⚛️ phenomenology

Principle of no paradoxical Universe

Motivated by recent DESI results suggesting a finite universe lifetime via a "Big Crunch," this paper conjectures that the universe may be configured to prevent the black hole information paradox from ever occurring in reality by ensuring black holes evaporate only after the universe's end, thereby deriving a lower mass bound for black holes based on cosmic longevity.

Original authors: Ngo Phuc Duc Loc

Published 2026-10-19

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CC BY 4.0

Original authors: Ngo Phuc Duc Loc

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

For decades, the prevailing story of our cosmos has been one of endless expansion. Astronomers observed that the universe is not just growing, but accelerating, driven by a mysterious force called dark energy. In this standard view, the universe will stretch forever, growing colder and emptier until time itself loses its meaning. This infinite timeline creates a profound problem for physicists. They have long suspected that black holes, the densest objects in existence, eventually vanish by leaking energy, a process known as evaporation. If a black hole lives long enough, it disappears completely, taking with it the information about everything that ever fell inside. This scenario creates a logical contradiction between the two pillars of modern physics: the rules governing the very small and the rules governing gravity. If the universe lasts forever, this contradiction is inevitable; it is only a matter of time before every black hole reaches this point of vanishing.

However, a shift in perspective has emerged from recent observations. New data suggests that dark energy might not be a constant force but something that changes over time, potentially weakening or even reversing. If this is true, the universe might not expand forever. Instead, it could eventually stop growing, begin to shrink, and collapse back into a single point in a "Big Crunch." This possibility changes everything about the black hole puzzle. If the universe has a finite lifespan, it might end before the smallest black holes have time to evaporate and trigger that logical contradiction. A researcher at the National Center for Theoretical Sciences in Taiwan has explored this idea, proposing that the universe might be structured in a way that simply prevents this paradox from ever happening in reality.

The researcher began by looking at the timing of black hole evaporation. They calculated that for a black hole to lose enough mass to create the information paradox, it must reach a specific stage in its life, a moment they call the "Page time." This is the point where the black hole has lost half of its initial information-carrying capacity. In a universe that lasts forever, even the most massive black holes will eventually reach this stage. But in a universe that collapses, the clock stops ticking before that moment arrives for many black holes. The researcher proposed a guiding principle: the universe is configured so that the smallest black holes existing within it never live long enough to reach their Page time. If the universe ends before they can evaporate, the paradox never occurs.

To test this idea, the author calculated a minimum size for black holes based on how long the universe is expected to live. Using a specific model where the universe collapses in about 35 billion years, they found that any black hole smaller than roughly 7.5 times 10 to the 14th power grams would have evaporated too quickly, creating the paradox. Therefore, for their principle to hold true, no black holes smaller than this mass can exist. This is a significant constraint because it rules out the existence of tiny, primordial black holes that might have formed in the earliest moments of the universe. These tiny objects, if they existed, would have evaporated long ago, leaving behind a trail of high-energy particles and gravitational waves that we should be able to detect.

The paper offers several concrete ways to check if this idea is correct. First, it predicts that we will never detect particles with extremely high energy coming from evaporating black holes. If a black hole were to evaporate completely, it would release a burst of energy, including particles with energies far higher than what we see. The absence of such signals supports the idea that these black holes never finish evaporating. Second, the researcher looked at gravitational waves, ripples in space-time. They argued that if tiny black holes existed and evaporated, they would leave a distinct signature in these waves. Specifically, they predicted that we should not see a certain type of gravitational wave signal associated with the formation of very small black holes. If future detectors, such as the proposed Einstein Telescope or DECIGO, scan the sky and find nothing in the frequency range expected for these tiny, evaporating objects, it would strongly support the idea that such black holes do not exist.

The author also considered the possibility that the universe might bounce, expanding and contracting in endless cycles. They noted that even in such a scenario, the logic of their principle could still hold if the black holes merge and grow large enough during the contraction phase to survive into the next expansion. However, their primary focus remains on the simpler scenario where the universe ends in a final collapse. They emphasize that their work is a suggestion based on current data, not a proven fact. The existence of a finite universe is still a hypothesis, though one that recent observations make increasingly plausible. If the universe does indeed have a deadline, then the laws of physics might be protected from a contradiction that would otherwise arise in an infinite timeline.

This research invites us to rethink the relationship between the life of the cosmos and the life of its most extreme objects. It suggests that the universe might be "tuned" to avoid a fundamental inconsistency in our understanding of reality. If the universe ends before the smallest black holes can vanish, then the information paradox is not a problem to be solved, but a scenario that never happens. The paper concludes by highlighting that this is a testable idea. By looking for the absence of specific signals—high-energy particles or certain gravitational waves—we can determine if the universe is indeed configured to keep these paradoxes at bay. If future observations confirm that no black holes smaller than the calculated limit exist, it would be a profound discovery, suggesting that the fate of the universe and the rules of quantum mechanics are deeply intertwined in a way that preserves the consistency of physical law.

Technical Summary: Principle of No Paradoxical Universe

Problem Statement
The standard $\Lambda$ CDM cosmological model posits an eternally expanding universe dominated by a cosmological constant. In this scenario, the universe has an infinite lifetime, guaranteeing that even the most massive supermassive black holes (BHs) will eventually evaporate via Hawking radiation. Consequently, the black hole information paradox—the conflict between the unitary evolution of quantum mechanics and the equivalence principle of general relativity—is deemed an unavoidable future eventuality, occurring after the "Page time" (the time required for a BH to lose half its initial degrees of freedom).

However, recent observations from the Dark Energy Spectroscopic Instrument (DESI) suggest that dark energy (DE) may be dynamical rather than a static cosmological constant. These results open the possibility that the universe's expansion could decelerate and reverse, leading to a "Big Crunch" scenario with a finite lifetime. If the universe ends before black holes reach their Page time, the information paradox may never manifest in reality. This paper investigates whether the universe's configuration inherently prevents the realization of the information paradox.

Methodology
The author employs a semi-classical approach to black hole thermodynamics and dynamical dark energy models to derive constraints on black hole existence.

Page Time Estimation: The paper calculates the Page time ( $t_{\text{Page}}$ ) for black holes as a function of their initial mass ( $M_i$ ). Using the mass loss rate derived from Hawking radiation, they establish that $t_{\text{Page}} \propto M_i^3$ .
Universe Lifetime Modeling: The author analyzes the DESI results within the context of dynamical DE. They specifically utilize a quadratic Hilltop quintessence model (where the potential $V = V_0 + V_2\phi^2/2$ with $V_2 < 0$ ) to demonstrate a "Big Crunch" scenario. This model yields a finite universe lifetime ( $\tau_{\text{Universe}}$ ), estimated at approximately 35 Gyr in their benchmark case.
The "No Paradoxical Universe" Conjecture: The core methodology involves imposing a condition where the universe's lifetime is strictly less than the Page time of the smallest existing black hole. The author proposes that if $\tau_{\text{Universe}} < t_{\text{Page}}(M_{\text{min}})$ , the paradox is physically precluded because the universe collapses before the inconsistency between quantum mechanics and general relativity can arise.

Key Contributions and Results

The Principle of No Paradoxical Universe: The paper formulates a conjecture stating: "The Page time of the smallest black hole existing within the Universe must be greater than the Universe's lifetime." This principle suggests that nature selects a configuration where the information paradox is never realized.
Derivation of a Lower Mass Bound: By equating the Page time to the universe's lifetime, the author derives a lower bound on the initial mass of black holes ( $M_i$ ) required to avoid the paradox:
$\left(\frac{M_i}{\text{g}}\right) \gtrsim 2.29 \times 10^{14} \left(\frac{\tau_{\text{Universe}}}{\text{Gyr}}\right)^{1/3}$
For the benchmark crunching model ( $\tau_{\text{Universe}} \approx 35$ Gyr), this implies a minimum black hole mass of $M_i \gtrsim 7.5 \times 10^{14}$ g. This threshold is robust across various dynamical DE models.
Predictions for Primordial Black Holes (PBHs): Since stellar evolution cannot produce black holes below roughly $2.6 M_\odot$ ( $\sim 5 \times 10^{33}$ g), the existence of black holes near the derived lower bound ( $10^{14}$ – $10^{15}$ g) would imply a primordial origin. The conjecture predicts that no black holes with masses below $\sim 10^{15}$ g exist in nature.
Gravitational Wave (GW) Signatures: The paper outlines specific null tests for the conjecture based on GW backgrounds:
- Scalar-Induced Gravitational Waves (SIGW): The formation of PBHs with masses below $10^{15}$ g would generate a stochastic GW background. The conjecture predicts a null detection of SIGW peaks in the frequency range corresponding to $1 \text{ g} \lesssim M_i \lesssim 10^{15}$ g (roughly $1 \text{ Hz} \lesssim f_{\text{peak}} \lesssim 10^8 \text{ Hz}$ ).
- Evaporation Signals: The paper predicts the absence of GW spectra associated with fully evaporated black holes (which would require $M_i \lesssim 5 \times 10^{14}$ g) and specific isocurvature or "poltergeist" GW backgrounds arising from periods of PBH domination that would have led to complete evaporation.
- High-Energy Particles: The conjecture implies that particles evaporated from black holes must have energies less than $\sim 10$ MeV. The detection of ultra-high-energy neutrinos or cosmic rays from black hole evaporation would contradict the principle.

Significance and Claims
The paper claims that the "Principle of No Paradoxical Universe" offers a novel resolution to the black hole information paradox not by modifying the laws of quantum mechanics or general relativity, but by asserting that the paradox is a "foreseeable" event that the universe's finite lifespan prevents from occurring.

The author highlights that their derived mass bound ( $M_i \gtrsim 7.5 \times 10^{14}$ g) is comparable to, though slightly stronger than, bounds derived from the Trans-Planckian Censorship Conjecture (TCC). They suggest that if their conjecture holds, primordial black holes in the mass range $10^{17}$ – $10^{23}$ g could serve as dark matter candidates that are consistent with both the TCC and the avoidance of the information paradox.

The paper emphasizes that the most critical test of this hypothesis is the null detection of SIGW and other GW signatures associated with sub- $10^{15}$ g primordial black holes. While upcoming detectors like the Einstein Telescope (ET) may probe parts of this parameter space, the author notes that confirmation requires new detectors operating in the $\sim 100$ Hz to $10^8$ Hz band. The work reframes the information paradox as a question of cosmological timescales, suggesting that the consistency of physical laws may be preserved simply because the universe does not live long enough to expose their incompatibility.

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