The Big Bang model is one of the triumphs of modern cosmology. Since Edwin Hubble's (1889-1953) observations of the universe's expansion in the 1920s, to the discovery of the cosmic microwave background in 1965 by Arno Penzias (1933-2024) and Robert Wilson (1936-), this model has accumulated observational confirmations. Yet, a philosophical and methodological question remains: at what point does a model with too many free parameters lose its predictive power and become merely an adjustable description?
N.B.:
The Big Bang is primarily a model of cosmic evolution, not a model of cosmic origin. It tells us the story of the universe from a certain moment, but does not explain why that moment occurred or what preceded it.
The standard cosmological model, called Lambda-CDM, is based on a set of parameters measured with precision thanks to the anisotropies of the cosmic microwave background. These parameters are: the baryonic matter density \( \Omega_b \), the dark matter density \( \Omega_c \), the dark energy density \( \Omega_\Lambda \), the spectral index \( n_s \), the amplitude of primordial fluctuations \( A_s \), and the optical depth of reionization \( \tau \).
| Parameter | Parameter robustness | Symbol | Unitless value, measured (Planck 2018) | Physical meaning | Main measurement method |
|---|---|---|---|---|---|
| Density of ordinary matter (baryonic matter) | Robust: directly observable matter, well understood (primordial nucleosynthesis, spectroscopy) | \(\Omega_b h^2\) | 0.02237 ± 0.00015 ≈ 0.049 or 4.9% of the total density of the universe | 4.9%: Fraction of ordinary matter (atoms) in the universe | CMB anisotropies, by analyzing the fossil light of the Big Bang |
| Density of dark matter (Cold Dark Matter - CDM) | Speculative: gravitational effects well measured, but physical nature unknown, no direct detection to date | \(\Omega_c h^2\) | 0.1200 ± 0.0012 ≈ 0.264 or about 26.4% of the total density of the universe | 26.4%: Fraction of non-relativistic dark matter in the universe | By observing how galaxies rotate and how light is bent around galaxy clusters (large-scale structure, gravitational lenses) |
| Density of dark energy (Cosmological constant) | Highly speculative: effect measured with certainty, but nature completely mysterious, could be a property of the vacuum or new physics | \(\Omega_\Lambda\) | 0.6889 ± 0.0056 ≈ 68.9% of the total energy of the universe is dark energy | 68.9%: Fraction of dark energy, responsible for the acceleration of the universe's expansion | By observing distant star explosions (Type Ia supernovae) and their recession speed, baryon acoustic oscillations |
| Distribution of clumps (small vs large) | Robust: robust measurement, value slightly less than 1 consistent with predictions of cosmic inflation | \(n_s\) | 0.9649 ± 0.0042 | 1: A value close to 1 means that large structures (galaxy clusters) are slightly favored over small fluctuations | By comparing the sizes of hot and cold regions in the fossil radiation. CMB power spectrum at different angular scales |
| Intensity of primordial clumps (amplitude of fluctuations) | Robust: direct and precise measurement in the CMB, consistent with the current distribution of galaxies | \(A_s\) | (2.100 ± 0.030) × 10-9 (very low) | "Very low" indicates that the primordial universe was extremely homogeneous, with density variations on the order of one part per million | By mapping the tiny temperature variations (CMB power spectrum) |
| Opacity of reionization (optical depth of reionization) | Moderately robust: indirect measurement with uncertainties, depends on complex astrophysical processes but consistent with JWST observations | \(\tau\) | 0.054 ± 0.007 ≈ 5.4% | 5.4%: Fraction of CMB photons scattered by free electrons produced during reionization, between 150 million and 1 billion years after the Big Bang | By studying the polarization of CMB light at large angular scales |
N.B.:
The parameter H₀, although often presented among the six fundamental parameters of the ΛCDM model, is actually a derived parameter from the densities of baryonic matter (\(\Omega_b\)), dark matter (\(\Omega_c\)), and the cosmological constant (\(\Omega_\Lambda\)), as well as the geometry of the universe.
Source: Planck Collaboration 2018, Astronomy & Astrophysics and NASA LAMBDA Archives.
A model that is too flexible, with too many parameters, can fit any data and thus loses its real predictive power.
The introduction of the theory of cosmic inflation by Alan Guth (1947-) in 1980 perfectly illustrates this dilemma. This theory postulates an extremely rapid expansion phase of the universe in its very first moments (between 10-36 and 10-32 seconds after the Big Bang).
Thus, inflation elegantly solves several problems of the standard model: the horizon problem (why is the observable universe so homogeneous and almost constant in temperature?), the flatness problem (why is the curvature of the universe so close to zero?), and the absence of magnetic monopoles (theoretical entities predicted but never observed).
These two components remain mysterious despite decades of research. Dark matter, parameterized at 27% of the total energy content of the universe, only manifests itself through its indirect gravitational effects: galaxy rotation curves, gravitational lenses, formation of large-scale structures.
Dark energy, parameterized at 68% of the content, would be responsible for the acceleration of cosmic expansion observed since the late 1990s. These entities, although invisible and not directly detected, have become essential components of the model. Their ad hoc parameters are intended to save the model in the face of unexpected observations.
The Big Bang model relies on many fundamental constants and cosmological parameters that must take very precise values for the universe to resemble what we observe.
The problem of fine-tuning is that slight variations in these parameters would make the universe radically different: no galaxy formation, no complex chemistry, no star stability, or even no coherent expansion. The Big Bang model uses these values as input data and does not provide a fundamental mechanism to explain why they take precisely these values. This constitutes an important conceptual limitation: the model is predictive for the evolution of the universe once these parameters are set, but it does not resolve the question of why these specific values.
The cosmological model Lambda-CDM has provided a robust description of the evolution of the universe. However, increasingly precise observations, especially from Planck, the Sloan Digital Sky Survey, Gaia, and since 2022 from the JWST, reveal significant tensions between the model's predictions and observational data.
• The most discussed is the tension over the value of H0, i.e., the current expansion rate. Measurements from the cosmic microwave background give a value around 67 km s\(^{-1}\) Mpc\(^{-1}\), while independent local methods (Cepheids, Type Ia supernovae) converge to 73 km s\(^{-1}\) Mpc\(^{-1}\). This discrepancy now exceeds reasonable uncertainties.
• Another tension comes from the JWST's discovery of massive and already well-structured galaxies at very early epochs (less than 400 million years after the Big Bang). This phenomenon seems to contradict the expected speed of hierarchical structure formation. Some of these galaxies show high metallicity and stellar and halo masses well above what standard evolution would predict from the gradual merging of small halos.
• Although the cosmic microwave background appears remarkably uniform, we observe quite early in the universe's history a granular structure made of denser and less dense regions. This indicates that the initial density variations may not have been entirely "random."
Two main paths are possible: further complicate the model by adding additional parameters (e.g., evolving dark energy, self-interacting dark matter, residual curvature...) or explore conceptual alternatives such as modified gravity, inflation-free models, or cosmic bounce scenarios.
Whenever a new observation contradicts predictions, there is a strong temptation to add a new parameter rather than question the foundations of the model.
The model's inability to explain the zero moment leaves open fundamental questions that touch on both physics and metaphysics. The most vertiginous question remains the one formulated by the philosopher Gottfried Wilhelm Leibniz (1646-1716) in the 17th century: why is there something rather than nothing? The Big Bang model does not answer this question; it presupposes it. Similarly, the question of what existed before the Big Bang may be meaningless if time itself emerged with the universe. As Stephen Hawking (1942-2018) pointed out, asking what preceded the Big Bang is like asking what lies north of the North Pole: the question assumes the existence of something (a direction "further north") that simply does not exist. Finally, a crucial question remains: does the Big Bang represent an absolute beginning or simply a transition between a previous state and our current universe?
| Domain | What the model PREDICTS and EXPLAINS | What the model DOES NOT EXPLAIN | Scientific status |
|---|---|---|---|
| Origin of the universe | Evolution from a dense and hot state 13.8 billion years ago | Why the Big Bang occurred, what existed before (if this question makes sense), the first cause | Fundamental limit: beyond the Planck time (10-43 s), our theories collapse |
| Matter-antimatter asymmetry | Observation: the universe is composed almost exclusively of matter, very little antimatter | Why there is an imbalance between matter and antimatter (about 1 excess matter particle per 1 billion matter-antimatter pairs), mechanism of this primordial asymmetry | Major unresolved problem: according to the standard model, the Big Bang should have created as much matter as antimatter, which would have mutually annihilated |
| Expansion of the universe | Expansion rate (Hubble constant), expansion history, prediction verified by Hubble in 1929 | Why the universe is expanding rather than static, initial mechanism of expansion | Confirmed prediction, but unexplained origin |
| Primordial nucleosynthesis | Formation of light elements (hydrogen, helium, lithium) in the first 3 minutes, abundances predicted with precision | Why these nuclear laws exist, origin of the physical constants that allow nucleosynthesis | Spectacular prediction confirmed by observations |
| Cosmic microwave background (CMB) | Existence, temperature (2.7 K), blackbody spectrum, anisotropies 380,000 years after the Big Bang | Why the universe was homogeneous on a large scale, origin of primordial fluctuations | Major prediction confirmed (discovered in 1965), but origin of initial conditions unknown |
| Structure formation | Hierarchical formation of galaxies, clusters, and superclusters from primordial fluctuations | Exact origin of fluctuations, why this particular amplitude (2 × 10-9) | Process well understood, but initial conditions mysterious |
| Dark matter | Spatial distribution, gravitational effects, role in structure formation | Physical nature of particles, why it exists, why precisely 27% of the total content | Effects measured with precision, but nature completely unknown (no direct detection) |
| Dark energy | Acceleration of expansion since about 5 billion years ago, 68% contribution to energy content | Physical nature, why it exists, why its density has this precise value, is it really constant? | Observed effect (Nobel Prize 2011), but nature completely mysterious |
| Fine-tuning of constants | Precise measurements of fundamental constants (fine-structure constant, proton/electron mass ratio, etc.) | Why these particular values, why are they so finely tuned to allow life and complexity | Established observation, explanation absent (anthropic principle, multiverse?) |
| Cosmic inflation | Solves the horizon, flatness, and monopole problems | Exact mechanism, nature of the inflaton field, why inflation started and then stopped | Attractive hypothesis with partially verified predictions, but hundreds of possible variants |
| Fate of the universe | If dark energy remains constant: eternal expansion toward a Big Freeze (cold and empty universe) | Future evolution of dark energy, unknown physical phenomena that could intervene | Extrapolation based on current observations, but long-term uncertainty |
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