers
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In related studies, Refs. [ref] introduced the cosmic ruler and cosmic clock observables, for situations where the intrinsic shape or the proper time are known at the source's rest frame.
Covariant Decomposition of The Non-Linear Galaxy Number Counts and Their Monopole · Introduction · 0.85
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We refer interested readers to a systematic study of the relativistic projection effects on the galaxy power spectrum [ref] and on the squeezed galaxy bispectrum [ref] .
On Separate Universes · Squeezed matter bispectrum as measured by a local observer · 0.97
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The problem how the galaxy distribution, number counts and distance measurements are affected by the propagation of light in a perturbed geometry has also been investigated in other works; see, e.g. [ref] .
Cosmological Parameter Estimation with Large Scale Structure Observations · Introduction · 0.99
Challenges and discussion
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