Editing Observable universe (section)

=== Estimates based on critical density ===
Critical density is the energy density for which the universe is flat.<ref>See [[Friedmann equations#Density parameter]].</ref> If there is no dark energy, it is also the [[density]] for which the expansion of the universe is poised between continued expansion and collapse.<ref>{{cite book |author=Kaku |first=Michio |url=https://books.google.com/books?id=cKULZJpcJBwC |title=Parallel Worlds: A Journey Through Creation, Higher Dimensions, and the Future of the Cosmos |publisher=Knopf Doubleday |year=2006 |isbn=978-0307276988 |page=385 |language=en-us}}</ref> From the [[Friedmann equations]], the value for <math>\rho_\text{c}</math> critical density, is:<ref>{{cite book |author=Schutz |first=Bernard F. |url=https://books.google.com/books?id=iEZNXvYwyNwC&pg=PA361 |title=Gravity from the ground up |date=2003 |publisher=Cambridge University Press |isbn=978-0521455060 |pages=361– |language=en-uk}}</ref>
: <math>\rho_\text{c} = \frac{3 H^2}{8 \pi G},</math>
where ''G'' is the [[gravitational constant]] and {{nowrap|1=''H'' = ''H''<sub>0</sub>}} is the present value of the [[Hubble constant]]. The value for ''H''<sub>0</sub>, as given by the European Space Agency's Planck Telescope, is ''H''<sub>0</sub> = 67.15 kilometres per second per megaparsec. This gives a critical density of {{val|0.85|e=-26|u=kg/m3}}, or about 5 hydrogen atoms per cubic metre. This density includes four significant types of energy/mass: ordinary matter (4.8%), neutrinos (0.1%), [[cold dark matter]] (26.8%), and [[dark energy]] (68.3%).<ref name="planck_cosmological_parameters">{{cite journal | arxiv=1303.5076 | title=Planck 2013 results. XVI. Cosmological parameters | author=Planck collaboration | journal=Astronomy & Astrophysics | date=2013|bibcode = 2014A&A...571A..16P | doi=10.1051/0004-6361/201321591 | volume=571 | pages=A16| s2cid=118349591 }}</ref> 

Although neutrinos are [[Standard Model]] particles, they are listed separately because they are [[Scale factor (cosmology)#Radiation-dominated era|ultra-relativistic]] and hence [[Equation of state (cosmology)#Ultra-relativistic particles|behave]] like radiation rather than like matter. The density of ordinary matter, as measured by Planck, is 4.8% of the total critical density or {{val|4.08|e=-28|u=kg/m3}}. To convert this density to mass we must multiply by volume, a value based on the radius of the "observable universe". Since the universe has been expanding for 13.8 billion years, the [[Comoving and proper distances|comoving distance]] (radius) is now about 46.6 billion light-years. Thus, volume ({{sfrac|4|3}}''πr''<sup>3</sup>) equals {{val|3.58|e=80|u=m3}} and the mass of ordinary matter equals density ({{val|4.08|e=-28|u=kg/m3}}) times volume ({{val|3.58|e=80|u=m3}}) or {{val|1.46|e=53|u=kg}}.