More power on large scales

This paper proposes that primordial black holes (PBHs) as macroscopic dark matter, which begin clustering before matter-radiation equality and lose mass via Hawking radiation, can simultaneously explain the unexpectedly high cosmic microwave dipole and galaxy bulk flows while reducing the Hubble tension by altering the early universe's sound horizon.

The Gist

Here is an explanation of the paper "More power on large scales" by Jeremy Mould, translated into simple, everyday language with creative analogies.

The Big Problem: The Universe is Moving Too Fast

Imagine you are watching a crowd of people (galaxies) in a massive stadium. According to our current "rulebook" of how the universe works (called the Standard Model or $\Lambda$CDM), these people should be drifting apart at a gentle, predictable pace.

However, astronomers have been measuring the "bulk flow" of these galaxies—how fast entire groups of them are moving together—and they are moving much faster than the rulebook predicts. It's like the crowd is suddenly sprinting when they should be walking. This is a major mystery in cosmology.

The Proposed Solution: Ghostly "Rock" Seeds

The author, Jeremy Mould, suggests a radical idea: Dark Matter isn't a ghostly, invisible particle. Instead, he proposes it might be made of Primordial Black Holes (PBHs).

Think of standard dark matter as a fine mist of invisible gas. It's smooth and spreads out evenly.
Think of Mould's PBH dark matter as billions of tiny, invisible bowling balls scattered throughout the universe.

Here is why this changes everything:

1. The "Early Start" Analogy

In the standard model, the universe starts smooth. Gravity has to slowly pull the "mist" together to form clumps, which takes a long time. It's like trying to build a sandcastle by waiting for the wind to pile the sand up.

In Mould's model, the universe starts with those tiny bowling balls (PBHs) already in place. Because they are heavy and dense right from the start, they act as anchors.

• The Metaphor: Imagine a river. In the standard model, the water flows slowly until it hits a rock. In Mould's model, the river is full of rocks from the very beginning. The water (regular matter) crashes into these rocks immediately, creating massive whirlpools and currents much faster.
• The Result: Because these "bowling balls" started pulling things together billions of years earlier than standard theory allows, the galaxies ended up with much higher speeds (momentum) that they are still carrying today. This explains the "too fast" movement we see.

2. The "Melting Ice Cube" Analogy

There is a second, clever twist in the paper. Mould suggests that some of these tiny black holes are evaporating (losing mass) over time, turning into radiation (light/heat).

• The Metaphor: Imagine the universe is a giant pot of soup.
  • Standard Model: The soup has a fixed amount of solid ingredients (matter) and a fixed amount of broth (radiation).
  • Mould's Model: Some of the solid ingredients (the tiny black holes) are slowly melting into the broth.
• Why this matters: When these black holes melt, they change the balance of the soup. This subtle shift in the recipe affects how the universe expanded in its early days.
• The Fix: This change helps solve a different famous mystery called the Hubble Tension. Right now, two different ways of measuring the universe's expansion rate give different answers. By having these black holes "melt" and change the early universe's density, Mould's model tweaks the math just enough so that both measurement methods agree. It's like adjusting the thermostat so the room feels the same temperature whether you measure it from the floor or the ceiling.

The "Toy Model" Experiments

The author ran computer simulations (which he calls a "toy model") to test this.

• He created a universe with 256,000 "particles" (representing the black holes).
• He let them evolve from a very early time (when the universe was a baby) all the way to today.
• The Result: The galaxies in his simulation moved much faster and formed larger "bulk flows" than in standard simulations. They matched the real-world observations of fast-moving galaxies much better.

Why Should We Care?

This paper suggests we might not need to invent new, weird physics to explain the universe. We might just need to realize that Dark Matter is made of tiny black holes that started forming earlier and are slowly disappearing.

• If he's right: It solves the "fast galaxies" problem.
• If he's right: It also helps fix the "Hubble Tension" (the disagreement on how fast the universe is expanding).
• The Catch: This is currently just a "toy model." It's a simplified sketch. The author admits we need more powerful, complex computer simulations (including gas and stars, not just black holes) to see if this holds up under real scrutiny.

Summary

Imagine the universe as a giant dance floor.

• The Old Theory: The dancers (galaxies) are moving slowly because the music (gravity) started soft and slowly got louder.
• The New Theory: The dancers are moving fast because the DJ (Primordial Black Holes) dropped a heavy beat right at the start of the party, and some of the speakers are slowly melting, changing the rhythm just enough to make the math work out perfectly.

It's a bold, creative idea that turns the "invisible particle" theory on its head, suggesting the universe is full of tiny, ancient, melting rocks that set the stage for the cosmic dance we see today.

Technical Summary

Here is a detailed technical summary of the paper "More power on large scales" by Jeremy Mould (arXiv:2601.07106v1).

1. Problem Statement

The paper addresses two persistent tensions in modern cosmology:

• The Large-Scale Bulk Flow Problem: Observational data (e.g., Watkins et al. 2023) indicates that galaxies exhibit bulk flow velocities on scales of $>100 \, h^{-1}$ Mpc that are significantly higher (approx. 400 km/s) than predicted by the standard $\Lambda$CDM model. Standard models lack sufficient "power" on these large scales to generate such coherent motions.
• The Hubble Tension: There is a discrepancy between the Hubble constant ($H_0$) inferred from the Cosmic Microwave Background (CMB) under standard assumptions and local, late-time measurements.
• Simulation Limitations: Standard N-body simulations typically begin at redshift $z \sim 100$, assuming Cold Dark Matter (CDM) candidates are initially relativistic or possess thermal velocities. This may miss early structure formation mechanisms that could seed large-scale flows.

2. Methodology

The author proposes a "toy model" utilizing Primordial Black Holes (PBHs) as the dark matter candidate, specifically in the mass range of $10^{-20}$to$10^{-17} M_\odot$. The methodology involves:

• N-body Simulations:

  • Performed 256,000 particle simulations using a custom gravitational N-body code (Mould & Hurley 2025).
  • Initial Conditions: Unlike standard CDM, PBHs are treated as dense, non-relativistic matter from their inception in the radiation-dominated era. Simulations were initiated at very high redshifts ($z_0$ ranging from 500 to 30,000), well before matter-radiation equality ($z \sim 3400$).
  • Mass Loss Mechanism: The model incorporates Hawking radiation, where PBHs lose mass over cosmological timescales. Two prescriptions were tested:
    1. Dynamical reduction of particle mass based on the evaporation rate ($\dot{M} \propto M^{-2}$).
    2. Stochastic removal of a fixed percentage of particles per timestep.
  • Scale-Free Framework: The simulations are scale-free in mass, distance, and velocity, allowing results to be normalized to physical scales later. Baryons were excluded to isolate the dark matter dynamics.

• Analytical Framework:

  • The Friedmann equation was modified to account for time-varying matter density ($\Omega_m$) due to mass loss. The mass loss term ($\Omega'_m$) is treated as a boosted radiation term in the expansion history:
    $$\left(\frac{H}{H_0}\right)^2 = (\Omega_r + \Omega'_m)(1+z)^4 + \Omega_{m0}(1+z)^3 + \Omega_\Lambda$$
  • This modification reduces the sound horizon at recombination, theoretically increasing the CMB-inferred $H_0$.

• Data Analysis:

  • Bulk flows were calculated using the median velocity of particles within spherical top-hat volumes to avoid outliers from close two-body encounters.
  • "Galaxies" were identified heuristically by grouping particles (proto-halos) to estimate bulk flows of dark matter halos.

3. Key Contributions

• Early Seeding of Structure: The paper demonstrates that starting simulations at $z \gg 100$ with non-relativistic PBH seeds allows for the formation of high-density concentrations much earlier than in standard $\Lambda$CDM.
• Mass-Losing Dark Matter: It introduces a specific mechanism where dark matter loses mass via Hawking radiation, dynamically altering the expansion history and the gravitational potential wells.
• Unified Solution: The model attempts to simultaneously address the large-scale bulk flow anomaly and the Hubble tension through a single physical mechanism (PBH mass loss and early formation).

4. Key Results

• Enhanced Bulk Flows:

  • Simulations starting at high redshifts ($z_0 \sim 30,000$) with mass loss (Run 102) produced bulk flow velocities approximately twice as large as constant-mass control runs (Run 103).
  • The mass-losing model generated bulk flows with amplitudes consistent with observational tensions ($\sim 400$ km/s on scales $>100 \, h^{-1}$ Mpc), whereas standard models underpredict these values.
  • The enhancement is attributed to early gravitational acceleration by dense seeds and the subsequent reduction of gravitational potential due to mass loss, which prevents the deceleration of these high velocities.

• Hubble Constant Adjustment:

  • The evaporation of PBHs converts matter into radiation, effectively increasing the radiation density parameter ($\Omega_r$) in the early universe.
  • This reduces the sound horizon at recombination. To preserve the observed angular scale of the CMB, the inferred $H_0$ must increase by approximately 1%, bringing CMB-derived values closer to local measurements.
  • The model suggests a mass loss rate calibrated to a 10% decline in $\Omega_m$ between recombination and today, which remains consistent with late-time probes (Type Ia supernovae, weak lensing).

• Equation of State Implications:

  • The time-varying matter density mimics a dynamic dark energy equation of state. The paper suggests that a PBH mass-loss parameter could serve as a physical alternative to the phenomenological $w_a$ parameter used in DESI analyses.

5. Significance and Future Work

• Paradigm Shift: The paper argues that the "large-scale power" problem may not require modifying gravity or abandoning $\Lambda$CDM, but rather reconsidering the nature of dark matter (macroscopic PBHs) and the initial conditions of simulations (starting before $z=100$).
• Observational Tests:
  • The model predicts specific signatures in the CMB dipole and bulk flow measurements.
  • Future surveys like DESI and WALLABY, with improved peculiar velocity measurements, will be able to test these predictions.
• Limitations & Next Steps:
  • The current results are based on a "toy model" without baryons. The author emphasizes the need for high-resolution ($N > 10^7$) simulations including gas dynamics and baryonic feedback to confirm these findings.
  • The Initial Mass Function (IMF) of PBHs needs further refinement to match the specific mass loss rates required to fit observational data without violating constraints on late-time expansion.

Conclusion:
Mould proposes that if dark matter consists of evaporating Primordial Black Holes formed in the early radiation-dominated era, the resulting early gravitational clustering and subsequent mass loss can naturally explain the observed high bulk flow velocities and slightly alleviate the Hubble tension. This challenges the standard practice of starting cosmological simulations at $z \sim 100$ and suggests a re-evaluation of dark matter candidates in the context of large-scale structure formation.