Cosmic Expansion: Key to the Puzzles

 

Modern cosmology grapples with two significant and perplexing issues concerning the universe's expansion and energy content. Astronomical observations—spanning distant Type Ia supernovae, the cosmic microwave background, and large-scale structure—consistently show that the universe's expansion is accelerating. The first major challenge stems from a fundamental conflict between theory and observation, known as the cosmological constant problem. Our most successful theory of particle physics, quantum field theory, predicts that the vacuum of space should possess an intrinsic energy density due to quantum fluctuations, yielding an enormous theoretical value. However, Within the standard cosmological model (ΛCDM), this acceleration is attributed to dark energy, best described by a cosmological constant (Λ) with an extraordinarily small measured energy density. The core of the puzzle is the vast discrepancy, famously estimated at 120 orders of magnitude, between the theoretically predicted vacuum energy and the tiny value inferred for Λ from observations, posing a severe fine-tuning challenge to our understanding of fundamental physics.
Distinct from this theory-versus-observation conflict is the Hubble tension, an observational puzzle concerning the universe's current expansion rate (H₀). There is a persistent disagreement between the value of H₀ derived from early-universe measurements (primarily the cosmic microwave background, analyzed within the ΛCDM framework) and the higher value obtained from late-universe measurements (such as supernovae calibrated with local distance indicators). This statistically significant tension represents a conflict between different observational techniques interpreted through the same standard model, suggesting either unresolved systematic issues in the measurements or potential inadequacies in the ΛCDM model's description of the cosmic expansion history.

Recent re-analyses of observational data, such as those presented in studies examining supernova evidence, highlight the critical importance of the underlying cosmological model used for interpretation. These studies often question the standard ΛCDM model's core assumption of perfect large-scale homogeneity and isotropy, as described by the Friedmann-Lemaître-Robertson-Walker (FLRW) metric within General Relativity (GR). By exploring alternative frameworks, potentially incorporating the effects of cosmic structures and inhomogeneities more fully within a GR context (going beyond the simplified FLRW application, which could be seen as closer to a Newtonian-like idealization in its simplicity despite using GR equations), these analyses suggest that phenomena like cosmic acceleration or the specific value of the Hubble constant might be partially misinterpreted. Crucially, such work typically does not claim the raw astrophysical measurements (e.g., supernova brightness or redshift) are false. Instead, it posits that the model used to translate these observations into cosmological parameters like Λ or H₀ might be inadequate. If the universe deviates significantly from the perfect smoothness assumed in the standard model, applying a more realistic, inhomogeneous GR framework could lead to different conclusions about dark energy or the expansion rate, potentially alleviating tensions like the Hubble discrepancy by demonstrating they are artifacts of an oversimplified theoretical interpretation rather than flawed measurements.

Addressing the first puzzle, the cosmological constant problem, Laurent Nottale proposes a solution rooted in his theory of Scale Relativity (SR). This framework fundamentally departs from standard physics by postulating that spacetime is intrinsically fractal and non-differentiable, and that the laws of physics must exhibit covariance under transformations of scale (resolution). Nottale argues against the standard quantum field theory calculation of vacuum energy, suggesting it is based on the flawed assumption of a smooth spacetime background. Instead, his work identifies the origin of the observed cosmological constant with the negative gravitational self-energy of quantum fluctuations within the quark vacuum. Invoking the Mach-Einstein principle (that the total energy, including gravitational coupling, must vanish), this negative self-energy must be precisely cancelled by a positive energy density inherent to the vacuum. Crucially, Scale Relativity predicts this gravitational self-energy density scales differently (as r⁻⁶, where r is the scale) than typically assumed, implying the positive vacuum density must also scale this way. For this density to act as a constant Λ, these vacuum fluctuations must effectively 'freeze' at a specific transition scale, r₀, such that Λ is determined by the relation Λ = r_P⁴/r₀⁶ (where r_P is the Planck length). Nottale proposes this freezing mechanism is intrinsically linked to quark confinement. As virtual quark-antiquark pairs fluctuate into existence and are stretched apart by cosmic expansion, the strong force's linear confinement potential eventually leads to the creation of new virtual pairs ('string breaking'). This continuous pair creation from the confinement field compensates for the dilution due to expansion, maintaining a constant fluctuation density below this characteristic scale. This critical transition scale, r₀, is identified with the physics of the lightest hadrons, specifically the Compton wavelength associated with the effective mass of quarks within the neutral pion (r₀ = 2ħ/m_π₀c). By calculating Λ using the measured pion mass and the Planck length within this SR framework, Nottale derives a value for the cosmological constant density that shows remarkable agreement with the value observed through cosmological measurements. This approach aims to resolve the 120 order-of-magnitude discrepancy by identifying the correct physical scale (QCD/pion scale, not Planck scale) and the appropriate scaling law (r⁻⁶) dictated by the fractal geometry, thus deriving the cosmological constant from microphysical principles rather than treating it as an unexplained fine-tuned value.

Considering these distinct cosmological challenges, the research streams exemplified by the recent supernova re-analysis and Nottale's work within Scale Relativity offer compelling alternative perspectives. The re-examination of supernova data, by questioning the standard model's foundational assumptions like perfect homogeneity and potentially requiring a more nuanced application of General Relativity to account for cosmic structure, directly addresses the interpretation of observational data. Such foundational changes could significantly alter the derived values of cosmological parameters, including the expansion rate H₀, thereby offering a potential path towards resolving the Hubble tension by demonstrating it might stem from an oversimplified cosmological model. Complementing this large-scale re-evaluation, Nottale's Scale Relativity framework tackles the cosmological constant problem at its quantum roots. By deriving the observed value of Λ from the microphysical principles of a fractal spacetime and the scale-dependent behaviour of the quark vacuum, SR provides a potential explanation for the constant's magnitude, sidestepping the fine-tuning issue inherent in standard vacuum energy calculations. Taken together, these approaches – one scrutinizing the cosmological model used to interpret large-scale observations and the other providing a fundamental derivation of Λ from a revised spacetime geometry – represent promising, synergistic avenues towards potentially resolving both the Hubble tension and the cosmological constant problem, suggesting that a deeper understanding of relativity across all scales may hold the key.