暗能量是個謎，尤其暗能量是否會隨時間而變我們很難知曉。近期有研究提出，在次毫米波段所觀測到的高紅移 (high redshift, z > 1) 星系，透過偵測其一氧化碳（ＣＯ）放射譜線，其星系光度（luminosity）與譜線寬度（FWHM）存有ㄧ相關性。這種相關性有其潛在的重要性因為這樣的特性可作為一種方法來瞭解暗能量的時變性。然而，過去對於高紅移星系所觀測到的一氧化碳光度與譜線寬度的相關性(此後記做一氧化碳光度-譜線寬度相關性)時排除此相關性是否對於紅移（redshift）有變化。主要的問題是對於一氧化碳光度-譜線相關性的過去研究中，對同一星系且同樣是一氧化碳分子觀測，不同能階躍遷時的觀測資料也一併被引用。而所引用的觀測資料也存在較大的不確定性。為了降低觀測資料的不確定性，對於透過偵測星系一氧化碳的放射譜線，我們在本次的研究中只考慮單一的能階躍遷（分子旋轉量子數由第一激發態至基本能態，Ｊ＝1 - 0）以移除來自使用不同能階躍遷的數據所產生的不確定性。也因為一氧化碳Ｊ＝1 - 0的觀測數據頗多，我們在數據篩選時可以得到較多的同質性數據資料。除了一氧化碳，我們也彙集多個星系的碳離子放射譜線資料並研究是否和一氧化碳一樣也有類似的光度-譜線寬度相關性。由於碳離子的放射譜線強度一般比一氧化碳來得強，或許對於碳離子的相關研究可以幫助我們觸及到宇宙中更為遙遠也更高紅移的區域。對於一氧化碳的觀測資料篩選之後，我們將所得數據分為低紅移（z < 1）與高紅移（z > 1）兩組數據以探究這各自兩組數據中的光度-譜線寬度相關性是否會因紅移而有變化。一氧化碳的數據如此，碳離子數據也如此分類。而高紅移數據中，只要數據所屬星系有重力透鏡效應出現，其星系光度也會給予修正。不論一氧化碳或碳離子的放射譜線數據，其各自兩組資料（低紅移與高紅移）都以線性迴歸分析法找尋星系光度與譜線寬度的相關性。我們的研究發現其兩者物理量存有高度相關性，不論是高紅移或低紅移數據。更重要的是，兩組紅移數據的線性模型函數在統計上是一致的。也就是說，我們可以認定光度-譜線寬度線性關係是跟紅移無關，也幫助我們有能力估計遙遠星系的距離。有此甚者，我們也透過這樣的線性關係式去估計不同宇宙學模型中不同參數的值域。同時我們也討論未來對於此議題有何重要延伸研究。

Nature of dark energy remains unknown. Especially we do not know if it varies over time.
A correlation between CO luminosity (Lco) and full-width at half maximum(FWHM)
for high-redshift (z > 1) sub-millimeter galaxies has been proposed. This correlation is
potentially important because it may be used to constrain time variability of dark energy.
However, previous claims have been inadequate in ruling out possible redshift evolution
of the relation. Major problems include the use of heterogeneous samples (e.g., different
transition lines) and data with large observational uncertainties. In order to reduce the
uncertainty caused by using different rotational transitions, in this work, we only use
CO(J = 1 − 0) data, removing the large uncertainly in conversion between different
CO transitions. Such a homogeneous sample selection was possible because we have
much larger data than previous work thorough intensive archival search. In addition to
CO, as a new attempt, we investigated the [CII] luminosity-FWHM correlation. [CII]
emission line is in general brighter than CO lines. Therefore, the [CII] luminosity-FWHM
correlation may open a new possibility to reach even higher redshifts. To investigate
potential redshift evolution, for both CO and [CII] data, we separate the sample into the
low-z (z < 1) and high-z (z > 1) samples. We corrected for magnification factors as much
as possible. The linear regression results show that there exist a robust and significant
Lco-FWHM correlation in both low-z and high-z samples. Similarly, for the regressions
with [CII] data, significant L[CII]-FWHM correlations exist in the low-z and high-z
samples. Importantly, for both CO and [CII], no significant sign of redshift evolution
was detected between the two (low-z and high-z) samples. Therefore, the luminosity-
FWHM relation can be regarded as redshift-independent, opening a possibility to use
this relation to estimate distances toward higher redshifts. Motivated by the results, we
use the relation to constrain cosmological models. Data used are our high-z data (CO
and [CII]) and Type Ia Supernova data in the Union 2.1. The obtained constraints are
w0 = −1.01 ± 0.15 and wa = 2.46 ± 0.20. We discuss possible future prospects in using
the relation to further constrain cosmological parameters with expected data in the near
future.

Abstract i
List of Figures iv
List of Tables vi
Abbreviations viii
Physical Constants ix
Symbols x

1 Introduction 1

2 Data 5
2.1 CO Emission Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.1 Low-z Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.2 High-z Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 [CII]158μm Emission Line . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.1 Low-z Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.2 High-z Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3 Methods and Analysis 18
3.1 Line Luminosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.1.1 Correction For Gravitationally Lensing . . . . . . . . . . . . . . . . 19
3.2 FWHM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2.1 Correction For Inclination . . . . . . . . . . . . . . . . . . . . . . . 19
3.3 Linear Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4 Result 22
4.1 CO(1-0) Sample Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.1.1 The Significance of A Linear Relation . . . . . . . . . . . . . . . . 22
4.1.2 The Comparison Between The Correlations in Low-z and High-z
Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.2 [CII] Sample Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2.1 The Significance of A Linear Relation . . . . . . . . . . . . . . . . 24
4.2.2 The Comparison of Correlations in Low-z and High-z Samples . . 24
4.3 Discussions For the Statistical Results . . . . . . . . . . . . . . . . . . . . 26

5 Application 30
5.1 To Extend The Hubble Diagram . . . . . . . . . . . . . . . . . . . . . . . 35
5.2 Cosmological Constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

6 Discussions and Conclusions 40

Bibliography 43

[1] M. Aravena, E. J. Murphy, J. E. Aguirre, M. L. N. Ashby, B. A. Benson, M. Bothwell,
M. Brodwin, J. E. Carlstrom, S. C. Chapman, T. M. Crawford, C. de Breuck,
C. D. Fassnacht, A. H. Gonzalez, T. R. Greve, B. Gullberg, Y. Hezaveh, G. P.
Holder, W. L. Holzapfel, R. Keisler, M. Malkan, D. P. Marrone, V. McIntyre, C. L.
Reichardt, K. Sharon, J. S. Spilker, B. Stalder, A. A. Stark, J. D. Vieira, and
A. Weiß. Large gas reservoirs and free-free emission in two lensed star-forming
galaxies at z = 2.7. , 433:498–505, July 2013. doi: 10.1093/mnras/stt741.
[2] M. Aravena, J. S. Spilker, M. Bethermin, M. Bothwell, S. C. Chapman, C. de
Breuck, R. M. Furstenau, J. G´onzalez-L´opez, T. R. Greve, K. Litke, J. Ma,
M. Malkan, D. P. Marrone, E. J. Murphy, A. Stark, M. Strandet, J. D. Vieira,
A. Weiss, N. Welikala, G. F. Wong, and J. D. Collier. A survey of the cold molecular
gas in gravitationally lensed star-forming galaxies at z 2. , 457:4406–4420, Apr.
2016. doi: 10.1093/mnras/stw275.
[3] E. Ba˜nados, R. Decarli, F. Walter, B. P. Venemans, E. P. Farina, and X. Fan.
Bright [C II] 158 μm Emission in a Quasar Host Galaxy at z = 6.54. , 805:L8, May
2015. doi: 10.1088/2041-8205/805/1/L8.
[4] R. Bean and A. Melchiorri. Current constraints on the dark energy equation of
state. , 65(4):041302, Feb. 2002. doi: 10.1103/PhysRevD.65.041302.
[5] M. S. Bothwell, I. Smail, S. C. Chapman, R. Genzel, R. J. Ivison, L. J. Tacconi,
S. Alaghband-Zadeh, F. Bertoldi, A. W. Blain, C. M. Casey, P. Cox, T. R. Greve,
D. Lutz, R. Neri, A. Omont, and A. M. Swinbank. A survey of molecular gas in
luminous sub-millimetre galaxies. , 429:3047–3067, Mar. 2013. doi: 10.1093/mnras/
sts562.
[6] C. L. Carilli and F. Walter. Cool Gas in High-Redshift Galaxies. , 51:105–161,
Aug. 2013. doi: 10.1146/annurev-astro-082812-140953.
[7] C. L. Carilli, P. Cox, F. Bertoldi, K. M. Menten, A. Omont, S. G. Djorgovski,
A. Petric, A. Beelen, K. G. Isaak, and R. G. McMahon. Imaging Low-Order CO
Emission from the z=4.12 Quasi-Stellar Object PSS J2322+1944. , 575:145–149,
Aug. 2002. doi: 10.1086/341269.
[8] S. Chatterjee, C. J. Law, R. S. Wharton, S. Burke-Spolaor, J. W. T. Hessels, G. C.
Bower, J. M. Cordes, S. P. Tendulkar, C. G. Bassa, P. Demorest, B. J. Butler,
A. Seymour, P. Scholz, M. W. Abruzzo, S. Bogdanov, V. M. Kaspi, A. Keimpema,
T. J.W. Lazio, B. Marcote, M. A. McLaughlin, Z. Paragi, S. M. Ransom, M. Rupen,
L. G. Spitler, and H. J. van Langevelde. A direct localization of a fast radio burst
and its host. , 541:58–61, Jan. 2017. doi: 10.1038/nature20797.
[9] M. Chevallier and D. Polarski. Accelerating Universes with Scaling Dark Matter.
International Journal of Modern Physics D, 10:213–223, 2001. doi: 10.1142/
S0218271801000822.
[10] C. De Breuck, R. J. Williams, M. Swinbank, P. Caselli, K. Coppin, T. A. Davis,
R. Maiolino, T. Nagao, I. Smail, F. Walter, A. Weiß, and M. A. Zwaan. ALMA
resolves turbulent, rotating [CII] emission in a young starburst galaxy at z = 4.8. ,
565:A59, May 2014. doi: 10.1051/0004-6361/201323331.
[11] R. Decarli, F. Walter, B. P. Venemans, E. Ba˜nados, F. Bertoldi, C. Carilli, X. Fan,
E. P. Farina, C. Mazzucchelli, D. Riechers, H.-W. Rix, M. A. Strauss, R. Wang,
and Y. Yang. An ALMA [C II] Survey of 27 Quasars at z5.94. , 854:97, Feb. 2018.
doi: 10.3847/1538-4357/aaa5aa.
[12] B. H. C. Emonts, I. Feain, M. Y. Mao, R. P. Norris, G. Miley, R. D. Ekers, M. Villar-
Mart´ın, H. J. A. R¨ottgering, E. M. Sadler, G. Rees, R. Morganti, D. J. Saikia, T. A.
Oosterloo, J. B. Stevens, and C. N. Tadhunter. Molecular CO(1-0) Gas in the z ˜ 2
Radio Galaxy MRC 0152-209. , 734:L25, June 2011. doi: 10.1088/2041-8205/734/
1/L25.
[13] B. H. C. Emonts, R. P. Norris, I. Feain, M. Y. Mao, R. D. Ekers, G. Miley, N. Seymour,
H. J. A. Rttgering, M. Villar-Martn, E. M. Sadler, C. L. Carilli, E. K. Mahony,
C. de Breuck, A. Stroe, L. Pentericci, G. A. van Moorsel, G. Drouart, R. J. Ivison,
T. R. Greve, A. Humphrey, D. Wylezalek, and C. N. Tadhunter. Co(10) survey
of high-z radio galaxies: alignment of molecular halo gas with distant radio sources.
Monthly Notices of the Royal Astronomical Society, 438(4):2898–2915, 2014. doi:
10.1093/mnras/stt2398. URL http://dx.doi.org/10.1093/mnras/stt2398.
[14] D. Farrah, V. Lebouteiller, H. W. W. Spoon, J. Bernard-Salas, C. Pearson,
D. Rigopoulou, H. A. Smith, E. Gonz´alez-Alfonso, D. L. Clements, A. Efstathiou,
D. Cormier, J. Afonso, S. M. Petty, K. Harris, P. Hurley, C. Borys, A. Verma,
A. Cooray, and V. Salvatelli. Far-infrared Fine-structure Line Diagnostics of Ultraluminous
Infrared Galaxies. , 776:38, Oct. 2013. doi: 10.1088/0004-637X/776/1/38.
[15] D. T. Frayer, A. I. Harris, A. J. Baker, R. J. Ivison, I. Smail, M. Negrello, R. Maddalena,
I. Aretxaga, M. Baes, M. Birkinshaw, D. G. Bonfield, D. Burgarella,
S. Buttiglione, A. Cava, D. L. Clements, A. Cooray, H. Dannerbauer, A. Dariush,
G. De Zotti, J. S. Dunlop, L. Dunne, S. Dye, S. Eales, J. Fritz, J. Gonzalez-Nuevo,
D. Herranz, R. Hopwood, D. H. Hughes, E. Ibar, M. J. Jarvis, G. Lagache, L. L.
Leeuw, M. Lopez-Caniego, S. Maddox, M. J. Micha lowski, A. Omont, M. Pohlen,
E. Rigby, G. Rodighiero, D. Scott, S. Serjeant, D. J. B. Smith, A. M. Swinbank,
P. Temi, M. A. Thompson, I. Valtchanov, P. P. van der Werf, and A. Verma.
Green Bank Telescope Zpectrometer CO(1-0) Observations of the Strongly Lensed
Submillimeter Galaxies from the Herschel ATLAS. , 726:L22, Jan. 2011. doi:
10.1088/2041-8205/726/2/L22.
[16] W. L. Freedman, B. F. Madore, B. K. Gibson, L. Ferrarese, D. D. Kelson, S. Sakai,
J. R. Mould, R. C. Kennicutt, Jr., H. C. Ford, J. A. Graham, J. P. Huchra, S. M. G.
Hughes, G. D. Illingworth, L. M. Macri, and P. B. Stetson. Final Results from the
Hubble Space Telescope Key Project to Measure the Hubble Constant. , 553:47–72,
May 2001. doi: 10.1086/320638.
[17] A. Friedmann. ¨Uber die M¨oglichkeit einerWelt mit konstanter negativer Kr¨ummung
des Raumes. Zeitschrift fur Physik, 21:326–332, Dec. 1924. doi: 10.1007/
BF01328280.
[18] H. Fu, A. Cooray, C. Feruglio, R. J. Ivison, D. A. Riechers, M. Gurwell, R. S. Bussmann,
A. I. Harris, B. Altieri, H. Aussel, A. J. Baker, J. Bock, M. Boylan-Kolchin,
C. Bridge, J. A. Calanog, C. M. Casey, A. Cava, S. C. Chapman, D. L. Clements,
A. Conley, P. Cox, D. Farrah, D. Frayer, R. Hopwood, J. Jia, G. Magdis, G. Marsden,
P. Mart´ınez-Navajas, M. Negrello, R. Neri, S. J. Oliver, A. Omont, M. J. Page,
I. P´erez-Fournon, B. Schulz, D. Scott, A. Smith, M. Vaccari, I. Valtchanov, J. D.
Vieira, M. Viero, L. Wang, J. L. Wardlow, and M. Zemcov. The rapid assembly of
an elliptical galaxy of 400 billion solar masses at a redshift of 2.3. , 498:338–341,
June 2013. doi: 10.1038/nature12184.
[19] H. Gao, Z. Li, and B. Zhang. FAST RADIO BURST/GAMMA-RAY BURST
COSMOGRAPHY. The Astrophysical Journal, 788(2):189, jun 2014. doi:
10.1088/0004-637x/788/2/189. URL https://doi.org/10.1088%2F0004-637x%
2F788%2F2%2F189.
[20] T. Goto and S. Toft. CO luminosity - line-width correlation of submillimeter
galaxies and a possible cosmological application. , 579:A17, July 2015. doi:
10.1051/0004-6361/201526062.
[21] O. Graur, D. Poznanski, D. Maoz, N. Yasuda, T. Totani, M. Fukugita, A. V.
Filippenko, R. J. Foley, J. M. Silverman, A. Gal-Yam, A. Horesh, and B. T. Jannuzi.
Supernovae in the Subaru Deep Field: the rate and delay-time distribution of Type
Ia supernovae out to redshift 2. , 417:916–940, Oct. 2011. doi: 10.1111/j.1365-2966.
2011.19287.x.
[22] B. Gullberg, C. De Breuck, J. D. Vieira, A. Weiß, J. E. Aguirre, M. Aravena,
M. B´ethermin, C. M. Bradford, M. S. Bothwell, J. E. Carlstrom, S. C. Chapman,
C. D. Fassnacht, A. H. Gonzalez, T. R. Greve, Y. Hezaveh, W. L. Holzapfel, K. Husband,
J. Ma, M. Malkan, D. P. Marrone, K. Menten, E. J. Murphy, C. L. Reichardt,
J. S. Spilker, A. A. Stark, M. Strandet, and N. Welikala. The nature of the [C II]
emission in dusty star-forming galaxies from the SPT survey. , 449:2883–2900, May
2015. doi: 10.1093/mnras/stv372.
[23] L. J. Hainline, A. W. Blain, T. R. Greve, S. C. Chapman, I. Smail, and R. J. Ivison.
Observing Cold Gas in Submillimeter Galaxies: Detection of CO (1–0) Emission in
SMM J13120+4242 with the Green Bank Telescope. , 650:614–623, Oct. 2006. doi:
10.1086/507443.
[24] A. I. Harris, A. J. Baker, S. G. Zonak, C. E. Sharon, R. Genzel, K. Rauch, G.Watts,
and R. Creager. CO J = 1-0 Spectroscopy of Four Submillimeter Galaxies with the
Zpectrometer on the Green Bank Telescope. , 723:1139–1149, Nov. 2010. doi:
10.1088/0004-637X/723/2/1139.
[25] A. I. Harris, A. J. Baker, D. T. Frayer, I. Smail, A. M. Swinbank, D. A. Riechers,
P. P. van derWerf, R. Auld, M. Baes, R. S. Bussmann, S. Buttiglione, A. Cava, D. L.
Clements, A. Cooray, H. Dannerbauer, A. Dariush, G. De Zotti, L. Dunne, S. Dye,
S. Eales, J. Fritz, J. Gonz´alez-Nuevo, R. Hopwood, E. Ibar, R. J. Ivison, M. J.
Jarvis, S. Maddox, M. Negrello, E. Rigby, D. J. B. Smith, P. Temi, and J. Wardlow.
Blind Detections of CO J = 1-0 in 11 H-ATLAS Galaxies at z = 2.1-3.5 with the
GBT/Zpectrometer. , 752:152, June 2012. doi: 10.1088/0004-637X/752/2/152.
[26] E. Hubble. A Relation between Distance and Radial Velocity among Extra-Galactic
Nebulae. , 15:168–173, Mar. 1929. doi: 10.1073/pnas.15.3.168.
[27] E. Ibar, M. A. Lara-L´opez, R. Herrera-Camus, R. Hopwood, A. Bauer, R. J. Ivison,
M. J. Micha lowski, H. Dannerbauer, P. van der Werf, D. Riechers, N. Bourne,
M. Baes, I. Valtchanov, L. Dunne, A. Verma, S. Brough, A. Cooray, G. De Zotti,
S. Dye, S. Eales, C. Furlanetto, S. Maddox, M. Smith, O. Steele, D. Thomas,
and E. Valiante. A multiwavelength exploration of the [C II]/IR ratio in HATLAS/
GAMA galaxies out to z = 0.2. , 449:2498–2513, May 2015. doi:
10.1093/mnras/stv439.
[28] R. J. Ivison, P. P. Papadopoulos, I. Smail, T. R. Greve, A. P. Thomson, E. M.
Xilouris, and S. C. Chapman. Tracing the molecular gas in distant submillimetre
galaxies via CO(1-0) imaging with the Expanded Very Large Array. , 412:1913–
1925, Apr. 2011. doi: 10.1111/j.1365-2966.2010.18028.x.
[29] M. Jaroszynski. Fast Radio Bursts and cosmological tests. 2018. doi: 10.1093/
mnras/sty3529.
[30] D. O. Jones, S. A. Rodney, A. G. Riess, B. Mobasher, T. Dahlen, C. McCully, T. F.
Frederiksen, S. Casertano, J. Hjorth, C. R. Keeton, A. Koekemoer, L.-G. Strolger,
T. G. Wiklind, P. Challis, O. Graur, B. Hayden, B. Patel, B. J. Weiner, A. V.
Filippenko, P. Garnavich, S. W. Jha, R. P. Kirshner, H. C. Ferguson, N. A. Grogin,
and D. Kocevski. The Discovery of the Most Distant Known Type Ia Supernova at
Redshift 1.914. , 768:166, May 2013. doi: 10.1088/0004-637X/768/2/166.
[31] B. C. Kelly. Some Aspects of Measurement Error in Linear Regression of Astronomical
Data. , 665:1489–1506, Aug. 2007. doi: 10.1086/519947.
[32] A. L. King, T. M. Davis, K. D. Denney, M. Vestergaard, and D. Watson. Highredshift
standard candles: predicted cosmological constraints. , 441:3454–3476, July
2014. doi: 10.1093/mnras/stu793.
[33] K. K. Knudsen, J. Richard, J.-P. Kneib, M. Jauzac, B. Cl´ement, G. Drouart,
E. Egami, and L. Lindroos. [C II] emission in z
6 strongly lensed, star-forming galaxies. , 462:L6–L10, Oct. 2016. doi: 10.1093/
mnrasl/slw114.
[34] G. Lemaˆıtre. Expansion of the universe, A homogeneous universe of constant mass
and increasing radius accounting for the radial velocity of extra-galactic nebulae. ,
91:483–490, Mar. 1931. doi: 10.1093/mnras/91.5.483.
[35] J.-F. Lestrade, C. L. Carilli, K. Thanjavur, J.-P. Kneib, D. A. Riechers, F. Bertoldi,
F. Walter, and A. Omont. A Molecular Einstein Ring Toward the z = 3.93 Submillimeter
Galaxy MM18423+5938. , 739:L30, Sept. 2011. doi: 10.1088/2041-8205/
739/1/L30.
[36] E. V. Linder. Exploring the Expansion History of the Universe. Physical Review
Letters, 90(9):091301, Mar. 2003. doi: 10.1103/PhysRevLett.90.091301.
[37] D. Lorimer. Cosmology: Home of a fast radio burst. , 530:427–428, Feb. 2016. doi:
10.1038/530427a.
[38] B. Magnelli, A. Saintonge, D. Lutz, L. J. Tacconi, S. Berta, F. Bournaud, V. Charmandaris,
H. Dannerbauer, D. Elbaz, N. M. F¨orster-Schreiber, J. Graci´a-Carpio,
R. Ivison, R. Maiolino, R. Nordon, P. Popesso, G. Rodighiero, P. Santini, and
S. Wuyts. Dust temperature and CO H2 conversion factor variations in the SFRM
plane. , 548:A22, Dec. 2012. doi: 10.1051/0004-6361/201220074.
[39] M. Neeleman, N. Kanekar, J. X. Prochaska, M. Rafelski, C. L. Carilli, and A. M.
Wolfe. [C II] 158-μm emission from the host galaxies of damped Lyman-alpha
systems. Science, 355:1285–1288, Mar. 2017. doi: 10.1126/science.aal1737.
[40] M. Negrello, R. Hopwood, S. Dye, E. d. Cunha, S. Serjeant, J. Fritz, K. Rowlands,
S. Fleuren, R. S. Bussmann, A. Cooray, H. Dannerbauer, J. Gonzalez-Nuevo,
A. Lapi, A. Omont, S. Amber, R. Auld, M. Baes, S. Buttiglione, A. Cava, L. Danese,
A. Dariush, G. De Zotti, L. Dunne, S. Eales, E. Ibar, R. J. Ivison, S. Kim, L. Leeuw,
S. Maddox, M. J. Micha lowski, M. Massardi, E. Pascale, M. Pohlen, E. Rigby,
D. J. B. Smith, W. Sutherland, P. Temi, and J. Wardlow. Herschel *-ATLAS: deep
HST/WFC3 imaging of strongly lensed submillimetre galaxies. , 440:1999–2012,
May 2014. doi: 10.1093/mnras/stu413.
[41] R. Pavesi, D. A. Riechers, P. L. Capak, C. L. Carilli, C. E. Sharon, G. J. Stacey,
A. Karim, N. Z. Scoville, and V. Smolˇci´c. ALMA Reveals Weak [N II] Emission in
“Typical” Galaxies and Intense Starbursts at z = 5-6. , 832:151, Dec. 2016. doi:
10.3847/0004-637X/832/2/151.
[42] S. Perlmutter, G. Aldering, G. Goldhaber, R. A. Knop, P. Nugent, P. G. Castro,
S. Deustua, S. Fabbro, A. Goobar, D. E. Groom, I. M. Hook, A. G. Kim, M. Y.
Kim, J. C. Lee, N. J. Nunes, R. Pain, C. R. Pennypacker, R. Quimby, C. Lidman,
R. S. Ellis, M. Irwin, R. G. McMahon, P. Ruiz-Lapuente, N. Walton, B. Schaefer,
B. J. Boyle, A. V. Filippenko, T. Matheson, A. S. Fruchter, N. Panagia, H. J. M.
Newberg, W. J. Couch, and T. S. C. Project. Measurements of ⌦ and ⇤ from 42
High-Redshift Supernovae. , 517:565–586, June 1999. doi: 10.1086/307221.
[43] Planck Collaboration, N. Aghanim, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi,
M. Ballardini, A. J. Banday, R. B. Barreiro, N. Bartolo, S. Basak, R. Battye,
K. Benabed, J.-P. Bernard, M. Bersanelli, P. Bielewicz, J. J. Bock, J. R. Bond,
J. Borrill, F. R. Bouchet, F. Boulanger, M. Bucher, C. Burigana, R. C. Butler,
E. Calabrese, J.-F. Cardoso, J. Carron, A. Challinor, H. C. Chiang, J. Chluba,
L. P. L. Colombo, C. Combet, D. Contreras, B. P. Crill, F. Cuttaia, P. de Bernardis,
G. de Zotti, J. Delabrouille, J.-M. Delouis, E. Di Valentino, J. M. Diego, O. Dor´e,
M. Douspis, A. Ducout, X. Dupac, S. Dusini, G. Efstathiou, F. Elsner, T. A.
Enßlin, H. K. Eriksen, Y. Fantaye, M. Farhang, J. Fergusson, R. Fernandez-Cobos,
F. Finelli, F. Forastieri, M. Frailis, E. Franceschi, A. Frolov, S. Galeotta, S. Galli,
K. Ganga, R. T. G´enova-Santos, M. Gerbino, T. Ghosh, J. Gonz´alez-Nuevo, K. M.
G´orski, S. Gratton, A. Gruppuso, J. E. Gudmundsson, J. Hamann, W. Handley,
D. Herranz, E. Hivon, Z. Huang, A. H. Ja↵e, W. C. Jones, A. Karakci, E. Keih¨anen, R. Keskitalo, K. Kiiveri, J. Kim, T. S. Kisner, L. Knox, N. Krachmalnico↵,
M. Kunz, H. Kurki-Suonio, G. Lagache, J.-M. Lamarre, A. Lasenby, M. Lattanzi,
C. R. Lawrence, M. Le Jeune, P. Lemos, J. Lesgourgues, F. Levrier, A. Lewis,
M. Liguori, P. B. Lilje, M. Lilley, V. Lindholm, M. L´opez-Caniego, P. M. Lubin,
Y.-Z. Ma, J. F. Mac´ıas-P´erez, G. Maggio, D. Maino, N. Mandolesi, A. Mangilli,
A. Marcos-Caballero, M. Maris, P. G. Martin, M. Martinelli, E. Mart´ınez-Gonz´alez,
S. Matarrese, N. Mauri, J. D. McEwen, P. R. Meinhold, A. Melchiorri, A. Mennella,
M. Migliaccio, M. Millea, S. Mitra, M.-A. Miville-Deschˆenes, D. Molinari,
L. Montier, G. Morgante, A. Moss, P. Natoli, H. U. Nørgaard-Nielsen, L. Pagano,
D. Paoletti, B. Partridge, G. Patanchon, H. V. Peiris, F. Perrotta, V. Pettorino,
F. Piacentini, L. Polastri, G. Polenta, J.-L. Puget, J. P. Rachen, M. Reinecke,
M. Remazeilles, A. Renzi, G. Rocha, C. Rosset, G. Roudier, J. A. Rubi˜no-Mart´ın,
B. Ruiz-Granados, L. Salvati, M. Sandri, M. Savelainen, D. Scott, E. P. S. Shellard,
C. Sirignano, G. Sirri, L. D. Spencer, R. Sunyaev, A.-S. Suur-Uski, J. A. Tauber,
D. Tavagnacco, M. Tenti, L. To↵olatti, M. Tomasi, T. Trombetti, L. Valenziano,
J. Valiviita, B. Van Tent, L. Vibert, P. Vielva, F. Villa, N. Vittorio, B. D. Wandelt,
I. K. Wehus, M. White, S. D. M. White, A. Zacchei, and A. Zonca. Planck 2018
results. VI. Cosmological parameters. ArXiv e-prints, July 2018.
[44] D. A. Riechers. Molecular Gas in Lensed z 2 Quasar Host Galaxies and the Star
Formation Law for Galaxies with Luminous Active Galactic Nuclei. , 730:108, Apr.
2011. doi: 10.1088/0004-637X/730/2/108.
[45] D. A. Riechers, F. Walter, C. L. Carilli, K. K. Knudsen, K. Y. Lo, D. J. Benford,
J. G. Staguhn, T. R. Hunter, F. Bertoldi, C. Henkel, K. M. Menten, A. Weiss, M. S.
Yun, and N. Z. Scoville. CO(1-0) in z ˜ 4 Quasar Host Galaxies: No Evidence for
Extended Molecular Gas Reservoirs. , 650:604–613, Oct. 2006. doi: 10.1086/507014.
[46] D. A. Riechers, F. Walter, C. L. Carilli, and G. F. Lewis. Imaging The Molecular
Gas in a z = 3.9 Quasar Host Galaxy at 0farcs3 Resolution: A Central, Sub-
Kiloparsec Scale Star Formation Reservoir in APM 08279+5255. , 690:463–485,
Jan. 2009. doi: 10.1088/0004-637X/690/1/463.
[47] D. A. Riechers, C. L. Carilli, F. Walter, and E. Momjian. Total Molecular Gas
Masses of z ˜ 3 Lyman- break Galaxies: CO(J = 1 0) Emission in MS 1512-cB58 and
the Cosmic Eye. , 724:L153–L157, Dec. 2010. doi: 10.1088/2041-8205/724/2/L153.
[48] D. A. Riechers, C. L. Carilli, R. J. Maddalena, J. Hodge, A. I. Harris, A. J. Baker,
F. Walter, J. Wagg, P. A. Vanden Bout, A. Weiß, and C. E. Sharon. CO(J = 10)
in z 2 Quasar Host Galaxies: No Evidence for Extended Molecular Gas Reservoirs.
, 739:L32, Sept. 2011. doi: 10.1088/2041-8205/739/1/L32.
[49] D. A. Riechers, A. Cooray, A. Omont, R. Neri, A. I. Harris, A. J. Baker, P. Cox,
D. T. Frayer, J. M. Carpenter, R. Auld, H. Aussel, A. Beelen, R. Blundell, J. Bock,
D. Brisbin, D. Burgarella, P. Chanial, S. C. Chapman, D. L. Clements, A. Conley,
C. D. Dowell, S. Eales, D. Farrah, A. Franceschini, R. Gavazzi, J. Glenn, M. Griffin,
M. Gurwell, R. J. Ivison, S. Kim, M. Krips, A. M. J. Mortier, S. J. Oliver, M. J.
Page, A. Papageorgiou, C. P. Pearson, I. P´erez-Fournon, M. Pohlen, J. I. Rawlings,
G. Raymond, G. Rodighiero, I. G. Roseboom, M. Rowan-Robinson, K. S. Scott,
N. Seymour, A. J. Smith, M. Symeonidis, K. E. Tugwell, M. Vaccari, J. D. Vieira,
L. Vigroux, L. Wang, J. Wardlow, and G. Wright. Dynamical Structure of the
Molecular Interstellar Medium in an Extremely Bright, Multiply Lensed z ˜= 3
Submillimeter Galaxy Discovered with Herschel. , 733:L12, May 2011. doi: 10.
1088/2041-8205/733/1/L12.
[50] D. A. Riechers, C. M. Bradford, D. L. Clements, C. D. Dowell, I. P´erez-Fournon,
R. J. Ivison, C. Bridge, A. Conley, H. Fu, J. D. Vieira, J. Wardlow, J. Calanog,
A. Cooray, P. Hurley, R. Neri, J. Kamenetzky, J. E. Aguirre, B. Altieri, V. Arumugam,
D. J. Benford, M. B´ethermin, J. Bock, D. Burgarella, A. Cabrera-Lavers,
S. C. Chapman, P. Cox, J. S. Dunlop, L. Earle, D. Farrah, P. Ferrero, A. Franceschini,
R. Gavazzi, J. Glenn, E. A. G. Solares, M. A. Gurwell, M. Halpern, E. Hatziminaoglou,
A. Hyde, E. Ibar, A. Kov´acs, M. Krips, R. E. Lupu, P. R. Maloney,
P. Martinez-Navajas, H. Matsuhara, E. J. Murphy, B. J. Naylor, H. T. Nguyen, S. J.
Oliver, A. Omont, M. J. Page, G. Petitpas, N. Rangwala, I. G. Roseboom, D. Scott,
A. J. Smith, J. G. Staguhn, A. Streblyanska, A. P. Thomson, I. Valtchanov,
M. Viero, L. Wang, M. Zemcov, and J. Zmuidzinas. A dust-obscured massive
maximum-starburst galaxy at a redshift of 6.34. , 496:329–333, Apr. 2013. doi:
10.1038/nature12050.
[51] A. G. Riess, A. V. Filippenko, P. Challis, A. Clocchiatti, A. Diercks, P. M. Garnavich,
R. L. Gilliland, C. J. Hogan, S. Jha, R. P. Kirshner, B. Leibundgut, M. M.
Phillips, D. Reiss, B. P. Schmidt, R. A. Schommer, R. C. Smith, J. Spyromilio, C. Stubbs, N. B. Suntze↵, and J. Tonry. Observational Evidence from Supernovae
for an Accelerating Universe and a Cosmological Constant. , 116:1009–1038, Sept.
1998. doi: 10.1086/300499.
[52] A. G. Riess, L.-G. Strolger, J. Tonry, S. Casertano, H. C. Ferguson, B. Mobasher,
P. Challis, A. V. Filippenko, S. Jha, W. Li, R. Chornock, R. P. Kirshner, B. Leibundgut,
M. Dickinson, M. Livio, M. Giavalisco, C. C. Steidel, T. Benitez, and
Z. Tsvetanov. Type ia supernova discoveries atz 1 from theHubble space telescope:
Evidence for past deceleration and constraints on dark energy evolution.
The Astrophysical Journal, 607(2):665–687, jun 2004. doi: 10.1086/383612. URL
https://doi.org/10.1086%2F383612.
[53] A. G. Riess, L. Macri, S. Casertano, H. Lampeitl, H. C. Ferguson, A. V. Filippenko,
S. W. Jha, W. Li, and R. Chornock. A 3% Solution: Determination of the Hubble
Constant with the Hubble Space Telescope and Wide Field Camera 3. , 730:119,
Apr. 2011. doi: 10.1088/0004-637X/730/2/119.
[54] H. P. Robertson. Kinematics and World-Structure III. , 83:257, May 1936. doi:
10.1086/143726.
[55] L. Sargsyan, V. Lebouteiller, D. Weedman, H. Spoon, J. Bernard-Salas, D. Engels,
G. Stacey, J. Houck, D. Barry, J. Miles, and A. Samsonyan. [c ii] 158 m
luminosities and star formation rate in dusty starbursts and active galactic nuclei.
The Astrophysical Journal, 755(2):171, 2012. URL http://stacks.iop.org/
0004-637X/755/i=2/a=171.
[56] C. E. Sharon, A. J. Baker, A. I. Harris, and A. P. Thomson. Very Large Array
Mapping of the CO(1-0) Line in SMM J14011+0252. , 765:6, Mar. 2013. doi:
10.1088/0004-637X/765/1/6.
[57] C. E. Sharon, D. A. Riechers, J. Hodge, C. L. Carilli, F. Walter, A. Weiß, K. K.
Knudsen, and J. Wagg. A Total Molecular Gas Mass Census in Z
2-3 Star-forming Galaxies: Low-J CO Excitation Probes of Galaxies Evolutionary
States. , 827:18, Aug. 2016. doi: 10.3847/0004-637X/827/1/18.
[58] R. Smit, R. J. Bouwens, S. Carniani, P. A. Oesch, I. Labb´e, G. D. Illingworth, P. van
der Werf, L. D. Bradley, V. Gonzalez, J. A. Hodge, B. W. Holwerda, R. Maiolino, and W. Zheng. Rotation in [C II]-emitting gas in two galaxies at a redshift of 6.8.
, 553:178–181, Jan. 2018. doi: 10.1038/nature24631.
[59] P. Solomon and P. V. Bout. Molecular gas at high redshift. Annual Review of
Astronomy and Astrophysics, 43(1):677–725, 2005. doi: 10.1146/annurev.astro.
43.051804.102221. URL https://doi.org/10.1146/annurev.astro.43.051804.
102221.
[60] P. M. Solomon, D. Downes, S. J. E. Radford, and J. W. Barrett. The Molecular
Interstellar Medium in Ultraluminous Infrared Galaxies. , 478:144–161, Mar. 1997.
[61] N. Suzuki, D. Rubin, C. Lidman, G. Aldering, R. Amanullah, K. Barbary, L. F. Barrientos,
J. Botyanszki, M. Brodwin, N. Connolly, K. S. Dawson, A. Dey, M. Doi,
M. Donahue, S. Deustua, P. Eisenhardt, E. Ellingson, L. Faccioli, V. Fadeyev,
H. K. Fakhouri, A. S. Fruchter, D. G. Gilbank, M. D. Gladders, G. Goldhaber,
A. H. Gonzalez, A. Goobar, A. Gude, T. Hattori, H. Hoekstra, E. Hsiao, X. Huang,
Y. Ihara, M. J. Jee, D. Johnston, N. Kashikawa, B. Koester, K. Konishi, M. Kowalski,
E. V. Linder, L. Lubin, J. Melbourne, J. Meyers, T. Morokuma, F. Munshi,
C. Mullis, T. Oda, N. Panagia, S. Perlmutter, M. Postman, T. Pritchard, J. Rhodes,
P. Ripoche, P. Rosati, D. J. Schlegel, A. Spadafora, S. A. Stanford, V. Stanishev,
D. Stern, M. Strovink, N. Takanashi, K. Tokita, M. Wagner, L. Wang, N. Yasuda,
H. K. C. Yee, and T. Supernova Cosmology Project. The Hubble Space Telescope
Cluster Supernova Survey. V. Improving the Dark-energy Constraints above z 1
and Building an Early-type-hosted Supernova Sample. , 746:85, Feb. 2012. doi:
10.1088/0004-637X/746/1/85.
[62] A. M. Swinbank, I. Smail, S. Longmore, A. I. Harris, A. J. Baker, C. De Breuck,
J. Richard, A. C. Edge, R. J. Ivison, R. Blundell, K. E. K. Coppin, P. Cox, M. Gurwell,
L. J. Hainline, M. Krips, A. Lundgren, R. Neri, B. Siana, G. Siringo, D. P.
Stark, D.Wilner, and J. D. Younger. Intense star formation within resolved compact
regions in a galaxy at z = 2.3. , 464:733–736, Apr. 2010. doi: 10.1038/nature08880.
[63] M. Swinbank, I. Smail, A. Karim, J. Hodge, F. Walter, D. Alexander, F. Bertoldi,
A. Biggs, N. Brandt, C. De Breuck, S. Chapman, K. Coppin, P. Cox, A. Danielson,
H. Dannerbauer, A. Edge, R. Ivison, T. Greve, K. Knudsen, K. Menten, J. Simpson,
E. Schinnerer, J. Wardlow, A. Weiss, and P. van der Werf. An ALMA Survey of Submillimetre Galaxies in the Extended Chandra Deep Field South: First Results.
The Messenger, 149:40–43, Sept. 2012.
[64] S. P. Tendulkar, C. G. Bassa, J. M. Cordes, G. C. Bower, C. J. Law, S. Chatterjee,
E. A. K. Adams, S. Bogdanov, S. Burke-Spolaor, B. J. Butler, P. Demorest,
J. W. T. Hessels, V. M. Kaspi, T. J. W. Lazio, N. Maddox, B. Marcote,
M. A. McLaughlin, Z. Paragi, S. M. Ransom, P. Scholz, A. Seymour, L. G. Spitler,
H. J. van Langevelde, and R. S. Wharton. The host galaxy and redshift of the
repeating fast radio burst FRB 121102. The Astrophysical Journal, 834(2):L7,
jan 2017. doi: 10.3847/2041-8213/834/2/l7. URL https://doi.org/10.3847%
2F2041-8213%2F834%2F2%2Fl7.
[65] A. L. Tiley, M. Bureau, A. Saintonge, S. Topal, T. A. Davis, and K. Torii. The
Tully-Fisher relation of COLD GASS Galaxies. , 461:3494–3515, Oct. 2016. doi:
10.1093/mnras/stw1545.
[66] H. Umehata, Y. Matsuda, Y. Tamura, K. Kohno, I. Smail, R. J. Ivison, C. C.
Steidel, S. C. Chapman, J. E. Geach, M. Hayes, T. Nagao, Y. Ao, R. Kawabe,
M. S. Yun, B. Hatsukade, M. Kubo, Y. Kato, T. Saito, S. Ikarashi, K. Nakanishi,
M. Lee, T. Izumi, M. Mori, and M. Ouchi. ALMA Reveals Strong [C II] Emission
in a Galaxy Embedded in a Giant Ly↵ Blob at z = 3.1. , 834:L16, Jan. 2017. doi:
10.3847/2041-8213/834/2/L16.
[67] B. P. Venemans, R. G. McMahon, F. Walter, R. Decarli, P. Cox, R. Neri, P. Hewett,
D. J. Mortlock, C. Simpson, and S. J. Warren. Detection of Atomic Carbon [C II]
158 μm and Dust Emission from a z = 7.1 Quasar Host Galaxy. , 751:L25, June
2012. doi: 10.1088/2041-8205/751/2/L25.
[68] B. P. Venemans, F. Walter, L. Zschaechner, R. Decarli, G. De Rosa, J. R. Findlay,
R. G. McMahon, and W. J. Sutherland. Bright [C II] and Dust Emission in Three z
6.6 Quasar Host Galaxies Observed by ALMA. , 816:37, Jan. 2016. doi: 10.3847/
0004-637X/816/1/37.
[69] J. Wagg, C. L. Carilli, D. J. Wilner, P. Cox, C. De Breuck, K. Menten, D. A.
Riechers, and F. Walter. [CII] line emission in BRI 1335-0417 at z = 4.4. , 519:L1,
Sept. 2010. doi: 10.1051/0004-6361/201015424.
[70] A. G. Walker. On Milne’s Theory of World-Structure. Proceedings of the London
Mathematical Society, (Series 2) volume 42, p. 90-127, 42:90–127, 1937. doi: 10.
1112/plms/s2-42.1.90.
[71] F. Walter, D. Riechers, P. Cox, R. Neri, C. Carilli, F. Bertoldi, A. Weiss, and
R. Maiolino. A kiloparsec-scale hyper-starburst in a quasar host less than 1gigayear
after the Big Bang. , 457:699–701, Feb. 2009. doi: 10.1038/nature07681.
[72] R.Wang, J.Wagg, C. Carilli, F.Walter, L. Lentati, X. Fan, D. Riechers, F. Bertoldi,
D. Narayanan, M. Strauss, P. Cox, A. Omont, K. Menten, K. Knudsen, R. Neri,
and L. Jiang. Star formation and gas kinematics of quasar host galaxies at z 6:
New insights from alma. Astrophysical Journal, 773(1), 8 2013. ISSN 0004-637X.
doi: 10.1088/0004-637X/773/1/44.
[73] R. Wang, J. Wagg, C. L. Carilli, F. Walter, L. Lentati, X. Fan, D. A. Riechers,
F. Bertoldi, D. Narayanan, M. A. Strauss, P. Cox, A. Omont, K. M. Menten, K. K.
Knudsen, R. Neri, and L. Jiang. Star Formation and Gas Kinematics of Quasar
Host Galaxies at z ˜ 6: New Insights from ALMA. , 773:44, Aug. 2013. doi:
10.1088/0004-637X/773/1/44.
[74] R. Wang, X.-B. Wu, R. Neri, X. Fan, F. Walter, C. L. Carilli, E. Momjian,
F. Bertoldi, M. A. Strauss, Q. Li, F. Wang, D. A. Riechers, L. Jiang, A. Omont,
J. Wagg, and P. Cox. Probing the Interstellar Medium and Star Formation of the
Most Luminous Quasar at z = 6.3. , 830:53, Oct. 2016. doi: 10.3847/0004-637X/
830/1/53.
[75] C. J. Willott, A. Omont, and J. Bergeron. Redshift 6.4 Host Galaxies of 108 Solar
Mass Black Holes: Low Star Formation Rate and Dynamical Mass. , 770:13, June
2013. doi: 10.1088/0004-637X/770/1/13.
[76] J. S. Young and N. Scoville. Extragalactic CO - Gas distributions which follow the
light in IC 342 and NGC 6946. , 258:467–489, July 1982. doi: 10.1086/160099.
[77] J. S. Young, S. Xie, L. Tacconi, P. Knezek, P. Viscuso, L. Tacconi-Garman, N. Scoville,
S. Schneider, F. P. Schloerb, S. Lord, A. Lesser, J. Kenney, Y.-L. Huang, N. Devereux,
M. Claussen, J. Case, J. Carpenter, M. Berry, and L. Allen. The FCRAO
Extragalactic CO Survey. I. The Data. , 98:219, May 1995. doi: 10.1086/192159.
[78] H. Yu and F. Y. Wang. Measuring the cosmic proper distance from fast radio
bursts. , 606:A3, Sept. 2017. doi: 10.1051/0004-6361/201731607.
[79] B. Zhou, X. Li, T. Wang, Y.-Z. Fan, and D.-M. Wei. Fast radio bursts as a cosmic
probe? Phys. Rev., D89(10):107303, 2014. doi: 10.1103/PhysRevD.89.107303.