It is generally believed that in the epoch prior to the formation of the first stars, the Universe was completely dark (the period is therefore known as the Dark Ages). Usually, the start of this epoch is placed at photon decoupling. In this work, we investigate the question whether there was enough light during the dark epoch for a human eye to see. We use the black body spectrum of the Universe to find the flux of photon energy for different temperatures and compare them with visual limits of brightness and darkness. We find that the Dark Ages actually began approximately 6 × 106 years later than commonly stated.
References
1.
Edward W.
Kolb
and Michael S.
Turner
, The Early Universe
, 1st ed. (Addison-Wesley Publishing Company
, Redwood City
, 1988
). pp. 70
–82
.2.
Barbara
Ryden
, Introduction to Cosmology
, 1st ed. (Pearson Education Limited
, Harlow
, 2006
).3.
Sujan
Sengupta
, Worlds Beyond Our Own: The Search for Habitable Planets
, 1st ed. (Springer
, New York
, 2015
). p. 5
.4.
Volker
Bromm
, “Formation of the first stars
,” Rep. Prog. Phys.
76
(11
), 112901
(2013
); e-print arXiv:1305.5178 [astro-ph.CO].5.
Judd D.
Bowman
et al., “An absorption profile centred at 78 megahertz in the sky-averaged spectrum
,” Nature
555
, 67
–70
(2018
).6.
J.
Miralda-Escude
, “The Dark Age of the Universe
,” Science
300
(5627
), 1904
–1909
(2003
); e-print arXiv:astro-ph/0307396.7.
Andrew J. S.
Hamilton
and Gavin
Polhemus
, “The edge of locality: Visualizing a black hole from the inside
,” e-print arXiv:0903.4717 [gr-qc].8.
S.
Krasnikov
, “Falling into the Schwarzschild black hole. Important details
,” Gravit. Cosmol.
14
(4
), 362
–367
(2008); e-print arXiv:0804.3619 [gr-qc].9.
A. A.
Grib
and Yu. V.
Pavlov
, “Is it possible to see the infinite future of the Universe when falling into a black hole?
,” Usp. Fiz. Nauk 173(3), 279–283 (2009
) (in Russian) [Phys. Usp.
52
(3
), 257
–261
(2009
)]; e-print arXiv:0906.1442 [gr-qc].10.
K.
Nagamine
and A.
Loeb
, “Future evolution of the intergalactic medium in a universe dominated by a cosmological constant
,” New Astron.
9
(8
), 573
–583
(2004
);K.
Nagamine
and A.
Loeb
, e-print arXiv:astro-ph/0310505.11.
S. P.
Kashyap
et al., “Surviving in a metastable de sitter space-time
,” J. High Energy Phys.
2015
(9
), 139
(2015
); e-print arXiv:1506.00772 [hep-th].12.
A.
Loeb
, “The optimal cosmic epoch for precision cosmology
,” J. Cosmol. Astropart. P.
2012
(05
), 028
(2012
); e-print arXiv:1203.2622 [astro-ph.CO].13.
A.
Loeb
, “Cosmology with hypervelocity stars
,” J. Cosmol. Astropart. P.
2011
(04
), 023
(2011
); e-print arXiv:1102.0007 [astro-ph.CO].14.
L. M.
Krauss
and G. D.
Starkman
, “Life, the universe, and nothing: Life and death in an ever-expanding universe
,” Astrophys. J.
531
, 22
–30
(2000
); e-print arXiv:astro-ph/9902189.15.
L. M.
Krauss
and R. J.
Scherrer
, “The end of cosmology?
,” Sci. Am.
298
(3
), 34
–41
(2008
).16.
L. M.
Krauss
, “The Big Bang, modern cosmology and the fate of the Universe: impacts upon culture
,” IAU Symp.
260
, 33
–38
(2011
); e-print arXiv:1002.1952 [astro-ph.CO].17.
L. M.
Krauss
and R. J.
Scherrer
, “The return of a static universe and the end of cosmology
,” Gen. Relat. Gravit.
39
, 1545
–1550
(2007
);L. M.
Krauss
and R. J.
Scherrer
, Int. J. Mod. Phys. D
17
, 685
–690
(2008
); e-print arXiv:0704.0221 [astro-ph].18.
T.
Opatrný
, L.
Richterek
, and P.
Bakala
, “Life under a black sun
,” Am. J. Phys.
85
(1
), 14
–22
(2017
); e-print arXiv:1601.02897 [gr-qc].19.
K. T.
Smith
, “GRBs not fatal for life in early universe
,” Science
350
(6256
), 53
–54
(2015
).20.
Z.
Merali
, “Life possible in the early Universe
,” Nature
504
(7479
), 201
(2013
).21.
A.
Loeb
, “The habitable epoch of the early Universe
,” Int. J. Astrobiol.
13
(4
), 337
–339
(2014
); e-print arXiv:1312.0613 [astro-ph.CO].22.
23.
Y.
Li
and B.
Zhang
, “Can life survive gamma-ray bursts in the high-redshift universe?
,” Astrophys. J.
810
(1
), 41
(2015
); e-print arXiv:1507.05966 [astro-ph.HE].24.
S. J.
Olson
, “Life-hostile conditions in the early universe can increase the present-day odds of observing extragalactic life
,” e-print arXiv:1704.04125 [physics.pop-ph].25.
L. M.
Krauss
, “Cosmology as seen from Venice
,” in Neutrino Telescopes, Proceedings, 9th International Workshop, Venice, Italy, March 6-9 (2001)
, Vol. 1, 2
, pp. 673
–689
(2001
); e-print arXiv:astro-ph/0106149.26.
M. S.
Morris
and K. S.
Thorne
, “Wormholes in space-time and their use for interstellar travel: A tool for teaching general relativity
,” Am. J. Phys.
56
, 395
–412
(1988
).27.
T.
Muller
, “Visual appearance of a Morris-Thorne-wormhole
,” Am. J. Phys.
72
(a), 1045
–1050
(2004
).28.
O.
James
et al., “Visualizing Interstellar's Wormhole
,” Am. J. Phys.
83
(6
), 486
–499
(2015
); e-print arXiv:1502.03809 [gr-qc].29.
O.
James
et al., “Gravitational lensing by spinning black holes in astrophysics, and in the movie Interstellar
,” Classical Quant. Grav.
32
(06
), 065001
(2015
); <http://stacks.iop.org/0264-9381/32/i=6/a=065001>.30.
31.
E.
Fred Schubert
, Light-Emitting Diodes
, 2nd ed. (University Cambridge Press
, Cambridge
, 2006
), pp. 275
–276
, 283, and 290–291.32.
Robert
Snowden
, Peter
Thompson
, and Tom
Troscianko
, Basic Vision: An Introduction to Visual Perception
, revised edition (Oxford U.P.
, Oxford
, 2006
), pp. 20
–25
and 47.33.
Malgorzata
Rozanowska
, Bartosz
Rozanowski
, and Michael
Boulton
, “Light-induced damage to the retina
,” Photochem. Photobiol.
88
(6
), 1303
–1308
(2012
).34.
Jonathan M.
Marr
and Francis P.
Wilkin
, “A better presentation of Planck's radiation law
,” Am. J. Phys.
80
(5
), 399
–405
(2012
).35.
Ian
Ashdown
, Radiosity: A Programmer's Perspective
(John Wiley and Sons
, New York
, 1994
), pp. 483
–486
.36.
M. S.
Bessell
, F.
Castelli
, and B.
Plez
, “Model atmospheres broad-band colors, bolometric corrections and temperature calibrations for O-M stars
,” Astron. Astrophys.
333
, 231
–250
(1998
).37.
Information concerning the Sun can be found at the NSSDC website under Fact Sheets, <https://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html>.
38.
S.
Hecht
, S.
Shlaer
, and M. H.
Pirenne
, “Energy, quanta, and vision
,” J. Gen. Physiol.
25
, 819
–840
(1942
).39.
J.
Chariton
and C. A.
Lea
, “Some experiments concerning the counting of scintillations produced by alpha particles
,” Proc. Roy. Soc. A.
122
, 304
–319
(1929
).40.
S. P.
Langley
, “Energy and vision
,” Philos. Mag.
27
, 1
–23
(1889
).41.
P.
Cinzano
, F.
Falchi
, and C. D.
Elvidge
, “Naked star visibility and limiting magnitude mapped from DSMP-OLS satellite data
,” Mon. Not. R. Astron. Soc.
323
(1
), 34
–46
(2001
).42.
Bradley E.
Schaeffer
“Telescopic limiting magnitudes
,” Astr. Soc. P.
102
, 212
–229
(1990
).43.
H.
Richard Blackwell
“Contrast thresholds of the human eye
,” J. Opt. Soc. Am.
36
, 624
–643
(1946
).44.
Andrew
Crumey
, “Human contrast threshold and astronomical visibility
,” Mon. Not. R. Astron. Soc.
442
(3
), 2600
–2619
(2014
); e-print arXiv:1405.4209 [astro-ph.IM].45.
S.
Hecht
, S.
Shlaer
, and M. H.
Pirenne
, “Energy at the threshold of vision
”, Science
93
(2425
), 585
–587
(1941
).46.
S. I.
Vavilov
, “Eksperimentalnye issledovaniya svetovyh kvantovyx fluktuacij visualnym metodom
,” Usp. Fizi. Nauk
36
(3
), 247
–283
(1948
) (in Russian).47.
S. I.
Vavilov
, The Microstructure of Light (Investigation and Essays)
(USSR Acad. Sci.
, Moscow
, 1950) (in Russian); German translation: Berlin, Akad. Verl. VII (1953
).48.
Gislin
Dagnelie
et al., Visual Prosthetics: Physiology, Bioengineering, Rehabilitation
(Springer
, New York
, 2011
), p. 398
.49.
50.
Planck Collaboration
, “Planck 2015 Result. XIII. Cosmological parameters
,” Astron. Astrophys.
594
, A13
(2016
).© 2019 American Association of Physics Teachers.
2019
American Association of Physics Teachers
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.