<p>We revisit well-established mechanisms for primordial black hole (PBH) production, namely inflation, phase transitions, and cosmic strings, in the context of the dark dimension scenario, which is motivated by swampland principles. Applying quantum gravity constraints, we demonstrate that any viable mechanism, barring exotic new physics at low energies, inevitably leads to the formation of five-dimensional PBHs. We further show that PBHs formed from cosmic strings can have lifetimes comparable to the age of the Universe. We comment on the observational implications of this result, including a potential connection to the recent detection of a high-energy neutrino by KM3NeT, whose energy is intriguingly close to the five-dimensional Planck scale in the dark dimension scenario.</p>

United States

Luis A. Anchordoqui

Alek Bedroya

Germany

Dieter Lüst

Primordial black holes are five dimensional

<p>Quantum gravity (QG) has a natural cutoff given by the Planck scale <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>M</mi><mi>pl</mi></msub></math>. However, it is known that the effective field theory (EFT) of gravity can break down at a lower scale, the species scale <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>s</mi></msub><mo>≲</mo><msub><mi>M</mi><mi>pl</mi></msub></math>, if there are light species of particles. Here we point out that there is a third scale <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mrow><mi>BH</mi></mrow></msub><mo>≲</mo><msub><mi mathvariant="normal">Λ</mi><mi>s</mi></msub><mo>≲</mo><msub><mi>M</mi><mi>pl</mi></msub></math>, which marks the inverse length (or the temperature) of the smallest black hole where the EFT gives a correct description of its entropy and free energy. This latter scale is hard to detect from the viewpoint of EFT as it represents a phase transition to a state with lower free energy. We illustrate this using examples drawn from consistent QG landscape. In particular <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mrow><mi>BH</mi></mrow></msub></math> gets related to Gregory-Laflamme transition in the decompactification limits of quantum gravity and to the Horowitz-Polchinski solution in the light perturbative string limits. We propose the existence of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mrow><mi>BH</mi></mrow></msub></math> marking the temperature at which neutral black holes undergo a phase transition, as a new Swampland condition for all consistent quantum theories of gravity. In the asymptotic regimes of field space <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mrow><mi>BH</mi></mrow></msub></math> is close to the mass scale of the lightest tower but deviates from it as we move inwards in the moduli space.</p>

Cumrun Vafa

David H. Wu

Tale of three scales: The Planck, the species, and the black hole scales

We raise a thermodynamic puzzle for Horowitz-Polchinski (HP) solutions in the presence of extra compact dimensions and show that it can be resolved by the existence of higher-dimensional string stars. We provide non-trivial evidence for the existence of such string stars in spacetime dimensions $\textit{d}$ ≥ 7 as higher-dimensional counterparts of HP solutions. In particular, we explicitly construct string star solutions in $\textit{d}$ = 7 that are under perturbative control. In $\textit{d}$ > 7, at the Hagedorn temperature, we identify these string stars as a specific normalizable representative of a new one-parameter bounded family of Euclidean solutions which can be under perturbative control. The higher-order $\textit{α}$ corrections play a crucial role in our arguments and, as pointed by other works, nullify the previous arguments against the existence of string stars in $\textit{d}$ ≥ 7. The higher-dimensional string stars have non-zero free energy at Hagedorn temperature and their mass and free energy are of the same order as those of a string-sized black hole. In $\textit{d}$ > 7, these solutions are string sized, but in $\textit{d}$ = 7, the size of these solutions diverges as ∼ ($\textit{T}$ − $\textit{T}$) near the Hagedorn temperature.

David Wu

String stars in $\textit{d}$ ≥ 7

We consider the classical Friedmann-Robertson-Walker solutions that describe a universe undergoing a transition from an accelerating expansion phase in the past to an eternal decelerating expansion phase in the future, driven by a scalar field evolving in a potential energy landscape. We show that any solution for which the accelerating phase violates the Trans-Planckian Censorship Conjecture (TCC), even in the interior of moduli space, never approaches the asymptotic vacuum with zero particles. Based on the assumption that the effective field theory must be valid for the vacuum on the asymptotic boundary, as motivated by holography and string theory, we argue that (multi-field) scalar potentials with such solutions are disallowed, thus strengthening the case for TCC. In particular, assuming the regularity of the future vacuum state in the string landscape, we derive results that imply a new set of highly-nonlinear constraints across the string landscape which in the absence of certain meta-stable vacua make realizing inflation impossible.

Qianshu Lu

Paul Steinhardt

TCC in the interior of moduli space and its implications for the string landscape and cosmology

We study universal features of the density of one-particle states $\textit{ρ}$($\textit{E}$) in weakly coupled theories of gravity at energies above the quantum gravity cutoff Λ, defined as the scale suppressing higher-derivative corrections to the Einstein-Hilbert action. Using thermodynamic properties of black holes, we show that in asymptotically flat spacetimes, certain features of $\textit{ρ}$($\textit{E}$) above the black hole threshold $\textit{M}$ are an indicator for the existence of large extra dimensions, and cannot be reproduced by any lower-dimensional field theory with finitely many fields satisfying the weak energy condition. Based on the properties of gravitational scattering amplitudes, we argue that there needs to exist a (possibly higher-dimensional) effective description of gravity valid up to the cutoff Λ. Combining this with thermodynamic arguments we demonstrate that $\textit{ρ}$($\textit{E}$) has to grow exponentially for energies Λ ≪ $\textit{E}$ ≪ $\textit{M}$ . Furthermore we show that the tension of any weakly coupled $\textit{p}$-brane with $\textit{p}$ ≥ 1 is bounded from below by Λ . We use this to argue that any tower of weakly coupled states with mass below Λ has to be a Kaluza-Klein (KK) tower. Altogether these results indicate that in gravitational weak-coupling limits the lightest tower of states is either a KK tower, or has an exponentially growing degeneracy thereby resembling a string tower. This provides evidence for the Emergent String Conjecture without explicitly relying on string theory or supersymmetry.

Rashmish Mishra

Max Wiesner

Density of states, black holes and the Emergent String Conjecture

One of the unique features of quantum gravity is the lack of local observables and the completeness of boundary observables. We show that the existence of boundary observables for particles with masses   <math> <munder> <mo>lim</mo> <mrow> <mi>t</mi> <mo>−</mo> <mo>∞</mo> </mrow> </munder> <mfrac> <mi>m</mi> <mi>H</mi> </mfrac> <mo>=</mo> <mo>∞</mo> </math>  $$ \underset{t-\infty }{\lim}\frac{m}{H}=\infty $$  in scalar fieldcosmologies where a(t) ∼ t  p  is equivalent to TCC, which implies p ≤ 1. Moreover, the mass of weakly-coupled particles must decay like m ≲ t 1 − 2p  to ensure that they yield non-trivial boundary observables. This condition can be expressed in terms of the scalar field that drives the cosmology as m ≲ exp(−cϕ) where c depends on the scalar potential. The strongest bound we find is achieved for   <math> <mi>V</mi> <mo>~</mo> <mo>exp</mo> <mfenced> <mrow> <mo>−</mo> <mn>2</mn> <mi>ϕ</mi> <mo>/</mo> <msqrt> <mrow> <mi>d</mi> <mo>−</mo> <mn>2</mn> </mrow> </msqrt> </mrow> </mfenced> </math>  $$ V\sim \exp \left(-2\phi /\sqrt{d-2}\right) $$  where   <math> <mi>c</mi> <mo>=</mo> <mn>1</mn> <mo>/</mo> <msqrt> <mrow> <mi>d</mi> <mo>−</mo> <mn>2</mn> </mrow> </msqrt> </math>  $$ c=1/\sqrt{d-2} $$ . These results connect some of the most phenomenologically interesting Swampland conjectures to the most basic version of holography.

Holographic origin of TCC and the distance conjecture

We initiate the program of bottom-up derivation of string theory dualities using Swampland principles. In particular, we clarify the relation between Swampland arguments and all the string theory dualities in d ≥ 9 dimensional supersymmetric theories. Our arguments center around the sharpened distance conjecture and rely on various other Swampland principles.

Japan

Yuta Hamada

Dualities from Swampland principles

We demonstrate the validity of the String Lamppost Principle — that all consistent theories of quantum gravity are in the String Landscape — for supersymmetric theories in d &gt; 6 using compactness and connectedness of the moduli space of small instantons, as well as the classification of the associated Coulomb branch.

Miguel Montero

Compactness of brane moduli and the String Lamppost Principle in d &gt; 6

In this paper, we propose a new Swampland condition, the Trans-Planckian Censorship Conjecture (TCC), based on the idea that in a consistent quantum theory of gravity sub-Planckian quantum fluctuations should remain quantum and never become larger than the Hubble horizon and freeze in an expanding universe. Applied to the case of scalar fields, it leads to conditions that are similar to the refined dS Swampland conjecture. For large field ranges, TCC is stronger than the dS Swampland conjecture but it is weaker for small field ranges. In particular for asymptotic regions of field space, TCC leads to a bound   <math> <mfenced> <mrow> <mi>V</mi> <mo>′</mo> </mrow> </mfenced> <mo>≥</mo> <mfrac> <mn>2</mn> <msqrt> <mrow> <mfenced> <mrow> <mi>d</mi> <mo>−</mo> <mn>1</mn> </mrow> </mfenced> <mfenced> <mrow> <mi>d</mi> <mo>−</mo> <mn>2</mn> </mrow> </mfenced> </mrow> </msqrt> </mfrac> <mi>V</mi> <mo>,</mo> </math>  $$ \left|V^{\prime}\right|\ge \frac{2}{\sqrt{\left(d-1\right)\left(d-2\right)}}V, $$  which is consistent with all known cases in string theory. Like the dS Swampland conjecture, the TCC forbids long-lived meta-stable dS spaces, but it does allow sufficiently short-lived ones.

Trans-Planckian Censorship and the Swampland

We study the implications of the recently proposed Trans-Planckian censorship conjecture (TCC) for early Universe cosmology and in particular inflationary cosmology. The TCC leads to the conclusion that if we want inflationary cosmology to provide a successful scenario for cosmological structure formation, the energy scale of inflation has to be lower than <math><msup><mn>10</mn><mn>9</mn></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. Demanding the correct amplitude of the cosmological perturbations then forces the generalized slow-roll parameter <math><mi>ε</mi></math> of the model to be very small (<math><mo>&lt;</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>31</mn></mrow></msup></math>). This leads to the prediction of a negligible amplitude of primordial gravitational waves. For slow-roll inflation models, it also leads to severe fine-tuning of initial conditions.