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The proper distance provides a measurement of how far is a galaxy at a fixed moment in time. At the present time the proper distance equals the comoving distance since the cosmological scale factor has value one: ${\displaystyle a(t_{0})=1}$. The proper distance represents the distance obtained as if one were able to freeze the flow of time (set ${\displaystyle dt=0}$ in the FLRW metric) and walk all the way to a galaxy while using a meter stick^[1]. For practical reason is calculated as the distance traveled by light (set ${\displaystyle ds=0}$ in the FLRW metric) from the time of emission by the galaxy to an observer (on Earth) at the present time. It differs form the light travel distance since the proper distance takes into account the expansion of the universe, i.e. the space expands as the light travels through it, resulting in numerical values which locate the most distant galaxies beyond the Hubble sphere and therefore with recessional velocities greater than the speed of light.^[2]  

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Most distant spectroscopically-confirmed objects

Most distant astronomical objects with spectroscopic redshift determinations

Image	Name	Redshift (z)	Light travel distance§ (Gly)[3][4][5][6]	Proper distance (Gly)	Type	Notes
	JADES-GS-z13-0	z = 13.20+0.04 −0.07	13.576[3] / 13.596[4] / 13.474[5] / 13.473[6]	33.6	Galaxy	Lyman-break galaxy, detection of the Lyman break with JWST/NIRSpec.[7] Possibly a dark star.[8]
	UNCOVER-z13	z = 13.079+0.014 −0.001	13.51		Galaxy	Lyman-break galaxy, detection of the Lyman break with JWST/NIRSpec.[9]
	JADES-GS-z12-0	z = 12.63+0.24 −0.08	13.556[3] / 13.576[4] / 13.454[5] / 13.453[6]		Galaxy	Lyman-break galaxy, detection of the Lyman break with JWST/NIRSpec.[7] Possibly a dark star.[8]
	UNCOVER-z12	z = 12.393+0.004 −0.001	13.48		Galaxy	Lyman-break galaxy, detection of the Lyman break with JWST/NIRSpec.[9]
	GLASS-z12	z = 12.117+0.01 −0.01	13.536[3] / 13.556[4] / 13.434[5] / 13.433[6]	33.2	Galaxy	Lyman-break galaxy discovered by JWST/NIRCam, confirmed by ALMA detection of [O III] emission[10]
	UDFj-39546284	z = 11.58+0.05 −0.05	13.512[3] / 13.532[4] / 13.410[5] / 13.409[6]		Galaxy	Lyman-break galaxy, detection of the Lyman break with JWST/NIRSpec.[7] Possibly a dark star.[8]
	CEERS J141946.36+525632.8 (Maisie's Galaxy) [11]	z = 11.44+0.09 −0.08	13.4		Galaxy	Lyman-break galaxy discovered by JWST
	CEERS2 588 [12]	z = 11.04	13.45		Galaxy	Lyman-break galaxy discovered by JWST
	GN-z11	z = 10.6034 ± 0.0013	13.481[3] / 13.501[4] / 13.380[5] / 13.379[6]		Galaxy	Lyman-break galaxy; detection of the Lyman break with HST at 5.5σ[13] and carbon emission lines with Keck/MOSFIRE at 5.3σ.[14] Conclusive redshift by JWST in February 2023[15]
	JADES-GS-z10-0 UDFj-39546284	z = 10.38+0.07 −0.06	13.449[3] / 13.469[4] / 13.348[5] / 13.347[6]		Galaxy	Lyman-break galaxy, detection of the Lyman break with JWST/NIRSpec[7]
	JD1	z = 9.793±0.002	13.409[3] / 13.429[4] / 13.308[5] / 13.307[6]		Galaxy	Lyman-break galaxy, detection of the Lyman break with JWST/NIRSpec[16]
	MACS1149-JD1	z = 9.1096±0.0006	13.361[3] / 13.381[4] / 13.261[5] / 13.260[6]	30.37	Galaxy	Detection of hydrogen emission line with the VLT, and oxygen line with ALMA[17]
	EGSY8p7	z = 8.683+0.001 −0.004	13.325[3] / 13.345[4] / 13.225[5] / 13.224[6]	30.05	Galaxy	Lyman-alpha emitter; detection of Lyman-alpha with Keck/MOSFIRE at 7.5σ confidence[18]
	SMACS-4590	z = 8.496	13.308[3] / 13.328[4] / 13.208[5] / 13.207[6]		Galaxy	Detection of hydrogen, oxygen, and neon emission lines with JWST/NIRSpec[19][20][21][22]
	A2744 YD4	z = 8.38	13.297[3] / 13.317[4] / 13.197[5] / 13.196[6]		Galaxy	Lyman-alpha and [O III] emission detected with ALMA at 4.0σ confidence[23]
	MACS0416 Y1	z = 8.3118±0.0003	13.290[3] / 13.310[4] / 13.190[5] / 13.189[6]		Galaxy	[O III] emission detected with ALMA at 6.3σ confidence[24]
	GRB 090423	z = 8.23+0.06 −0.07	13.282[3] / 13.302[4] / 13.182[5] / 13.181[6]	30.00	Gamma-ray burst	Lyman-alpha break detected[25]
	RXJ2129-11002	z = 8.16±0.01	13.175[3]		Galaxy	[O III] doublet, Hβ, and [O II] doublet as well as Lyman-alpha break detected with JWST/NIRSpec prism[26]
	RXJ2129-11022	z = 8.15±0.01	13.174[3]		Galaxy	[O III] doublet and Hβ as well as Lyman-alpha break detected with JWST/NIRSpec prism[26]
	EGS-zs8-1	z = 7.7302±0.0006	13.228[3] / 13.248[4] / 13.129[5] / 13.128[6]	29.5	Galaxy	Lyman-break galaxy[27]
	SMACS-6355	z = 7.665	13.221[3] / 13.241[4] / 13.121[5] / 13.120[6]		Galaxy	Detection of hydrogen, oxygen, and neon emission lines with JWST/NIRSpec[19][20][21][22]
	z7_GSD_3811	z = 7.6637±0.0011	13.221[3] / 13.240[4] / 13.121[5] / 13.120[6]		Galaxy	Lyman-alpha emitter[28]
	SMACS-10612	z = 7.658	13.221[3] / 13.241[4] / 13.120[5] / 13.119[6]		Galaxy	Detection of hydrogen, oxygen, and neon emission lines with JWST/NIRSpec[19][20][21]>[22]
	QSO J0313–1806	z = 7.6423±0.0013	13.218[3] / 13.238[4] / 13.119[5] / 13.118[6]	30.00	Quasar	Lyman-alpha break detected[29]
	ULAS J1342+0928	z = 7.5413±0.0007	13.206[3] / 13.226[4] / 13.107[5] / 13.106[6]	29.36	Quasar	Redshift estimated from [C II] emission[30]
	z8_GND_5296	z = 7.51	13.202[3] / 13.222[4] / 13.103[5] / 13.102[6]	30.01	Galaxy	Lyman-alpha emitter[31]
	A1689-zD1	z = 7.5±0.2	13.201[3] / 13.221[4] / 13.102[5] / 13.101[6]	30	Galaxy	Lyman-break galaxy[32]
	GS2_1406	z = 7.452±0.003	13.195[3] / 13.215[4] / 13.096[5] / 13.095[6]		Galaxy	Lyman-alpha emitter[33]
	GN-108036	z = 7.213	13.164[3] / 13.184[4] / 13.065[5] / 13.064[6]		Galaxy	Lyman alpha emitter[34]
	SXDF-NB1006-2	z = 7.2120±0.0003	13.164[3] / 13.184[4] / 13.065[5] / 13.064[6]		Galaxy	[O III] emission detected[35]
	BDF-3299	z = 7.109±0.002	13.149[3] / 13.169[4] / 13.051[5] / 13.050[6]		Galaxy	Lyman-break galaxy[36]
	ULAS J1120+0641	z = 7.085±0.003	13.146[3] / 13.166[4] / 13.048[5] / 13.047[6]		Quasar	Redshift estimated from Si III]+C III] and Mg II emission lines[37]
	A1703 zD6	z = 7.045±0.004	13.140[3] / 13.160[4] / 13.042[5] / 13.041[6]		Galaxy	Gravitationally-lensed Lyman-alpha emitter[38]
	BDF-521	z = 7.008±0.002	13.135[3] / 13.155[4] / 13.037[5] / 13.036[6]		Galaxy	Lyman-break galaxy[36]
	G2_1408	z = 6.972±0.002	13.130[3] / 13.150[4] / 13.032[5] / 13.030[6]		Galaxy	Lyman-alpha emitter[39]
	IOK-1	z = 6.965	13.129[3] / 13.149[4] / 13.030[5] / 13.029[6]		Galaxy	Lyman-alpha emitter[34]
	LAE J095950.99+021219.1	z = 6.944	13.126[3] / 13.146[4] / 13.028[5] / 13.027[6]		Galaxy	Lyman-alpha emitter[40]
	SDF-46975	z = 6.844	13.111[3] / 13.131[4] / 13.013[5] / 13.012[6]		Galaxy	Lyman-alpha emitter[34]
	PSO J172.3556+18.7734	z = 6.823+0.003 −0.001	13.107[3] / 13.127[4] / 13.010[5] / 13.009[6]		Quasar (astrophysical jet)	Redshift estimated from Mg II emission[41]
§ The tabulated distance is the light travel distance, which has no direct physical significance. See discussion at distance measures and Observable Universe

Test citation^[42]

1. Guidry, Mike (2019). Modern general relativity: black holes, gravitational waves, and cosmology. Cambridge New York: Cambridge university press. ISBN 978-1-107-19789-3.
2. Davis, Tamara M.; Lineweaver, Charles H. (2004). "Expanding Confusion: Common Misconceptions of Cosmological Horizons and the Superluminal Expansion of the Universe". Publications of the Astronomical Society of Australia. 21 (1): 97–109. doi:10.1071/AS03040. ISSN 1323-3580.
3. Staff (2015). "UCLA Cosmological Calculator". UCLA. Retrieved 6 August 2022. Light travel distance was calculated from redshift value using the UCLA Cosmological Calculator, with parameters values as of 2015: H₀=67.74 and Omega_M=0.3089 (see Table/Planck2015 at "Lambda-CDM model#Parameters" )
4. Staff (2018). "UCLA Cosmological Calculator". UCLA. Retrieved 6 August 2022. Light travel distance was calculated from redshift value using the UCLA Cosmological Calculator, with parameters values as of 2018: H₀=67.4 and Omega_M=0.315 (see Table/Planck2018 at "Lambda-CDM model#Parameters" )
5. Staff (2022). "ICRAR Cosmology Calculator". International Centre for Radio Astronomy Research. Retrieved 6 August 2022. ICRAR Cosmology Calculator - Set H₀=67.4 and Omega_M=0.315 (see Table/Planck2018 at "Lambda-CDM model#Parameters")
6. Kempner, Joshua (2022). "KEMPNER Cosmology Calculator". Kempner.net. Retrieved 6 August 2022. KEMP Cosmology Calculator - Set H₀=67.4, Omega_M=0.315, and Omega_Λ=0.6847 (see Table/Planck2018 at "Lambda-CDM model#Parameters")
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12. A bot will complete this citation soon. Click here to jump the queue arXiv:2304.06658.
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