Graphical timeline from Big Bang to Heat Death

This is the timeline of the Universe from Big Bang to Heat Death scenario. The different eras of the universe are shown. The heat death will occur in 10¹⁰³ years, if protons decay.

Usually the logarithmic scale is used for such timelines but it compresses the most interesting Stelliferous Era too much as this example shows. Therefore, a double-logarithmic scale s (s*100 in the graphics) is used instead. The minimum of it is unfortunately only 1, not 0 as needed, and the negative outputs for inputs smaller than 10 are useless. Therefore, the time from 0.1 to 10 years is collapsed to a single point 0, but that doesn't matter in this case because nothing special happens in the history of the universe during that time.

$s={\begin{cases}\log _{{10}}\log _{{10}}year&{\mbox{if }}year>10{\mbox{ , corresponding to }}year=10^{{10^{{s}}}}\\0&{\mbox{if }}0.1\leq year\leq 10\\-\log _{{10}}(-\log _{{10}}year)&{\mbox{if }}year<0.1{\mbox{ , corresponding to }}year=10^{{-10^{{-s}}}}\end{cases}}$

Comparison of log₁₀ and log₁₀log₁₀ scales

year	log10 year	combination of log10log10 year and -log10(-log10 year)
10^10000	10000	4
10^1000	1000	3
10^100	100	2
10^10	10	1
10^2	2	0.30
10^1	1	0
10^0	0	undefined but here forced to 0
10^−1	-1	0
10^−2	-2	-0.30
10^−10	-10	-1
10^−100	-100	-2

The seconds in the timescale have been converted to years by $second/31557600$ using the Julian year.

See also

• Graphical timeline of the Big Bang
• Graphical timeline of the Stelliferous Era
• Heat death of the universe
• Life timeline and Nature timeline
• List of other end scenarios than Heat Death
• Timeline from Big Bang to the near cosmological future
• Timeline of the Big Bang
• Tiny Graphical timeline from Big Bang to Heat Death - Timeline uses the log scale for comparison with the double-logarithmic scale in this article.

References

• Fred C. Adams; Greg Laughlin (19 June 2000). The Five Ages of the Universe: Inside the Physics of Eternity. Simon and Schuster. ISBN 978-0-684-86576-8.