We study the formation of primordial black holes (PBHs) and stochastic gravitational waves background (SGWB) produced by the supercooled radion phase transition (PT) in warped extra-dimension models solving the gauge hierarchy problem. We first determine how the SGWB and the produced PBH mass and abundance depend on the warped model’s infrared energy scale $\textit{ρ}$, and the number of holographic colors $\textit{N}$. With this finding, we recast on the plane {$\textit{ρ}$, $\textit{N}$} the current SGWB and PBH constraints, as well as the expected parameter reaches of GW detectors, as LISA and ET, and the gravitational lensing ones, such as NGRST. On the same plane, we also map the collider bounds on massive graviton production, and cosmological bounds on the radion phenomenology. We find that, for $\textit{N}$ ∼ 10 − 50, the considered PT predicts a PBH population mass in the range $\textit{M}$ ∼ (10 − 10 )$\textit{M}$ for $\textit{ρ}$ ∼ (10 − 10 ) TeV. In the range $\textit{ρ}$ ≃ (0.05 − 0.5) GeV, it can explain the recent SGWB hint at nHz frequencies and generate PBH binaries with mass $\textit{M}$ ∼ (0.1 – 1)$\textit{M}$ detectable at LISA and ET. The experimentally allowed mass region where PBHs can account for the whole dark matter abundance, and are produced with a tuning ≲ 10 , corresponds to 10 TeV ≲ $\textit{ρ}$ ≲ 10 TeV. These PBHs can compensate the lack of natural candidates for dark matter in warped extra dimensional models. Such a region represents a great science case where forthcoming and future colliders like HE-LHC and FCC-hh, gravitational-wave observatories and other PBHs probes play a key complementary role.

Poland

Anish Ghoshal

Spain

Eugenio Megías

Norway

Germano Nardini

Mariano Quirós

Complementary probes of warped extra dimension: colliders, gravitational waves and primordial black holes from phase transitions

We study holographic entanglement entropy and revisit thermodynamics and confinement in the dilaton-gravity system. Our analysis focuses on a solvable class of backgrounds that includes AdS and linear dilaton spacetimes as particular cases, with some results extended to general warped metrics. A general lesson is that the behavior of the holographic theory is tied to the bulk curvature singularities. We find that a singular background is confining if and only if $\textit{i)}$ the singularity coincides with a boundary or $\textit{ii)}$ it is the linear dilaton. In the former case, for which the singularity cuts off spacetime, we demonstrate that both entanglement entropy and thermodynamics exhibit a first order phase transition. In the linear dilaton case we find instead that both entanglement entropy and thermal phase transitions are of second order. Additionally, along the process we thoroughly derive the radion effective action at quadratic order.

Brazil

Sergio Barbosa

Sylvain Fichet

Entanglement entropy and thermal phase transitions from curvature singularities

<p>We investigate the impact of preheating on baryogenesis in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>R</mi><mn>2</mn></msup></math>-Higgs inflation. In this scenario, the inclusion of a dimension-six operator <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mi>R</mi><mo>/</mo><msup><mi mathvariant="normal">Λ</mi><mn>2</mn></msup><mo stretchy="false">)</mo></mrow><msub><mi>B</mi><mrow><mi>μ</mi><mi>ν</mi></mrow></msub><msup><mover accent="true"><mi>B</mi><mo stretchy="false">˜</mo></mover><mrow><mi>μ</mi><mi>ν</mi></mrow></msup></math> abundantly generates helical hypermagnetic fields during inflation, leading to a baryon asymmetric Universe at the electroweak crossover. Focusing on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>R</mi><mn>2</mn></msup></math>-like regime, we first derive the relevant dynamics of preheating using a doubly covariant formalism. We find that preheating can happen for the Higgs, transverse gauge, and Goldstone bosons, however, it is dependent on the value of the nonminimal coupling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ξ</mi><mi>H</mi></msub></math> between the Standard Model Higgs field and the Ricci scalar. We identify the preheating temperature to determine the appropriate scale <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi></math> for driving baryogenesis, which is around <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">Λ</mi><mo>∼</mo><mn>2.2</mn><mo stretchy="false">(</mo><mn>2.6</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>5</mn></mrow></msup><msub><mrow><mi>M</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow></msub></mrow></math> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ξ</mi><mi>H</mi></msub><mo>∼</mo><mn>1</mn><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></math>. Our results represent the most accurate estimation of the scale of gravity induced baryogenesis in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>R</mi><mn>2</mn></msup></math>-Higgs inflation to date. Areas for further improvement are identified.</p>

France

Yann Cado

United Kingdom

Christoph Englert

India

Tanmoy Modak

Implication of preheating on gravity assisted baryogenesis in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>R</mi><mn>2</mn></msup></math>-Higgs inflation

We propose a setup for the origin of dark matter based on spacetime with a warped extra dimension and three branes: the Planck brane, the TeV brane, at a (few) TeV scale <math><mrow><msub><mrow><mi>ρ</mi></mrow><mrow><mi>T</mi></mrow></msub></mrow></math>, and a dark brane, at a (sub-)GeV scale <math><msub><mi>ρ</mi><mn>1</mn></msub><mo>≲</mo><mn>100</mn><mtext> </mtext><mtext> </mtext><mrow><mi>GeV</mi></mrow><mo>≪</mo><msub><mi>ρ</mi><mi>T</mi></msub></math>. The Standard Model (SM) is localized in the TeV brane, thus solving the Higgs hierarchy problem, while the dark matter <math><mi>χ</mi></math>, a Dirac fermion with mass <math><msub><mi>m</mi><mi>χ</mi></msub><mo>&lt;</mo><msub><mi>ρ</mi><mn>1</mn></msub></math>, is localized in the dark brane. The radion, with mass <math><msub><mi>m</mi><mi>r</mi></msub><mo>&lt;</mo><msub><mi>m</mi><mi>χ</mi></msub></math>, interacts strongly [<math><mrow><mo>∼</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>χ</mi></mrow></msub><mo>/</mo><msub><mrow><mi>ρ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>∼</mo><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></math>] with dark matter and very weakly (<math><mo>∼</mo><msub><mi>m</mi><mi>f</mi></msub><msub><mi>ρ</mi><mn>1</mn></msub><mo>/</mo><msubsup><mi>ρ</mi><mi>T</mi><mn>2</mn></msubsup><mo>≪</mo><mn>1</mn></math>) with the Standard Model matter <math><mi>f</mi></math>. The generic conflict between the bounds on its detection signatures and its proper relic abundance is avoided as dark matter annihilation is <math><mi>p</mi></math>-wave suppressed. The former is determined by its very weak interactions with the SM and the latter by its much stronger annihilation into radions. Therefore, there is a vast range in the dark matter’s parameter space where the correct relic abundance is achieved consistently with the existing bounds. Moreover, for the dark brane with <math><msub><mi>ρ</mi><mn>1</mn></msub><mo>≲</mo><mn>3</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, a confinement/deconfinement first order phase transition, where the radion condensates, produces a stochastic gravitational wave background at the nanohertz frequencies, which can be identified with the signal detected by the Pulsar Timing Array (PTA) experiments. In the PTA window, for <math><mn>0.15</mn><mo>≲</mo><msub><mi>m</mi><mi>χ</mi></msub><mo>≲</mo><mn>2</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> the relic abundance is reproduced and all constraints are satisfied.

Fotis Koutroulis

Stefan Pokorski

Dark branes for dark matter

We study a solvable class of five-dimensional dilaton gravity models that continuously interpolate between anti-de Sitter (AdS5), linear dilaton (LD5) and positively curved spacetimes as a function of a continuous parameter ν. The dilaton vacuum expectation value is set by a potential localized on a flat brane. We chart the elementary properties of these backgrounds for any admissible ν, and determine stability conditions of the brane-dilaton system. We find that the spectrum of metric fluctuations can be either continuous or discrete. It features a massless graviton mode confined between the brane and the curvature singularity, and a massive radion mode tied to brane-dilaton stability. We show that, in the presence of a bulk black hole, the holographic theory living on the brane features a perfect fluid. The equation of state of the holographic fluid interpolates between radiation, pressureless matter and vacuum energy as a function of ν. This extends earlier findings on holographic fluids. Our results suggest that the thermodynamics of the fluid mirrors precisely the thermodynamics of the bulk black hole.

Holographic fluids from 5D dilaton gravity

Unstable particles decay sooner or later, so they are not described by asymptotic one-particle states and they should not be included as independent states in unitarity relations such as the optical theorem. The same applies to any countable collection of unstable particles. We show that the behaviour of unparticle stuff, that is, a continuous collection of particles with different masses and common decay channels, is pretty different: it has a non-vanishing probability of surviving for ever and the corresponding asymptotic states must be taken into account to comply with unitarity. We also discuss compressed spectra and the transition from the discrete to the continuous case.

Manuel Pérez-Victoria

Undecay

The linear dilaton (LD) background is the keystone of a string-derived holographic correspondence beyond <math><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>/</mo><msub><mrow><mi>CFT</mi></mrow><mrow><mi>d</mi></mrow></msub></mrow></math>. This motivates an exploration of the (<math><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></math>)-dimensional linear dilaton spacetime (<math><mrow><msub><mrow><mi>LD</mi></mrow><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msub></mrow></math>) and its holographic properties from the low-energy viewpoint. We first notice that the <math><mrow><msub><mrow><mi>LD</mi></mrow><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msub></mrow></math> space has simple conformal symmetries, that we use to shape an effective field theory (EFT) on the LD background. We then place a brane in the background to study holography at the level of quantum fields and gravity. We find that the holographic correlators from the EFT feature a pattern of singularities at certain kinematic thresholds. We argue that such singularities can be used to bootstrap the putative <math><mi>d</mi></math>-dimensional dual theory using techniques analogous to those of the cosmological bootstrap program. Turning on finite temperature, we study the holographic fluid emerging on the brane in the presence of a bulk black hole. We find that the holographic fluid is pressureless for any <math><mi>d</mi></math> due to a cancellation between Weyl curvature and dilaton stress tensor, and verify consistency with the time evolution of the theory. From the fluid thermodynamics, we find a universal temperature and Hagedorn behavior for any <math><mi>d</mi></math>. This matches the properties of a <math><mrow><msub><mrow><mi>CFT</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math> with large <math><mi>T</mi><mover><mi>T</mi><mo>¯</mo></mover></math> deformation, and of little string theory for <math><mi>d</mi><mo>=</mo><mn>6</mn></math>. We also find that the holographic fluid entropy exactly matches the bulk black hole Bekenstein-Hawking entropy. Both the fluid equation of state and the spectrum of quantum fluctuations suggest that the <math><mi>d</mi></math>-dimensional dual theory arising from <math><mrow><msub><mrow><mi>LD</mi></mrow><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msub></mrow></math> is generically gapped.

Holography of linear dilaton spacetimes from the bottom up

We investigate the potential of the warped extradimension framework as an explanation for the recently observed stochastic gravitational background at nHz frequencies in pulsar timing arrays (PTA). Our analysis reveals that the PTA data can be effectively accommodated by a first-order phase transition triggered by a radion at the MeV-GeV scale feebly coupled to the Standard Model. Remarkably, this outcome remains robust irrespective of the specific details of the warped extradimension embedding, providing a foundation for future investigations aiming to develop concrete extradimension descriptions of Nature. We also demonstrate that many existing embeddings are not viable, as their radion and graviton phenomenology clash with a MeV–GeV scale radion. As a possible way out, we sketch a promising solution involving multiple branes, wherein the light radion, graviton, and ensuing light resonances remain consistent with collider bounds and gravity tests.

Pulsar timing array stochastic background from light Kaluza-Klein resonances

If the inflaton field is coupled to the hypercharge Chern-Simons density <math><mi>F</mi><mover><mi>F</mi><mo>˜</mo></mover></math>, an explosive production of helical gauge fields when inflation ends can trigger baryogenesis at the electroweak phase transition. Besides, Higgs inflation identifies the inflaton with the Higgs field <math><mi>H</mi></math>, thus relating cosmological observables to properties of electroweak physics. In this paper we merge both approaches; the helical gauge fields are produced at the end of Higgs inflation from the coupling <math><mrow><mo>|</mo><mi>H</mi><msup><mo>|</mo><mn>2</mn></msup><mi>F</mi><mover><mi>F</mi><mo>˜</mo></mover></mrow></math>. In the metric formulation of gravity we found a window in the parameter space for electroweak baryogenesis consistent with all experimental observations. Conversely, for the Palatini formalism the non-Gaussianity bounds strongly constrain the helicity produced at the end of inflation, forbidding an efficient baryogenesis.

Baryogenesis from Higgs inflation

We study the cosmology of a 3-brane in a specific five-dimensional scalar-gravity (i.e., soft-wall) background, known as the linear dilaton background. We discover that the Friedmann equation of the brane world automatically contains a term mimicking pressureless matter. We propose to identify this term as dark matter. This dark matter arises as a projection of the bulk black hole on the brane, which contributes to the brane Friedmann equation via both the Weyl tensor and the scalar stress tensor. The nontrivial matterlike behavior is due to an exact cancellation between the Weyl and scalar pressures. We show that the Newtonian potential receives only a mild short-distance correction going as inverse distance squared, ensuring compatibility of the linear dilaton brane world with observed 4D gravity. Our setup can be viewed as a consistent cosmological description of the holographic theories arising in the linear dilaton background. We also present more general scalar-gravity models where the brane cosmology features an effective energy density whose behavior smoothly interpolates between dark radiation, dark matter, and dark energy depending on a model parameter.