9.8 KiB
| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Age of the universe | 2/4 | https://en.wikipedia.org/wiki/Age_of_the_universe | reference | science, encyclopedia | 2026-05-05T13:31:45.824475+00:00 | kb-cron |
Experimental observations confirm expansion of the universe according to Hubble's law. Since the universe is expanding, the equation for that expansion can be "run backwards" to its starting point.
The Lambda-CDM concordance model describes the expansion of the universe from a very uniform, hot, dense primordial state to its existing state over a span of about 13.77 billion years of cosmological time. This model is well understood theoretically and strongly supported by recent high-precision astronomical observations such as WMAP. The International Astronomical Union uses the term "age of the universe" to mean the duration of the Lambda-CDM expansion, or equivalently, the time elapsed within the observable universe since the Big Bang. The expansion rate at any time
t
{\displaystyle t}
is called the Hubble parameter
H
(
t
)
≡
a
˙
a
,
{\displaystyle H(t)\equiv {\frac {\dot {a}}{a}},}
which is modeled as
H
(
a
)
≡
a
˙
a
=
H
0
Ω
m
a
−
3
+
Ω
r
a
d
a
−
4
+
Ω
Λ
+
(
1
−
Ω
m
−
Ω
r
a
d
−
Ω
Λ
)
a
−
2
,
{\displaystyle H(a)\equiv {\frac {\dot {a}}{a}}=H_{0}{\sqrt {\Omega _{\rm {m}}a^{-3}+\Omega _{\mathrm {rad} }a^{-4}+\Omega _{\Lambda }+(1-\Omega _{\rm {m}}-\Omega _{\mathrm {rad} }-\Omega _{\Lambda })a^{-2}}},}
where
Ω
x
{\displaystyle \Omega _{x}}
are density parameters, with
m
{\displaystyle \mathrm {m} }
for mass (baryons and cold dark matter),
r
a
d
{\displaystyle \mathrm {rad} }
for radiation (photons plus relativistic neutrinos), and
Λ
{\displaystyle \Lambda }
for dark energy. The value
H
0
{\displaystyle H_{0}}
, called the Hubble constant, is the Hubble parameter (
t
=
0
{\displaystyle t=0}
) and it has units of inverse time. The age of the universe is then defined as
t
age
=
1
H
0
∫
0
1
d
a
Ω
m
a
−
1
+
Ω
r
a
d
a
−
2
+
Ω
Λ
a
2
+
(
1
−
Ω
m
−
Ω
r
a
d
−
Ω
Λ
)
,
{\displaystyle t_{\textrm {age}}={\frac {1}{H_{0}}}\int _{0}^{1}{\frac {da}{\sqrt {\Omega _{\rm {m}}a^{-1}+\Omega _{\mathrm {rad} }a^{-2}+\Omega _{\Lambda }a^{2}+(1-\Omega _{\rm {m}}-\Omega _{\mathrm {rad} }-\Omega _{\Lambda })}}},}
The integral is close to 1 so
H
0
−
1
{\displaystyle H_{0}^{-1}}
is close to the age of the universe.
== Observational limits == Since the universe must be at least as old as the oldest things in it, there are a number of observations that put a lower limit on the age of the universe; these include
the temperature of the coolest white dwarfs, which gradually cool as they age, and the dimmest turnoff point of main sequence stars in clusters (lower-mass stars spend a greater amount of time on the main sequence, so the lowest-mass stars that have evolved away from the main sequence set a minimum age). Before the incorporation of dark energy in the model of cosmic expansion, the age was awkwardly less than the oldest observed astronomical objects. This connection can be used in reverse: the oldest objects found constrain the values of the density parameter for dark energy.
== Cosmological parameters ==
The problem of determining the age of the universe is closely tied to the problem of determining the values of the cosmological parameters. This is largely carried out in the context of the ΛCDM model, where the universe is assumed to contain normal (baryonic) matter, cold dark matter, radiation (including both photons and neutrinos), and a cosmological constant. The fractional contribution of each to the energy density of the universe is given by the density parameters
Ω
m
,
{\displaystyle ~\Omega _{\text{m}}~,}
Ω
r
,
{\displaystyle ~\Omega _{\text{r}}~,}
and
Ω
Λ
.
{\displaystyle ~\Omega _{\Lambda }~.}
The full ΛCDM model is described by a number of other parameters, but for the purpose of computing its age these three, along with the Hubble parameter
H
0
{\displaystyle ~H_{0}~}
, are the most important. With accurate measurements of these parameters, the age of the universe can be determined by using the Friedmann equation. This equation relates the rate of change in the scale factor
a
(
t
)
{\displaystyle ~a(t)~}
to the matter content of the universe. Turning this relation around, we can calculate the change in time per change in scale factor and thus calculate the total age of the universe by integrating this formula. The age
t
0
{\displaystyle ~t_{0}~}
is then given by an expression of the form
t
0
=
1
H
0
F
(
Ω
r
,
Ω
m
,
Ω
Λ
,
…
)
{\displaystyle t_{0}={\frac {1}{H_{0}}}\,F(\,\Omega _{\text{r}},\,\Omega _{\text{m}},\,\Omega _{\Lambda },\,\dots \,)~}