Cosmic Friction: How Galaxy Surveys Will Probe Dark Matter’s Hidden Properties

Author: Denis Avetisyan

New research suggests upcoming astronomical observations can reveal the subtle effects of ‘cosmic friction’ within dark matter and test the fundamental principles of gravity.

The study demonstrates that viscous dark matter exhibits suppressed growth of density contrast relative to baryons, as numerically solved from Eqs. (106) and (107) at $k=0.05$ and $k=0.12$ hh/Mpc, with analysis focused solely on bulk viscosity under the conditions $Θ=Γ=0, μ_G=η=1$.

This review explores the potential of large-scale structure surveys to constrain dark matter viscosity and probe violations of the equivalence principle beyond General Relativity.

Current cosmological models assume perfect fluid dark matter, yet its internal dynamics remain largely unexplored, potentially masking subtle effects on large-scale structure. In the paper ‘Testing the cosmological Euler equation: viscosity, equivalence principle, and gravity beyond general relativity’, we investigate how viscosity in dark matter, alongside potential violations of the equivalence principle and modifications to gravity, could manifest in observable cosmological signatures. Our analysis demonstrates that forthcoming galaxy surveys – notably DESI, Euclid, and SKA Phase 2 – will be sensitive enough to constrain dark matter viscosity to levels approaching 10^-7, providing a novel probe of fundamental physics. Could these constraints reveal deviations from standard cosmology and unlock a deeper understanding of the universe’s unseen components?

The Universe’s Shadows: A Dark Matter Paradox

The current understanding of the universe’s large-scale structure hinges on the concept of Cold Dark Matter, a hypothetical substance comprising roughly 85% of the matter in the universe. Cosmological models posit this dark matter as “cold” – meaning the particles move slowly compared to the speed of light – and “collisionless,” behaving as a fluid where particles rarely interact with each other except through gravity. This framework is crucial for explaining how initial density fluctuations in the early universe grew over billions of years, ultimately forming the galaxies and cosmic web observed today. Simulations, built upon this collisionless fluid model, demonstrate how gravity amplified these tiny fluctuations, with dark matter forming a scaffolding upon which visible matter subsequently coalesced. However, increasingly precise observations are revealing discrepancies between these simulations and reality, suggesting the simple collisionless fluid picture may be incomplete and prompting investigation into more complex dark matter interactions.

Cosmological simulations, built upon the established Cold Dark Matter model, increasingly diverge from detailed astronomical observations, especially when examining structures on smaller scales – like dwarf galaxies and the internal dynamics of galactic halos. These discrepancies aren’t merely statistical fluctuations; they suggest the underlying assumptions about dark matter’s behavior may be incomplete. Specifically, predictions for the abundance and distribution of these smaller structures exceed what astronomers actually observe, creating a ‘missing satellites’ problem. Furthermore, simulations struggle to accurately reproduce the observed diversity in the rotation curves of dwarf galaxies, and the density profiles of their cores. These persistent tensions strongly imply that the current model, while successful on large scales, fails to capture all the relevant physics governing dark matter, prompting researchers to explore alternative models incorporating self-interactions, warm dark matter, or even modifications to gravity itself.

At the heart of cosmological simulations lies the Cosmological Euler Equation, a fundamental principle governing the evolution of matter in the universe. This equation, derived from the laws of gravity and fluid dynamics, mathematically describes how dark matter and ordinary matter respond to both gravitational forces and their initial conditions after the Big Bang. It essentially maps the universe’s early density fluctuations – tiny variations in the distribution of matter – into the large-scale structures observed today, such as galaxies and galaxy clusters. By solving this equation, scientists can model the formation of these structures and compare the results to observational data. The equation considers factors like expansion of space, gravitational attraction, and the pressure – or lack thereof – within the cosmic fluid, providing a framework to understand the universe’s dynamic history. However, the precision of these simulations is critically dependent on the accuracy of the assumptions made within the Euler Equation, especially concerning the behavior of dark matter itself.

The prevailing understanding of dark matter rests on the DarkMatterColdFluid model, which posits that this enigmatic substance behaves as a fluid devoid of internal pressure. This simplification is foundational to cosmological simulations aiming to recreate the universe’s large-scale structure; it allows physicists to treat dark matter as responding solely to gravity and initial density fluctuations. Mathematically, this is often expressed through the Cosmological Euler Equation, a fluid dynamics equation adapted for the expanding universe. However, assuming a perfectly pressureless fluid is an approximation – a convenient simplification that may not fully capture the true nature of dark matter. Deviations from this ideal behavior, even subtle ones, could explain the growing discrepancies observed between simulations based on this model and actual astronomical observations, particularly regarding the distribution of matter in smaller galactic structures. Exploring alternatives to the pressureless fluid model is therefore crucial for refining cosmological understanding and potentially uncovering new physics beyond the Standard Model.

A Universe Less Empty: Introducing Viscous Dark Matter

Viscous Dark Matter (VDM) posits that dark matter is not perfectly collisionless, but rather exhibits intrinsic dissipative properties analogous to viscosity observed in fluids. Specifically, VDM introduces $BulkViscosity$, representing resistance to volumetric compression, and $ShearViscosity$, representing resistance to shear stress. These viscous forces imply that dark matter particles can lose kinetic energy through interactions, deviating from the standard Cold Dark Matter (CDM) model which assumes negligible particle interactions. This dissipation affects the free-streaming length of dark matter, suppressing small-scale structure formation and potentially resolving discrepancies between CDM simulations and observational data regarding the abundance and distribution of dwarf galaxies and other structures.

The introduction of bulk and shear viscosity into dark matter models fundamentally alters the dynamics of cosmic structure formation by providing a mechanism for energy dissipation. Bulk viscosity resists compression, effectively damping sound waves in the early universe and suppressing the growth of density perturbations on small scales. Shear viscosity, conversely, resists deformation and introduces a drag force between dark matter particles, influencing the velocity distribution and hindering the formation of filamentary structures. This resistance to both compressive and shear stresses results in a slower rate of structure growth compared to standard cold dark matter models, potentially resolving discrepancies between simulations and observed large-scale structure. The magnitude of these viscous effects is directly related to the strength of the viscosity, impacting the power spectrum of matter fluctuations and the abundance of halos at different redshifts.

Quantifying the viscous properties of dark matter requires the introduction of parameters that define the magnitude of its internal resistance to flow. The $C_{vis}$ parameter, specifically, serves as a dimensionless quantity characterizing the strength of bulk viscosity within the dark matter fluid. It represents the ratio of viscous stresses to flow rates, effectively scaling the impact of viscosity on cosmological dynamics. A higher $C_{vis}$ value indicates a greater degree of internal friction, leading to enhanced dissipation of energy and a modified growth rate of cosmic structures. Precise determination of $C_{vis}$ through observational constraints is crucial for validating the Viscous Dark Matter model and distinguishing it from standard Cold Dark Matter scenarios. The parameter allows for a systematic investigation of the influence of dark matter viscosity on large-scale structure formation.

Incorporating viscosity into the $CosmologicalEulerEquation$ allows for a more nuanced modeling of structure formation by introducing a pressure gradient dependent on the velocity field. Standard cosmological simulations, based on collisionless dark matter, often predict an excess of small-scale structure compared to observational data; viscous effects provide a mechanism to suppress this overabundance. The modified equation accounts for internal friction within the dark matter fluid, dissipating energy and damping the growth of density perturbations, particularly on smaller scales. This approach offers a potential pathway to bridge the gap between theoretical predictions and observations of galaxy formation and the cosmic microwave background, offering a more realistic representation of dark matter’s role in the universe’s evolution.

Echoes of Interaction: Mapping Growth and the Power Spectrum

The growth rate of cosmic structures, specifically the rate at which density perturbations evolve into the large-scale structures observed today, is demonstrably affected by the viscous properties of dark matter. While traditionally modeled as collisionless, incorporating a finite viscosity – representing internal friction within the dark matter fluid – alters the dynamics of structure formation. This manifests as a suppression of power on small scales, as viscous damping counteracts gravitational collapse. The magnitude of this suppression is directly related to the dark matter viscosity coefficient, providing a potential observational probe. Current research focuses on quantifying these effects to determine if variations in the growth rate, detectable through large-scale structure surveys and weak lensing measurements, can constrain the viscosity of dark matter and differentiate it from standard collisionless cold dark matter models. The expected signal is a subtle but potentially measurable deviation from the predicted growth rate based on $\Lambda$CDM cosmology.

The Power Spectrum, denoted as $P(k)$, is a fundamental tool in cosmology used to characterize the amplitude of density fluctuations at different spatial scales, represented by the wavenumber $k$. It quantifies how much variance exists in density fluctuations as a function of wavelength; higher values of $P(k)$ at a given $k$ indicate greater fluctuation amplitude at that scale. Specifically, $P(k)$ is defined such that its integral over $k$-space yields the variance in the density field. Variations in the growth rate of cosmic structures, driven by factors like dark matter viscosity, directly alter the shape of the Power Spectrum, suppressing or enhancing power at specific scales. Analyzing the Power Spectrum, therefore, provides a means to constrain cosmological parameters and test models of structure formation, with deviations from standard predictions potentially indicating new physics.

Accurate modeling of the Power Spectrum, which quantifies the amplitude of density fluctuations at various scales, necessitates the inclusion of Relativistic Effects. These effects arise from the finite speed of light and the expansion of the universe, altering the observed distribution of matter. Specifically, terms involving the gravitational potential and peculiar velocities of galaxies must be considered within the linear perturbation theory framework. Ignoring these relativistic corrections can lead to systematic errors in the estimation of cosmological parameters derived from large-scale structure surveys, such as the matter density $ \Omega_m $ and the amplitude of primordial fluctuations $ \sigma_8 $. Consequently, accounting for relativistic effects is essential for precise cosmological inference from observational data obtained from galaxy surveys and the Cosmic Microwave Background.

The Alcock-Paczynski effect is a geometrical distortion arising in cosmological observations due to incorrect assumptions about the expansion history or geometry of the universe. This effect manifests as a stretching or squeezing of structures along the line of sight, altering the observed shapes of features in large-scale structure surveys. Relativistic effects, specifically those related to the spacetime metric and the propagation of light, directly influence the magnitude and characteristics of this distortion. Accurate modeling of these relativistic contributions is therefore essential for correctly interpreting the observed distribution of matter and extracting reliable cosmological parameters from surveys measuring the $P(k)$ power spectrum or the baryon acoustic oscillations.

The Universe Observed: Testing Viscous Dark Matter

Large-scale cosmological surveys, such as the Dark Energy Spectroscopic Instrument Survey (DESISurvey) and the EuclidSurvey, represent a pivotal effort to chart the Universe’s vast architecture and refine its fundamental parameters. These ambitious projects don’t simply create maps; they meticulously measure the distribution of galaxies and other cosmic structures, providing crucial data to test the prevailing cosmological model and explore potential modifications to General Relativity. By precisely determining quantities like the expansion rate of the Universe and the growth of structure over cosmic time, these surveys aim to discern whether observed discrepancies – like the accelerating expansion – can be explained by the standard model with dark energy, or if they necessitate exploring alternative theories of gravity, often referred to as ModifiedGravity. The detailed mapping of the large-scale structure provides a sensitive probe of gravity on the largest scales, allowing scientists to assess whether gravity behaves as predicted by Einstein’s theory or if deviations exist that could hint at new physics.

Large-scale cosmological surveys, such as the Dark Energy Survey, Euclid, and the planned Square Kilometre Array, offer a unique opportunity to probe the nature of dark matter and test the predictions of the Viscous Dark Matter model. This model proposes that dark matter isn’t perfectly collisionless, but possesses a small degree of viscosity – an internal friction – which affects the growth of cosmic structures. By meticulously mapping the distribution of galaxies and measuring subtle distortions in their shapes, these surveys can reveal how matter has clumped together over cosmic time. Discrepancies between the observed large-scale structure and predictions based on standard cosmological models – discrepancies that currently motivate explorations beyond the standard model – may be explained by the viscosity of dark matter. Specifically, the degree to which structures form, and the patterns of their distribution, serve as fingerprints that can distinguish the Viscous Dark Matter model from competing explanations, such as modified gravity theories or the existence of additional relativistic particles.

Upcoming large-scale structure surveys, particularly the SKASurvey, represent a significant leap in observational cosmology, poised to rigorously test the Viscous Dark Matter model. These next-generation experiments are designed with dramatically improved sensitivity, enabling the acquisition of far more precise measurements of the Universe’s expansion history and the distribution of matter. This enhanced precision is crucial for discerning subtle deviations from standard cosmological predictions, and specifically, for constraining the dimensionless viscosity parameter, $C_{vis,0}$, which characterizes the self-interacting nature of dark matter in this model. Forecasts suggest that the SKASurvey will achieve a one-sigma constraint on $C_{vis,0}$ of approximately $7.5 \times 10^{-8}$, offering an unprecedented opportunity to validate or refute the theoretical framework and potentially reveal the nature of dark matter’s internal dynamics.

Upcoming large-scale galaxy surveys, including DESI, Euclid, and SKA2, promise a significant leap in the precision with which the properties of dark matter can be determined. Forecasts suggest these Stage-IV surveys will be capable of constraining the dimensionless viscosity parameter, $C_{vis,0}$, of dark matter to levels below $10^{-6}$. Notably, the SKA2 telescope is projected to achieve the most stringent constraint, reaching a $1\sigma$ precision of $7.5 \times 10^{-8}$, while Euclid and DESI are expected to achieve $1.1 \times 10^{-7}$ and $1.4 \times 10^{-6}$ respectively. Complementing these measurements, the exploration of the EPE parameter—a quantity sensitive to violations of the Weak Equivalence Principle—offers an independent pathway to test the foundations of General Relativity and further validate or refine the Viscous Dark Matter model.

The pursuit of cosmological models, particularly those attempting to account for dark matter viscosity and modified gravity, feels remarkably like building castles on shifting sands. This paper’s focus on constraining dark matter viscosity to levels of 10^-7, and probing the equivalence principle, is a laudable effort, yet one tinged with the inevitable fragility of theoretical constructs. As Isaac Newton observed, “I have not been able to discover the composition of any mixed body, though my endeavors have been constant and unwearied.” The relentless refinement of models, and the increasing precision of observational constraints, only serve to highlight the limitations of any given theory. Physics is the art of guessing under cosmic pressure, and each new constraint is merely a test of how gracefully a theory accepts its impending obsolescence.

What Lies Beyond the Horizon?

The pursuit of dark matter viscosity, refined to levels approaching 10^-7, feels less like an answer and more like an exercise in precision measurement. Each decimal place revealed only sharpens the question of what fundamental physics governs this elusive substance. The cosmological Euler equation, even when amended for relativistic effects, remains a construct. Galaxy surveys, with their ever-increasing resolution, will undoubtedly constrain these parameters, but constraints are not explanations. A tighter bound on viscosity does not preclude a more radical revision of the underlying theory.

Similarly, the search for violations of the equivalence principle, while vital, operates under the implicit assumption that such violations can be detected within the framework of observable phenomena. Black holes do not argue; they consume. Any subtle deviation from established principles, any crack in the edifice of general relativity, may simply vanish beyond the event horizon of our observational capabilities. The universe, in its indifference, offers no guarantees.

The next generation of cosmological probes will undoubtedly deliver data of unprecedented quality. But data, however precise, are merely points on a map. The true challenge lies not in refining the map, but in acknowledging the vast, unchartable territories that lie beyond its edges – and the possibility that the territory itself is fundamentally unknowable.

Original article: https://arxiv.org/pdf/2511.11554.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

The Universe’s Shadows: A Dark Matter Paradox

A Universe Less Empty: Introducing Viscous Dark Matter

Echoes of Interaction: Mapping Growth and the Power Spectrum

The Universe Observed: Testing Viscous Dark Matter

What Lies Beyond the Horizon?

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