# The Numerical Error Behind Dark Matter's Greatest Challenge

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# Dark Matter’s Biggest Problem Might Simply Be A Numerical Error

## It’s one of cosmology’s biggest unsolved mysteries. The strongest argument against it may have just evaporated.

The overarching aim of cosmology is to unravel the mysteries surrounding the inception, development, and transformation of the Universe. This encompasses every particle, antiparticle, and quantum of energy, their interactions, and the evolution of spacetime itself. Theoretically, if one could articulate the initial conditions of the Universe, including its composition and the governing laws of physics, simulations could predict its future states.

However, executing this in reality is a monumental challenge. While some computations yield straightforward results, linking theoretical predictions to observable phenomena can be complex. These connections serve as crucial observational tests for dark matter, which constitutes about 27% of the observable Universe. Yet, one specific test has consistently shown dark matter failing, and scientists may have finally pinpointed the cause: a numerical error.

When considering the Universe today, its appearance varies significantly across different scales. On the scale of individual stars or planets, the Universe seems largely vacant, with Earth being approximately 1,000 times denser than the cosmic average. As one examines larger scales, however, the Universe becomes increasingly homogeneous.

For instance, individual galaxies like the Milky Way are only a few thousand times denser than the cosmic mean. When analyzing the Universe at the scale of vast galaxy groups or clusters, the densest regions are only a few times denser than typical areas. On the grandest scales, measuring billions of light-years, the Universe's density remains nearly constant, with a precision of about 0.01%.

If we model the Universe according to established theoretical expectations, supported by comprehensive observations, it should have begun filled with matter, antimatter, radiation, neutrinos, dark matter, and a small amount of dark energy, nearly uniform with minute variations.

In the initial moments, multiple interactions occur simultaneously:

- Gravitational forces amplify the overdense regions.
- Particle and photon interactions scatter normal matter, leaving dark matter unaffected.
- Radiation streams out from small overdense regions, blurring structures that develop too early.

By the time the Universe reached 380,000 years, intricate patterns of density and temperature fluctuations had already emerged. The largest fluctuations appeared at a specific scale where normal matter collapsed most effectively, while radiation had minimal opportunity to escape. On smaller angular scales, the fluctuations displayed periodic peaks and valleys that diminished in amplitude as predicted.

These density and temperature fluctuations, small in scale compared to average density, lend themselves to straightforward predictions. This fluctuation pattern should be observable in both the large-scale structure of the Universe and the temperature variations in the Cosmic Microwave Background (CMB).

In physical cosmology, such predictions are easier to derive theoretically. You can accurately model how a uniformly distributed Universe, regardless of its constituent matter, will evolve. Additionally, minor imperfections can be superimposed onto this model, allowing for precise approximations.

This linear approximation holds true during the early Universe's evolution, where density fluctuations are minimal compared to the average cosmic density. Thus, measuring the Universe at the largest scales should provide robust tests for dark matter and cosmological models. Consequently, predictions regarding dark matter, especially concerning galaxy clusters, have been remarkably successful.

Yet, on smaller scales, particularly those involving individual galaxies, this approximation fails. When density fluctuations become significant relative to the background density, manual calculations become unfeasible. Numerical simulations are necessary to navigate the transition from linear to non-linear regimes.

In the 1990s, pioneering simulations delved into non-linear structure formation, allowing scientists to understand how temperature affects dark matter structure formation. These insights, along with observations of small-scale structures, indicated that dark matter must be "cold" to align with observed structures.

During the same period, the first dark matter halo simulations emerged, revealing various common features:

- A central density peak,
- A gradual decline in density (approximately proportional to r^-1 to r^-1.5), until reaching a critical distance based on halo mass,
- A subsequent sharper decline (approximately proportional to r^-3) until it dips below the average cosmic density.

These simulations predicted "cuspy halos," where density peaks at the center, but observations of low-mass galaxies show inconsistent rotational dynamics, favoring "core-like halos" with constant central densities.

This discrepancy, termed the core-cusp problem, represents a longstanding issue in dark matter research. Theoretically, matter should coalesce into gravitational structures, undergoing violent relaxation, where massive objects sink to the center while lighter ones disperse.

Despite the observed phenomena aligning with expectations of violent relaxation, it remains possible that these features merely reflect numerical artifacts of the simulations.

Consider approximating a square wave using a Fourier series: as more sine wave terms are added, the approximation improves but consistently overshoots the desired value by about 18%. This overshoot illustrates a numerical artifact inherent to the approximation method rather than a genuine reflection of the waveform.

A recent paper by A.N. Baushev and S.V. Pilipenko, published in Astronomy & Astrophysics, posits that the observed central cusps in dark matter halos might be numerical artifacts resulting from the algorithms used in simulations, rather than genuine effects of violent relaxation.

In essence, the density profiles derived from simulations may not accurately reflect the physical processes governing dark matter. Instead, they could simply stem from numerical methods used in halo simulations. As the authors note:

> “This result casts doubts on the universally adopted criteria of the simulation reliability in the halo center. Though we use a halo model, which is theoretically proved to be stationary and stable, a sort of numerical ’violent relaxation’ occurs. Its properties suggest that this effect is highly likely responsible for the central cusp formation in cosmological modelling of the large-scale structure, and then the ’core-cusp problem’ is no more than a technical problem of N-body simulations.” - Baushev and Pilipenko

The challenges concerning dark matter predominantly arise on smaller cosmic scales, deeply entrenched in the non-linear evolution regime. For years, skeptics of dark matter have focused on these small-scale issues, believing they might unveil the fundamental flaws in dark matter theories.

If the findings of this recent paper hold true, cosmologists may have prematurely accepted the notion that dark matter forms halos with central cusps based solely on early simulation outcomes. In science, rigorous validation and independent verification of results are crucial. However, if multiple parties make the same error, such checks lose their independence.

Determining whether the results from simulations stem from actual dark matter physics or numerical artifacts could resolve one of the most significant debates surrounding dark matter. Should these results be rooted in genuine physics, the core-cusp issue will continue to challenge dark matter models. Conversely, if they arise from simulation techniques, a substantial controversy in cosmology could dissipate almost instantly.

*Starts With A Bang is now on Forbes, and republished on Medium thanks to our Patreon supporters. Ethan has authored two books, Beyond The Galaxy, and Treknology: The Science of Star Trek from Tricorders to Warp Drive.*