How is the age of the Universe measured?

Scientific summary

The Astronoo article explains how cosmologists estimate the age of the Universe at about 13.8 billion years. It presents the Big Bang model, the cosmic expansion described by the Hubble-Lemaître law, the cosmic microwave background, and the ΛCDM model. Observations of redshift, the CMB, and ancient stars constrain the cosmological parameters. General relativity and the Friedmann equations provide the theoretical framework. The article thus shows that the cosmic age is not based on a simple hypothesis, but on a convergent set of measurements and models.

How can we say that the Universe has an age?

This article answers a fundamental question: how can we say that the Universe has an age? The answer rests on several independent observations. First, the expansion of the Universe shows that distant galaxies are moving away from us: going back in time, the Universe was denser and hotter. The Hubble-Lemaître law allows us to estimate the time elapsed since this initial state. Next, the cosmic microwave background preserves the imprint of the Universe at 380,000 years of age. The WMAP and Planck satellites measure its anisotropies and constrain the density of matter, dark energy, and the expansion rate. The ΛCDM model combines these data with general relativity to calculate an age of about 13.8 billion years. Finally, the oldest stars in globular clusters provide a consistent lower bound. The measurements are not perfect, but they overlap and converge toward a robust value. The age of the Universe is therefore not a simple opinion: it is the result of a body of convergent evidence.

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The age of the Universe: 13.8 billion years

An estimate from cosmology

The assertion of the age of the Universe rests on several observations and physical theories that allow us to estimate what is called the "cosmological age". This estimate comes mainly from the understanding of the laws of physics, the properties of the expansion of the Universe, and the cosmic microwave background. How is this age determined?

The Big Bang Theory

The Big Bang model

The fundamental idea behind the age of the Universe rests on the Big Bang cosmological model, which suggests that the Universe began in an extremely dense and hot state about 13.8 billion years ago. The evolution of the Universe since that moment, in particular its expansion, is described by the equations of Einstein's general relativity.

$$ R_{\mu\nu} - \frac{1}{2}g_{\mu\nu}R + g_{\mu\nu}\Lambda = \frac{8 \pi G}{c^4} T_{\mu\nu} $$

The left side of the equation is related to the geometry of space-time, which is influenced by the distribution of matter and energy in the Universe, represented by the right side of the equation. All solutions of this equation are possible space-time geometries (universes). Is there a space-time that corresponds to our Universe?

The equations of general relativity are complex nonlinear partial differential equations, and although it is possible to solve them in certain very specific cases, there is no exact general solution for all possible configurations of matter and energy.

What is the correct geometry of the observable Universe?

Choosing a model compatible with observation

We must choose an approximate solution in agreement with observation, that is, a good mathematical model that corresponds to the description of the cosmos, depending on the accuracy of our measurements.

The expansion of the Universe

The Hubble-Lemaître law

One of the first solid pieces of evidence for the expansion of the Universe comes from the observation of the redshift of distant galaxies. This means that these galaxies are moving away from us at a speed proportional to their distance, a phenomenon described by the Hubble-Lemaître law published in 1929. The relationship between the distance of galaxies and their recession velocity allows us to trace back to the time when these galaxies were concentrated at a single point, marking the beginning of the Universe. By measuring this expansion (70 kilometers per second per megaparsec, the average used in calculations), cosmologists can calculate the time elapsed since the Big Bang.

The Cosmic Microwave Background (CMB)

The fossil radiation

The CMB, or fossil radiation, is a form of electromagnetic radiation that was emitted about 380,000 years after the Big Bang, when the Universe had cooled enough for electrons and protons to combine and form hydrogen atoms. This radiation, observed throughout the Universe, contains information about the state of the Universe at those early times. Precise measurements of the CMB, notably those obtained by satellites such as WMAP or Planck, provide clues about the structure of the early Universe and allow us to constrain the cosmological parameters, such as the density of matter and energy, and therefore the age of the Universe.

Standard cosmological model (ΛCDM)

The ΛCDM model

The current cosmological model, called the ΛCDM model (Lambda Cold Dark Matter), describes the evolution of the Universe as a function of matter, dark energy, and general relativity. Using observations such as the redshift of galaxies, the distribution of matter in the Universe, and the CMB, cosmologists can calculate an age of the Universe with "great precision". These calculations are based on the solution of the Friedmann equations, which are derived from the equations of general relativity and which describe the evolution of the Universe on large scales.

Indirect methods and stellar evolution models

Ancient stars as a constraint

Another approach consists in studying the evolution of stellar objects and star clusters. The oldest stars, such as those in globular clusters, offer an additional constraint on the age of the Universe. Scientists can estimate the age of these stars by studying their chemical composition and modeling their stellar evolution. These age estimates, although less precise than those based on the CMB and the expansion of the Universe, provide lower limits to the age of the Universe.

Conclusion

A dynamic space-time

The space-time of our Universe is a dynamic solution of the equation of general relativity. It is not a static solution but an expanding solution, where the properties of space-time vary with time according to the evolution of the density of matter and energy. In other words, our space-time (the one we observe) is an evolving solution that results from the distribution of matter and energy in the Universe, in accordance with general relativity.

References

FAQ: Everything you need to know about the age of the Universe

How do we know that the Universe is about 13.8 billion years old?

The value of 13.8 billion years comes from the combination of several measurements. The ΛCDM model fits the expansion rate, the density of matter, and dark energy to observations of the fossil radiation and distant galaxies. The uncertainties remain small, on the order of a few tens of millions of years.

What is the cosmic microwave background?

The cosmic microwave background is a fossil light emitted about 380,000 years after the Big Bang. It carries the imprint of the primordial fluctuations that gave birth to large-scale structures. Its anisotropies allow us to measure the geometry and composition of the Universe.

Why does the expansion of the Universe allow us to go back in time?

Because the Universe is expanding: if we reverse the film, matter and energy become concentrated. The Hubble-Lemaître law relates the distance of galaxies to their recession velocity. By measuring the expansion rate, we estimate the time elapsed since the initial very dense and hot state.

What is the Hubble constant?

The Hubble constant measures the current expansion rate of the Universe per unit of distance. Its value, close to 70 km/s/Mpc, is essential for calculating the cosmic age. Tensions persist between certain local measurements and those derived from the fossil radiation.

Can the age of the Universe be called into question?

The cosmic age depends on the model used. If new physics modified dark energy or dark matter, the estimate could change. However, the convergence between the CMB, the expansion, and ancient stars makes the figure of 13.8 billion years very robust.

Do the oldest stars confirm this age?

Yes, the stars in globular clusters are among the oldest known. Their age, estimated by stellar evolution models, reaches about 12 to 13 billion years. This provides a lower limit compatible with the cosmological age, without exceeding it.