The enduring mystery of dark matter receives fresh scrutiny as Oem Trivedi of Vanderbilt University and Abraham Loeb of Harvard University, along with their colleagues, investigate the possibility of Planck star remnants as potential constituents of this elusive substance. These remnants, theorised to form from gravitational collapse events that avoid singularities, offer a compelling alternative to traditional dark matter candidates. However, the team demonstrates that current observations from the Laser Interferometer Gravitational-Wave Observatory, specifically its upper limit on the gravitational wave background, effectively rules out the creation of these Planck mass relics through standard, Gaussian initial conditions. This finding significantly narrows the potential formation pathways for dark matter composed of Planck star remnants, leaving only non-Gaussian primordial fluctuations as a remaining viable explanation.
Recently, scientists proposed that such relics could constitute dark matter. Here, they demonstrate that current limits from gravitational wave observations rule out a formation pathway for Planck mass relics as dark matter originating from standard, Gaussian initial conditions. This leaves non-Gaussian primordial fluctuations as the only viable channel for creating Planck mass relics as dark matter. Few problems captivate as much attention in gravitational physics as the ultimate fate of matter undergoing complete collapse.
Loop Quantum Cosmology Prevents Black Hole Collapse
Scientists investigated the potential of Planck star remnants (PSRs) as a dark matter candidate, building upon the theoretical framework of loop quantum cosmology (LQC). The research team focused on demonstrating how quantum gravitational corrections could resolve the singularity predicted at the center of black hole collapse, leading to the formation of stable, long-lived remnants. The study employed LQC to model the evolution of the scale factor within a collapsing interior, utilizing a modified Friedmann equation that incorporates a correction term enforcing a bounce when the matter density reaches a critical value determined by loop quantum geometry. This mechanism prevents complete collapse and predicts the formation of a finite-density core.
To estimate the parameters of these PSRs, scientists calculated that when Hawking evaporation reduces a black hole’s mass to the Planck scale, approximately 10−5 grams, the corresponding Schwarzschild radius matches the Planck length. At this point, quantum pressure balances further collapse, halting evaporation and leaving behind a stable remnant. The team determined the present-day relic number density required to explain dark matter, calculating a value of approximately 2. 3 × 10−25cm−3, corresponding to a few hundred relics within the volume of the Earth. This low density aligns with the expectation that PSRs are non-interacting and invisible to direct detection, yet sufficient to account for the observed dark matter density.
The research also assessed PSRs in terms of entropy and temperature, noting that a semiclassical black hole evaporates at a Hawking temperature inversely proportional to its mass. However, as the mass approaches the Planck scale, this formula becomes unreliable due to the dominance of quantum gravitational effects. Within the PSR scenario, evaporation ceases before any runaway instability, leaving a cold, non-radiating remnant that behaves as cold dark matter, redshifted like pressureless dust and contributing to the growth of large-scale structure. This approach differs from previous proposals by emerging from a well-defined quantum gravitational process, a bounce in LQC, resulting in an LQG-modified internal geometry smoothly matched to a Schwarzschild exterior, guaranteeing stability through quantum geometry effects.
Planck Stars Rule Out High Curvature Power
The research team investigated the possibility of Planck star remnants serving as a form of dark matter, focusing on whether their formation is consistent with observational constraints. They demonstrated that under standard Gaussian statistics, creating sufficient Planck star remnants to account for dark matter requires a significant amount of primordial curvature power, specifically a power spectrum amplitude of approximately 10⁻² to 10⁻¹ at the time of horizon re-entry. However, this level of enhancement inevitably generates a second-order gravitational wave background with an energy density exceeding current limits established by gravitational wave detectors. The study reveals that this tension can be alleviated by considering non-Gaussian primordial fluctuations.
Calculations show that heavy-tailed distributions, such as lognormal or power-law forms, enhance the collapse fraction at a fixed variance. Specifically, for a power-law distribution with an index of approximately 5, the collapse fraction reaches a value of around 10⁻⁶, which is close to the required abundance for a primordial curvature power of approximately 10⁻³. This enhancement effectively reduces the necessary primordial curvature power and suppresses the induced gravitational wave background, bringing it into compatibility with current observational bounds.
Non-Gaussianity Resolves Planck Star Tension
The research demonstrates that Planck star remnants, proposed as potential dark matter candidates, face constraints from observations of the gravitational wave background. Calculations reveal that generating a sufficient abundance of these remnants from standard Gaussian initial conditions requires a significant enhancement of primordial fluctuations, which in turn produces a gravitational wave signal exceeding current observational limits. This finding establishes a tension between the Planck star dark matter hypothesis and the simplest models of the early universe. However, the team finds that this tension can be resolved if the primordial fluctuations exhibit substantial non-Gaussianity. Specifically, heavy-tailed distributions of these fluctuations enhance the collapse fraction of matter into Planck star remnants, reducing the required amplitude of primordial fluctuations and suppressing the resulting gravitational wave background. This suggests that the existence of Planck star dark matter implies a non-Gaussian origin for small-scale fluctuations in the early universe, pointing towards physics beyond standard inflationary models.