Cosmological constants: the fine-tuning of the universe

Cosmological and physical constants — Physical and cosmological constants: Gravitation G, speed of light c, reduced Planck constant ℏ, cosmological constant Λ, vacuum permittivity ε₀, Boltzmann constant k, fine-structure constant α and electron mass mₑ: these fundamental values govern the equilibrium and evolution of the universe since the Big Bang.
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Scientific summary

The Astronoo article presents the physical and cosmological constants, those numerical values that set the fundamental properties of the Universe, from the infinitesimally small to the infinitely large. It shows that quantities such as the gravitational constant G, the speed of light c, the Planck constant h or the fine-structure constant α make it possible to describe and predict the behaviour of matter and energy. The text emphasizes that these constants, perhaps inherited from the initial conditions of the Big Bang, above all serve to test the limits of the great physical theories and to verify the stability of the laws of nature over billions of years.

Why are physical and cosmological constants so important in science?

This article is devoted to the physical and cosmological constants, those numerical values that define the fundamental properties of the Universe and that appear in almost every equation of physics. But why does physics need constants, and what do they teach us? The answer lies first of all in coherence: without fixed values, it would be impossible to repeat an experiment, here and elsewhere, today and tomorrow, or to compare observations made at very different scales. The gravitational constant G, the speed of light c, the Planck constant h or the fine-structure constant α thus serve as tools to test the limits of our theories, from quantum mechanics to general relativity. Their origin remains enigmatic: they could stem from the initial conditions of the Big Bang or from a fine-tuning specific to our universe, which leads some theorists to envisage a multiverse in which each universe would have its own values. Constants are therefore both the foundation and the frontier of contemporary physics.

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Why does physics have constants?

Values inherited from the Big Bang

Their existence could be due to the initial conditions of the universe at the time of the Big Bang or to deep properties of fundamental reality that we do not yet understand. Indeed, the initial conditions of the universe may have fixed the values of the constants that subsequently influenced the evolution and structure of the universe as we know it. Some theorists evoke the idea of a multiverse, in which our universe would be only one among many possible realities. In this context, the constants could vary from one universe to another, and our universe would possess the values that allow the emergence of life and conscious observers.

A coherent framework for physical theories

As far as our material world is concerned, the constants of physics are "fixed" values that determine the fundamental properties of the universe as a whole, from the infinitesimally small to the infinitely large. These constants are necessary to describe and predict the behaviour of physical phenomena as well as the properties of matter and energy at different scales. These constants make it possible to maintain the coherence of physical laws and to account for the diversity of phenomena observed at different scales. They are also tools that allow us to study and test the limits of our scientific theories (Newtonian gravitation, Special Relativity, Quantum Mechanics, Quantum Electrodynamics, General Relativity…). For modern physics to develop, it needs universal laws. These laws make it possible to repeat experiments, here and elsewhere, today and tomorrow, within a framework that is the Universe. Constants therefore play a central role in physical theories. Paradoxically, constants may vary over very long periods of time. But this does not prevent the structuring of the domains of validity of the different physical and astrophysical theories.

What are the fundamental constants of physics?

An inventory of fundamental quantities

Physical constants are quantities whose numerical value is considered fixed within the framework of current theories. They appear in the equations that describe the laws of nature, from the infinitesimally small to the infinitely large, and condition both the structure of atoms and the expansion of the Universe.

Varied fields of application

The best known concern gravitation and electromagnetism, but the list extends to quantum mechanics, thermodynamics, particle physics and cosmology. Each constant has its own unit and a precise physical meaning: the gravitational constant G measures the strength of attraction between masses, the speed of light c sets the limit for the propagation of information and energy, the Planck constant h quantifies energy exchanges at the microscopic scale, the fine-structure constant α characterizes the electromagnetic force, etc.

Measured and adjusted values

These quantities are not deduced from abstract mathematical principles: they are measured experimentally with increasing precision, and their values are regularly adjusted by international organizations such as CODATA.

A constancy tested over billions of years

Their apparent constancy, tested over billions of years thanks to the observation of distant absorption spectra, constitutes one of the pillars of modern physics and makes it possible to compare experiments carried out in radically different contexts.

Summary table of fundamental physical constants

The table below summarizes the main physical and cosmological constants, their symbol, their approximate value, their role and their historical origin.

Main physical and cosmological constants
Constant	Symbol	Approximate value	Main role	Scientist / origin
Universal gravitation	G	6.674 × 10^-11 m^3·kg^-1·s^-2	Attractive force between masses	Isaac Newton, 1687
Elementary charge	e	1.602 × 10^-19 C	Smallest electric charge	Charles-Augustin de Coulomb, 1777-1785
Electric constant	kₑ	8.988 × 10^9 N·m²/C²	Electric force between charges in vacuum	Charles-Augustin de Coulomb, 1785
Vacuum permittivity	ε₀	8.854 × 10^-12 F/m	Propagation of electric fields in vacuum	James Clerk Maxwell, 19th century
Speed of light in vacuum	c	299,792,458 m/s	Maximum speed of information and energy	Albert A. Michelson, 1881-1887
Planck constant	h	6.626 × 10^-34 J·s	Relates a particle's energy to its frequency	Max Planck, 1900
Fine structure	α	≈ 1/137	Strength of electromagnetic interactions	Arnold Sommerfeld, 1916
Electron rest mass	mₑ	9.109 × 10^-31 kg	Intrinsic mass of the electron at rest	Michelson and Morley, late 19th century
Avogadro constant	Nₐ	6.022 × 10^23 mol^-1	Links amount of substance to number of particles	Amedeo Avogadro, 1865
Stefan-Boltzmann	σ	5.67 × 10^-8 W/m²K^4	Energy flux radiated by a black body	Josef Stefan and Ludwig Boltzmann, 1879-1884
Boltzmann constant	k	1.381 × 10^-23 J/K	Relates thermal energy to temperature	Ludwig Boltzmann, 19th century
Planck mass	m_P	2.176 × 10^-8 kg	Extreme scale of quantum and gravitational physics	Max Planck, 1900
Cosmological constant	Λ	2.3 × 10^-18 s^-2	Dark energy and accelerated expansion of the Universe	Albert Einstein, 1917
Proton mass	mₚ	1.672 × 10^-27 kg	Mass of a proton, constituent of atomic nuclei	Nuclear and particle physics, 20th century
Neutron mass	mₙ	1.675 × 10^-27 kg	Mass of a neutron, constituent of atomic nuclei	Richard E. Taylor et al., 1969
Strong coupling	αₛ	≈ 1	Strong interaction between quarks and gluons	Quantum chromodynamics, 1970s
Neutrino mass	m_ν	≈ 1 eV/c² (very small)	Mass of neutrinos in particle physics	International experiments, late 20th-21st century
Fermi constant	G_F	1.166 × 10^-5 GeV^-2	Weak interactions between subatomic particles	Enrico Fermi, 1930s
Bohr radius	a₀	5.292 × 10^-11 m	Average size of the electron orbit in hydrogen	Niels Bohr, 1913
Atomic mass	u	1.660 × 10^-27 kg	Atomic mass unit, one twelfth of carbon-12	IUPAC, 1961
Compton wavelength	λₑ	2.43 × 10^-12 m	Scattering of particles by electromagnetic forces	Arthur Holly Compton, 1920s

What are the cosmological parameters?

Cosmological parameters of the ΛCDM model

Unlike the fundamental physical constants, which fix the local laws of nature, the cosmological parameters describe the global state of the Universe: its age, its expansion rate, its composition and its geometry. These quantities are not necessarily constants in the strict sense: some vary with cosmic time, such as the dark energy density or the expansion rate. They are at the heart of the ΛCDM model (Lambda-CDM), which today constitutes the standard model of cosmology. The most precise values come from measurements of the cosmic microwave background made by the Planck satellite (2018), supplemented by supernova surveys and baryon acoustic oscillations (BAO).

Table of cosmological parameters of the ΛCDM model

The table below summarizes the essential cosmological parameters, their symbol, their value from the Planck 2018 data and their role in the description of the Universe.

Cosmological parameters of the ΛCDM model
Parameter	Symbol	Value (Planck 2018)	Main role
Hubble constant	H₀	67.36 ± 0.54 km·s⁻¹·Mpc⁻¹	Current expansion rate of the Universe
Age of the Universe	t₀	13.797 ± 0.023 billion years	Time elapsed since the Big Bang
Total matter density	Ω_m	0.315 ± 0.007	Fraction of the Universe made of matter (dark and baryonic)
Baryonic matter density	Ω_b	0.0493 ± 0.0006	Fraction of the Universe made of ordinary matter
Cold dark matter density	Ω_c	0.265 ± 0.007	Fraction of the Universe made of cold dark matter
Dark energy density	Ω_Λ	0.685 ± 0.007	Fraction of the Universe made of dark energy
Cosmological constant	Λ	1.088 ± 0.030 × 10⁻⁵⁶ cm⁻²	Vacuum energy responsible for accelerated expansion
Dark energy density	ρ_Λ	5.83 ± 0.16 × 10⁻³⁰ g·cm⁻³	Energy density associated with the cosmological constant
Primordial spectral index	n_s	0.965 ± 0.004	Slope of the primordial fluctuation spectrum
Amplitude of fluctuations	ln(10¹⁰A_s)	3.044 ± 0.014	Amplitude of quantum fluctuations at the origin of structures
Reionization optical depth	τ	0.054 ± 0.007	Epoch of reionization of the Universe
Matter-radiation equality redshift	z_eq	3402 ± 26	Transition between the radiation era and the matter era
Decoupling redshift	z_*	1089.92 ± 0.25	Emission of the cosmic microwave background
Fluctuation at 8 h⁻¹ Mpc	σ₈	0.811 ± 0.006	Amplitude of density fluctuations at cluster scale
Zero-acceleration redshift	z_q	0.636 ± 0.018	Transition between deceleration and acceleration of expansion
Effective number of neutrinos	N_eff	2.99 ± 0.17	Number of light neutrino families
Sum of neutrino masses	Σm_ν	< 0.12 eV (95% CL)	Constraint on the total mass of neutrinos

What have the constants made it possible to verify?

Decisive tests for the great theories

The fundamental constants have played a crucial role in the verification of scientific theories and physical models. They have made it possible to confirm that the absorption spectrum of the different elements has remained unchanged for about 10 billion years.

Constants and verifications of the great physical theories
Theory or field	Constants involved	Verifications enabled
Special relativity	c, h	Validation of Einstein's predictions: time dilation and space contraction at speeds close to that of light.
General relativity	G	Test of Einstein's predictions: deflection of light around massive objects and properties of black holes.
Quantum mechanics	e, m_e, h	Validation of predictions on the behaviour of subatomic particles.
Quantum electrodynamics	k_e, α	Verification of atomic spectra and interactions between charged particles.
Strong and weak interactions	α_s, G_F	Confirmation of predictions of the nuclear force and beta decay.
Particle physics	Masses of the electron, proton and neutron	Verification of particle physics models, notably the Standard Model.

The Hubble tension

Two families of measurements that do not agree

One of the major difficulties of contemporary cosmology lies in the divergence between measurements of the Hubble constant depending on the method used. Measurements based on the early Universe and the ΛCDM model give H₀ ≈ 67.4 km·s⁻¹·Mpc⁻¹ for Planck alone, and very close values, H₀ ≈ 67.2 ± 0.4, when Planck, ACT and SPT-3G are combined. Local measurements, based on Cepheids and type Ia supernovae, give H₀ ≈ 73 km·s⁻¹·Mpc⁻¹. This discrepancy, initially about 5 σ, is called the Hubble tension.

Main recent measurements of the Hubble constant
Method	H₀ (km·s⁻¹·Mpc⁻¹)	Reference
Cosmic microwave background (Planck, ΛCDM)	67.36 ± 0.54	Planck Collaboration, 2020
DESI DR2 BAO + primordial nucleosynthesis (ΛCDM)	68.51 ± 0.58	DESI DR2, cited by H0DN, 2026
Red giant branch (TRGB), Hubble + JWST	70.39 ± 1.22 (stat) ± 1.33 (syst) ± 0.70 (σ_SN)	Freedman et al., 2025 (CCHP)
Cepheids and type Ia supernovae (SH0ES, Hubble)	73.04 ± 1.04	Riess et al., 2022
Local distance network consensus (H0DN)	73.50 ± 0.81	H0DN Collaboration, 2026

Is the cosmological constant really constant?

Λ, a constant vacuum energy

In the ΛCDM model, dark energy is a true constant Λ: its density does not change over time, and its equation of state is \( w = p/(\rho c^2) = -1 \). This is the simplest hypothesis, and the one that so far agrees with most observations.

What DESI measured

The DESI spectroscopic instrument published in 2025 the results of its second data release (DR2, three years of observation): measurements of baryon acoustic oscillations covering more than 14 million galaxies and quasars. They are well described by a flat ΛCDM model, but the parameters they prefer are in moderate tension (2.3 σ) with those of the cosmic microwave background.

When DESI is combined with the microwave background and supernova catalogues, an evolving dark energy, described by the parameters \( (w_0, w_a) \), is preferred over the ΛCDM model with a significance of 2.8 to 4.2 σ depending on the supernova sample. A reanalysis of the DES-SN5YR catalogue ("DES-Dovekie") has since brought the maximum from 4.2 σ down to 3.2 σ.

A lead to be confirmed, not a discovery

These values remain below the 5 σ threshold generally required for a discovery. The DESI authors emphasize that, barring an unknown systematic error in one of the data sets, the ΛCDM model is being put to the test and that a dynamic dark energy could be a solution. If confirmed, Λ would no longer be a constant, but a field evolving over cosmic time.

The link with neutrino mass

In the laboratory, the KATRIN experiment directly measures the mass of the electron neutrino through tritium decay. Its 259 days of data (Science, 2025) give \( m_\nu < 0{,}45 \) eV at 90% confidence level, i.e. less than one millionth of the electron mass. Cosmology is far more constraining: DESI and the microwave background limit the sum of the masses of the three neutrinos to \( \sum m_\nu < 0{,}064 \) eV (ΛCDM, 95% CL). This limit is close to the minimum of about 0.06 eV imposed by neutrino oscillations, and it relaxes to 0.16 eV if dark energy is evolving: the two questions are therefore linked.

Key takeaways

A foundation for modern physics

The physical constants have served as the foundation for the validation of scientific theories. They have made it possible to build a coherent framework to explain and predict a wide range of phenomena observed in the universe, from the infinitesimally small to the infinitely large. Since 2019, several of them even define the units of measurement themselves.

Three still-open questions

No theory today explains why the constants have these values. The Hubble tension is unresolved, and the nature of dark energy remains open: a constant of space-time or an evolving field. Data from DESI, the Euclid space telescope, JWST and future surveys will provide answers.

References

FAQ: Everything you need to know about physical and cosmological constants

What is a physical constant?

A physical constant is a quantity whose numerical value is considered fixed within the framework of a given theory. It appears in the equations that describe the laws of nature, such as the gravitational constant G or the speed of light c. Its value depends neither on the place nor on the time of measurement, which makes it possible to compare experiments carried out in very different contexts.

Which constants have been exact since 2019?

Since 20 May 2019, the Planck constant h, the elementary charge e, the Boltzmann constant k and the Avogadro constant N_A have had exact values by definition, just like the speed of light c (fixed since 1983), the caesium transition frequency and the luminous efficacy K_cd. These seven constants define all the units of the International System. On the other hand, G, α, ε₀ and the particle masses remain measured.

Can physical constants vary?

In the standard model of physics, these constants are rigorously invariable. However, some speculative theories, such as those involving a multiverse or cosmological scalar fields, envisage a very slow variation over cosmic durations. Current observations have not demonstrated any variation: optical clocks limit the drift of α to about 10⁻¹⁸ per year, and the spectrum of quasar HE 0515-4414 (ESPRESSO) is compatible with a fine-structure constant unchanged to within a few millionths over more than 8 billion years.

What is the fine-tuning of constants?

Fine-tuning refers to the fact that slight modifications of the fundamental constants would make the Universe incompatible with the existence of life and observers. For example, a fine-structure constant α that was too different would prevent the formation of stable atoms. This observation fuels philosophical and cosmological debates about the origin of these values, without any definitive explanation being accepted today.

Why is the cosmological constant Λ problematic?

The cosmological constant Λ represents the vacuum energy responsible for the accelerated expansion of the Universe. However, estimates from quantum physics exceed the observed value by several tens of orders of magnitude (up to 120 with a cutoff at the Planck scale), which constitutes the famous cosmological constant problem. The DESI results further suggest that this energy could evolve with time, although this is not yet established.

What is the Hubble tension?

It is the disagreement between the value of the expansion rate H₀ deduced from the cosmic microwave background (about 67 km·s⁻¹·Mpc⁻¹) and that measured locally with supernovae and distance indicators (about 73 km·s⁻¹·Mpc⁻¹). It reaches more than 5 σ according to some analyses. It could reveal an unidentified systematic error or physics beyond the ΛCDM model.

Are constants really universal?

The universality of constants rests on the cosmological principle, according to which the laws of physics are the same everywhere in the Universe. Astronomical observations, notably the study of absorption spectra of very distant objects, confirm this hypothesis to a remarkable level of precision. No convincing evidence of spatial variation has been established to date.

How is the value of fundamental constants measured?

The values of the constants are determined by high-precision experiments: torsion balances and atomic interferometers for G, hydrogen spectroscopy and ion traps for α and particle masses. The speed of light has not been measured since 1983: it is fixed by definition, and the metre follows from it. CODATA regularly compiles the measurements to publish an adjusted ensemble value. Each new generation of instruments improves the uncertainty associated with these essential quantities.