There are statements in wiki like:

The current measurement of the age of the universe is 13.799±0.021 billion (109) years within the Lambda-CDM concordance model.

My question is how does scientists theorize this value, by relying on which observed facts and data?


marked as duplicate by Rob Jeffries, Bill N, Kyle Kanos, DilithiumMatrix, Jon Custer Mar 1 '17 at 21:51

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.


The age of the universe $t_0$ is computed in any cosmological model according to,

$$H_0t_0 = \int_0^\infty \frac{dz}{(1+z)E(z)}$$


$$E(z) = \left[\Omega_{\mathrm{matter}}(1+z)^3 + \Omega_{R}(1+z)^2 + \Omega_\Lambda\right]^{1/2}$$

where $\Omega_{\mathrm{matter}}$ is the matter fraction, $\Omega_\Lambda$ is the vacuum energy contribution and $\Omega_R$ is the curvature contribution; baryon matter is included in $\Omega_{\mathrm{matter}}$. In $\Lambda\mathrm{CDM}$, one has $\Omega_{\mathrm{matter}} = 0.26$, $\Omega_{\Lambda}= 0.74$ and $\Omega_{R} = 0$. The observed value of $H_0 = 71 \, \mathrm{km \, s^{-1} \, Mpc^{-1}}$ leads to,

$$t_0 \approx 13.7 \, \mathrm{billion \, yrs}.$$

The parameters of the model are found in the Planck mission paper. In general, for a flat model, by performing the integral one finds,

$$t_0 = \frac{1}{3H_0 \Omega^{1/2}_\Lambda} \log \left( \frac{2}{1-\Omega^{1/2}_\Lambda}-1\right).$$