The
age of the universe is the time elapsed
between the
Big Bang and the present day.
Current theory and observations suggest that the
universe is between 13.5 and 14
billion years old. The uncertainty range
has been obtained by the agreement of a number of scientific
research projects. These projects included
background radiation
measurements and more ways to measure
the
expansion of the
universe. Background radiation measurements give the cooling
time of the universe since the Big Bang.
Expansion of
the universe measurements give accurate data to calculate the age
of the universe.
Explanation
The
Lambda-CDM concordance model
describes the evolution of the universe from a very uniform, hot,
dense primordial state to its present state over a span of about
13.73 billion years of
cosmological
time. This model is well understood theoretically and strongly
supported by recent high-precision astronomical observations such
as
WMAP. In contrast, theories of the origin of
the primordial state remain very speculative. If one extrapolates
the Lambda-CDM model backward from the earliest well-understood
state, it quickly (within a small fraction of a second) reaches a
singularity called the
"Big Bang singularity". This singularity is not considered to have
any physical significance, but it is convenient to quote times
measured "since the Big Bang", even though they do not correspond
to a physically measurable time. For example, "10
^{−6}
second after the Big Bang" is a well-defined era in the universe's
evolution. In one sense it would be more meaningful to refer to the
same era as "13.7 billion years minus 10
^{−6} seconds ago",
but this is unworkable since the latter time interval is swamped by
uncertainty in the former.
Though the universe might in theory have a longer history,
cosmologists presently use "age of the universe" to mean the
duration of the Lambda-CDM expansion, or equivalently the elapsed
time since the Big Bang.
Observational limits
Since the universe must be at least as old as the oldest thing in
it, there are a number of observations which 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 off of the main sequence set a minimum age). On 23
April 2009 a
gamma-ray burst was detected
which was later confirmed at being over 13 billion years old.
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. Today 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 current energy density of
the Universe is given by the
density
parameters Ω
_{m}, Ω
_{r}, and
Ω
_{Λ}. 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} are the most important.
If one has accurate measurements of these parameters, then 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) 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} is then given by an
expression of the form
- t_0 = \frac{1}{H_0}
F(\Omega_r,\Omega_m,\Omega_\Lambda,\dots)
where the function
F depends only on the fractional
contribution to the universe's energy content that comes from
various components. The first observation that one can make from
this formula is that it is the Hubble parameter that controls that
age of the universe, with a correction arising from the matter and
energy content. So a rough estimate of the age of the universe
comes from the inverse of the Hubble parameter,
- \frac{1}{H_0} = \left(
\frac{H_0}{72\;\text{km/(s}\cdot\text{Mpc)} } \right)^{-1} \times
13.6 \; \text{Ga}.
To get a more accurate number, the correction factor
F
must be computed. In general this must be done numerically, and the
results for a range of cosmological parameter values are shown in
the figure. For the
WMAP values
(Ω
_{m}, Ω
_{Λ}) = (0.266, 0.732),
shown by the box in the upper left corner of the figure, this
correction factor is nearly one:
F = 0.996. For a flat
universe without any cosmological constant, shown by the star in
the lower right corner,
F = is much smaller and thus the
universe is younger for a fixed value of the Hubble parameter. To
make this figure, Ω
_{r} is held constant (roughly
equivalent to holding the
CMB temperature constant) and
the curvature density parameter is fixed by the value of the other
three.
The Wilkinson Microwave Anisotropy Probe (
WMAP)
was instrumental in establishing an accurate age of the universe,
though other measurements must be folded in to gain an accurate
number.
CMB measurements are very good at
constraining the matter content Ω
_{m} and
curvature parameter Ω
_{k}. It is not as sensitive
to Ω
_{Λ} directly, partly because the cosmological constant
only becomes important at low redshift. The most accurate
determinations of the Hubble parameter
H_{0} come
from
Type Ia supernovae. Combining
these measurements leads to the generally accepted value for the
age of the universe quoted above.
The cosmological constant makes the universe "older" for fixed
values of the other parameters. This is significant, since before
the cosmological constant became generally accepted, the Big Bang
model had difficulty explaining why
globular clusters in the Milky Way appeared
to be far older than the age of the universe as calculated from the
Hubble parameter and a matter-only universe. Introducing the
cosmological constant allows the universe to be older than these
clusters, as well as explaining other features that the matter-only
cosmological model could not.
WMAP
NASA's Wilkinson Microwave
Anisotropy Probe (WMAP) project estimates the age of the
universe to be years (13.73 billion years old, with an uncertainty
of 120 million years).
However, this age is based on the assumption that the project's
underlying model is correct; other methods of estimating the age of
the universe could give different ages. Assuming an extra
background of relativistic particles, for example, can enlarge the
error bars of the WMAP constraint by one order of magnitude.
This measurement is made by using the location of the first
acoustic peak in the
microwave background
power spectrum to determine the size of the decoupling surface
(size of universe at the time of recombination). The light travel
time to this surface (depending on the geometry used) yields a
reliable age for the universe. Assuming the validity of the models
used to determine this age, the residual accuracy yields a margin
of error near one percent.
This is the value currently most quoted by astronomers.
Assumption of strong priors
Calculating the age of the universe is only accurate if the
assumptions built into the models being used to estimate it are
also accurate. This is referred to as
strong priors and essentially involves
stripping the potential errors in other parts of the model to
render the accuracy of actual observational data directly into the
concluded result. Although this is not a valid procedure in all
contexts (as noted in the accompanying caveat: "based on the fact
we have assumed the underlying model we used is correct"), the age
given is thus accurate to the specified error (since this error
represents the error in the instrument used to gather the raw data
input into the model).
The age of the universe based on the "best fit" to WMAP data "only"
is 13.69±0.13 Ga (the slightly higher number of 13.73 includes some
other data mixed in). This number represents the first accurate
"direct" measurement of the age of the universe (other methods
typically involve
Hubble's law and age
of the oldest stars in globular clusters, etc). It is possible to
use different methods for determining the same parameter (in this
case – the age of the universe) and arrive at different answers
with no overlap in the "errors". To best avoid the problem, it is
common to show two sets of uncertainties; one related to the actual
measurement and the other related to the systematic errors of the
model being used.
An important component to the analysis of data used to determine
the age of the universe (e.g. from
WMAP)
therefore is to use a
Bayesian
Statistical analysis, which normalizes the results based upon
the priors (i.e. the model). This quantifies any uncertainty in the
accuracy of a measurement due to a particular model used.
See also
References
External links