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The age of the universe is a proper time along comoving cosmological observers, inferred within an expansion model; stellar ages provide partly independent consistency checks. In an expanding FLRW model with a big-bang origin,where $a_0=1$. The Hubble time $H_0^{-1}$ is a characteristic scale, not generally the age. For flat radiation and dust universes, $t_0=1/(2H_0)$ and $2/(3H_0)$, respectively.

For a flat matter-plus-vacuum model neglecting radiation in the age integral,As an explicitly illustrative contemporary model, the Planck2015 temperature-plus-lensing estimates $H_0\simeq 67.8\mathrm{km}{\mathrm{s}}^{-1}\mathrm{Mp}{\mathrm{c}}^{-1}$ and ${\Omega }_m\simeq 0.308$ give about $13.8\mathrm{Gyr}$. This is an inference under the assumed flat cosmology, not a model-independent clock reading or a numerical constant supplied in the examination.^[ref]

The lookback time to an object observed at redshift $z$ isThe object's age at emission cannot exceed this cosmic time, and its formation occurs later than the big bang. A stellar population observed at large redshift therefore constrains both stellar evolution and the cosmological time available, rather than simply carrying today's cosmic age.

A star cluster's main-sequence turnoff traces the most massive stars still burning core hydrogen. More massive stars generally consume their usable fuel faster; fitting a color-magnitude diagram with stellar-evolution tracks can infer the population's formation time. The estimate depends on distance, reddening, composition, helium abundance, mixing and the binary population. Old globular clusters give lower limits on the cosmic age, with a formation delay between the big bang and the cluster.

White-dwarf cooling sequences provide another clock: thermal energy and crystallization physics determine how luminosity decreases after the remnant forms. The faint-end population must be combined with progenitor lifetimes and the star-formation history. Radioactive abundance ratios supply nucleocosmochronology. If two isotopes with decay constants ${\lambda }_1,{\lambda }_2$ start at ratio ${\mathcal{Q}}_0$, their measured ratio satisfiesThe initial production ratio and subsequent chemical mixing can dominate the uncertainty; a measured abundance ratio alone is not an exact formation date.

Kinematic expansion ages $R/v$ can estimate young remnants but require a dynamical model because deceleration changes the relation between present speed and elapsed time. Agreement among cosmological, stellar, cooling and radioactive estimates is powerful precisely because their systematic errors differ. An apparently over-age object calls for examining both the astrophysical clock and the cosmological assumptions before claiming a contradiction.