Scale-Divergence Problem

In the paper's words

This document provides a rigorous examination of the Scale-Divergence Problem, a fundamental schism in modern cosmology that arises from the antithetical performance of the two leading theoretical frameworks—Lambda Cold Dark Matter (ΛCDM) and Modified Newtonian Dynamics (MOND)—across different physical scales. ΛCDM achieves remarkable success in explaining cosmological observations (Cosmic Microwave Background, large-scale structure) but encounters significant challenges at galactic scales (cusp-core problem, radial acceleration relation). Conversely, MOND provides a simple, parameter-minimal explanation for galactic dynamics but fails catastrophically at cosmological scales and in galaxy clusters. This analysis systematically evaluates the theoretical foundations, observational successes, and critical failures of both paradigms.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. In galaxy clusters, MOND systematically underpredicts the gravitational field by a factor of 2-3, requiring additional “missing mass” (Angus et al., 2008).

   from 2.2 Modified Newtonian

2. Early arguments suggested an energy budget problem, but these were based on a mischaracterization of the process as a single energetic event rather than a cumulative, dynamical process; state-of-the-art simulations show that the required energy transfer is plausible (Pontzen & Governato, 2012).

   from 3.1 The Cusp-Core Problem

How it is done

1. This approach recognizes that the resolution of the Scale-Divergence Problem may require fundamentally new physics that transcends the current dichotomy.

   from 1.2 Scope and Objective of

2. The central question is whether the complex, baryonic-feedback-inclusive version of ΛCDM provides a generic, predictive, and falsifiable model of the universe on all scales, or whether a fundamentally new approach is required.

   from 4.1 The

3. A direct empirical proof of the existence of dark matter.

   from 6.0 References

What would falsify it

1. High-resolution N-body simulations predict a universal density profile for virialized halos, most famously the Navarro-Frenk-White (NFW) profile: $$\rho_{\text{NFW}}(r) = \frac{\rho_0}{\frac{r}{r_s}\left(1+\frac{r}{r_s}\right)^2},$$ where $\rho_0$ is a characteristic density and $r_s$ is a scale radius.

   from 2.1 Lambda Cold Dark Matter

2. The model also correctly predicts the characteristic scale of Baryon Acoustic Oscillations (BAO) observed in the large-scale distribution of galaxies, which provides a “standard ruler” to measure the expansion history of the universe (Eisenstein et al., 2005).

   from 2.1 Lambda Cold Dark Matter

3. These include the Cusp-Core Problem, where simulations predict a central density cusp ($\rho \sim r^{-1}$) but observations of dwarf galaxies indicate a central density core ($\rho \sim \text{constant}$) (Moore, 1994).

   from 2.1 Lambda Cold Dark Matter

Where the claim stops

1. It will navigate the core principles of both frameworks with mathematical precision, clarifying their respective assumptions, predictions, and limitations.

   from 1.2 Scope and Objective of

2. Conversely, MOND provides a simple, parameter-minimal explanation for galactic dynamics but fails catastrophically at cosmological scales and in galaxy clusters.

   from The

3. The essence of this problem is that ΛCDM achieves remarkable success in explaining cosmological observations but encounters significant challenges at galactic scales, while MOND provides a simple, parameter-minimal explanation for galactic dynamics but fails catastrophically at cosmological scales and in galaxy clusters.

   from 1.1 The

Where to read

1. 1.0666 words · 3 min
2. 2.0 Theoretical Foundations1,135 words · 5 min
3. 3.0 Observational1,252 words · 5 min
4. 4.0607 words · 3 min
5. 5.0375 words · 2 min
6. 6.0 References648 words · 3 min