We explore the phenomenology of the “Dark Walker”—an SU(3) theory with eight flavors of massless fundamental fermions in the dark sector. During inflation, its walking dynamics generate primordial non-Gaussianities through the exchange of unparticles, while accounting for the current dark matter relic abundance if we consider freeze-in of Dark Walker coupled to the Standard Model through the Higgs portal. This provides a simple yet predictive example linking strongly coupled inflationary dynamics to present-day dark matter.

Italy

Chen Yang

Dark walker in the early universe: A strongly coupled sector model

The standard model of the universe, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi><mi>CDM</mi></math>, is based on the Friedmann-Lemaître-Robertson-Walker metric with a flat three-dimensional coordinate space and the Friedmann equations Navas et al. [<a href="http://dx.doi.org/10.1103/PhysRevD.110.030001">Phys. Rev. D 110, 030001 (2024)</a>.]. The cosmological constant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math> provides the cancellation of the matter field contributions in the flat (Minkowski) space, as was proposed long ago in 1967 by Zeldovich for the first time to our knowledge Zeldovich [JETP Lett. 6, 316 (1967)]; see also Krasinski and Zeldovich [<a href="http://dx.doi.org/10.1070/PU1968v011n03ABEH003927">Sov. Phys. Usp. 11, 381 (1968)</a>]. The dynamical dark energy appears on the surface of the vacuum energy of matter fields at the flat (Minkowski) space. Within the Standard Model, the gluon Yang-Mills (YM) fields are playing a specific role since the properties of their vacuum, where there is the presence of the gluon condensate, provide the nonperturbative vacuum energy. It is natural to apply the successful instanton liquid model of the QCD vacuum and its lowest excitations. Our aim is to calculate the contribution of gluon YM fields to the dark energy density. We find that the universe metric is generating the QCD vacuum excitation, which gives the contribution to the dark energy density. But this one may hardly play a central role in the dynamics of the universe, since its timescale is too small. We also find the equation-of-state parameters <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>w</mi><mn>0</mn></msub><mo>=</mo><mo>−</mo><mn>1</mn><mo>,</mo><msub><mi>w</mi><mi>a</mi></msub><mo>=</mo><mn>0</mn></math> in accordance with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi><mi>CDM</mi></math>, while the newest data, analyzed at Shajib and Frieman [<a href="http://dx.doi.org/10.1103/kjpb-r698">Phys. Rev. D 112, 063508 (2025)</a>.], give them at least in the range <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>0.91</mn><mo>&lt;</mo><msub><mi>w</mi><mn>0</mn></msub><mo>&lt;</mo><mo>−</mo><mn>0.73</mn><mo>,</mo><mspace linebreak="goodbreak"></mspace><mo>−</mo><mn>1.05</mn><mo>&lt;</mo><msub><mi>w</mi><mi>a</mi></msub><mo>&lt;</mo><mo>−</mo><mn>0.65</mn></math>. They are requesting a contribution from an ultralight scalar such as an axion, or from YM field topological configurations with the nontrivial holonomy due to the deviation from a pure de Sitter state Van Waerbeke and Zhitnitsky [DESI results and dark energy from QCD topological sectors, <a href="http://arXiv.org/abs/2506.14182">arXiv:2506.14182</a>.].

Uzbekistan

M.M. Musakhanov

Dark energy and QCD instanton vacuum in a Friedmann-Lemaître-Robertson-Walker universe

The nucleus 212Po has been produced through the fragmentation of a 238U primary beam at 1 GeV/nucleon at GSI, separated with the FRagment Separator, FRS, and studied via isomer <italic>&#947;</italic>-decay spectroscopy with the RISING setup. Two delayed previously unknown <italic>&#947;</italic> rays have been observed. One has been attributed to the E3 decay of a 21 &#8722; isomeric state feeding the <italic>&#945;</italic>-emitting 45-s (18 +) high-spin isomer. The other <italic>&#947;</italic>-ray line has been assigned to the decay of a higher-lying 23 + metastable state. These are the first observations of high-spin states above the 212Po (18 +) isomer, by virtue of the selectivity obtained via ion-by-ion identification of 238U fragmentation products. Comparison with shell-model calculations points to shortfalls in the nuclear interactions involving high- <italic>j</italic> proton and neutron orbitals, to which the region around <italic>Z</italic>&#8764;100 is sensitive.

L. Zago

A. Gottardo

J.J. Valiente-Dobón

G. Benzoni

Spain

A. Gadea

Germany

M. Górska

S. Lunardi

Zs. Podolyák

P.H. Regan

Sweden

D. Rudolph

Hungary

A. Algora

G. de Angelis

D. Bazzacco

J. Benlliure

P. Boutachkov

A. Bracco

United Kingdom

A.M. Bruce

F. Camera

E. Casarejos

M.L. Cortés

F.C.L. Crespi

A. Corsi

C. Domingo-Pardo

M. Doncel

T. Engert

H. Geissel

J. Gerl

A. Goasduff

N. Goel

Poland

J. Grebosz

E. Gregor

T. Habermann

S. Klupp

I. Kojouharov

N. Kurz

S.M. Lenzi

S. Leoni

India

S. Mandal

R. Menegazzo

D. Mengoni

B. Million

A.I. Morales

D.R. Napoli

F. Naqvi

C. Nociforo

M. Pfützner

S. Pietri

A. Prochazka

F. Recchia

E. Sahin

H. Schaffner

A. Sharma

Slovakia

B. Sitar

D. Siwal

P. Strmen

I. Szarka

C.A. Ur

P.M. Walker

H. Weick

O. Wieland

H.J. Wollersheim

High-spin states in 212Po above the <italic>&#945;</italic>-decaying (18 +) isomer

In our previous work (Zhang and Shu in Eur Phys J. C 84(3):256, 2024), we have explored quantum gravity induced entanglement of masses (QGEM) in curved spacetime, observing entanglement formation between particles moving along geodesics in a Schwarzschild spacetime background. We find that long interaction time induces entanglement, even for particles with microscopic mass, addressing decoherence concerns. In this work, we build upon our previous work (Zhang and Shu 2024) by extending our investigation to a time-dependent spacetime. Specifically, we explore the entanglement induced by the mutual gravitation of massive particles in the Friedmann–Lemaître–Robertson–Walker (FLRW) universe. With the help of the phase shift and the QGEM spectrum, our proposed scheme offers a potential method for observing the formation of entanglement caused by the quantum gravity of massive particles as they propagate in the FLRW universe. Consequently, it provides insights into the field of entanglement in cosmology.

China

Chi Zhang

United States

Fu-Wen Shu

Gravity-induced entanglement between two massive microscopic particles in curved spacetime: II. Friedmann–Lemaître–Robertson–Walker universe

For a spatially Friedmann–Lemaître–Robertson–Walker cosmology, we propose a multi-scalar field gravitational model. Specifically, we consider a two-scalar field cosmological model in which the kinetic components of the scalar fields establish a two-dimensional sphere of Lorentzian signature. For our Chiral-Quintom model we choose a mixed potential term $$V\left( \phi ,\psi \right) =V_{0}e^{\lambda \phi }+U_{0}e^{\kappa \phi }\psi ^{\frac{1}{\sigma } }$$ <math> <mrow> <mi>V</mi> <mfenced> <mi>ϕ</mi> <mo>,</mo> <mi>ψ</mi> </mfenced> <mo>=</mo> <msub> <mi>V</mi> <mn>0</mn> </msub> <msup> <mi>e</mi> <mrow> <mi>λ</mi> <mi>ϕ</mi> </mrow> </msup> <mo>+</mo> <msub> <mi>U</mi> <mn>0</mn> </msub> <msup> <mi>e</mi> <mrow> <mi>κ</mi> <mi>ϕ</mi> </mrow> </msup> <msup> <mi>ψ</mi> <mfrac> <mn>1</mn> <mi>σ</mi> </mfrac> </msup> </mrow> </math> and we investigate the asymptotic limits of the cosmological parameters. This model for $$U_{0}=0$$ <math> <mrow> <msub> <mi>U</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </math> , provides a generalization of the hyperbolic inflation where the equation of the state parameter can cross the phantom divide line. When $$U_{0}\ne 0$$ <math> <mrow> <msub> <mi>U</mi> <mn>0</mn> </msub> <mo>≠</mo> <mn>0</mn> </mrow> </math> we observe that this cosmological model exhibits asymptotic solutions that encompass accelerated universes, big rip singularities, and dust-like solutions. Hence, this multi-scalar field model it can be regarded as as a dark energy unify model which describes a variety of asymptotic cosmological scenarios.

Chile

South Africa

Andronikos Paliathanasis

Unified dark energy from Chiral-Quintom model with a mixed potential in Friedmann–Lemaître–Robertson–Walker cosmology

High-energy vector meson photoproduction is an important tool for studying the partonic structure of matter at low Bjorken <math><mi>x</mi></math>. In the Good-Walker (GW) paradigm, the cross section <math><mrow><mi>d</mi><mi>σ</mi><mo>/</mo><mi>d</mi><mi>t</mi></mrow></math> for coherent production of vector mesons or other final states depends the average transverse distribution of gluons, while the incoherent cross section depends on fluctuations in the nuclear structure, due to variations in nucleon positions, and/or gluonic hot spots. However, predictions of the the GW paradigm seemingly conflict with data from multiple experiments which observe coherent production of vector mesons accompanied by nuclear excitation, or in peripheral relativistic heavy-ion collisions. These data are consistent with a simpler, semiclassical approach. I will discuss this contradiction and explore how and why GW fails. I will also contrast the significant differences in incoherent photoproduction on <math><mmultiscripts><mi>Au</mi><mprescripts></mprescripts><none></none><mn>197</mn></mmultiscripts></math> and <math><mmultiscripts><mi>Pb</mi><mprescripts></mprescripts><none></none><mn>208</mn></mmultiscripts></math> targets in the GW approach with the much smaller expected differences in their low-<math><mi>x</mi></math> gluon content.

Spencer R. Klein

Challenges to the Good-Walker paradigm in coherent and incoherent photoproduction

Genly Leon

Sebastián Cuéllar

Esteban González

Samuel Lepe

Claudio Michea

Alfredo Millano

Erratum to: Averaging generalized scalar field cosmologies II: locally rotationally symmetric Bianchi I and flat Friedmann–Lemaître–Robertson–Walker models

Erratum to: Averaging generalized scalar field cosmologies I: locally rotationally symmetric Bianchi III and open Friedmann–Lemaître–Robertson–Walker models

Erratum to: Averaging generalized scalar-field cosmologies III: Kantowski–Sachs and closed Friedmann–Lemaître–Robertson–Walker models

Scalar-field cosmologies with a generalized harmonic potential and matter with energy density $$\rho _m$$ <math> <msub> <mi>ρ</mi> <mi>m</mi> </msub> </math> , pressure $$p_m$$ <math> <msub> <mi>p</mi> <mi>m</mi> </msub> </math> , and barotropic equation of state (EoS) $$p_m=(\gamma -1)\rho _m, \; \gamma \in [0,2]$$ <math> <mrow> <msub> <mi>p</mi> <mi>m</mi> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mi>γ</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <msub> <mi>ρ</mi> <mi>m</mi> </msub> <mo>,</mo> <mspace width="0.277778em"></mspace> <mi>γ</mi> <mo>∈</mo> <mrow> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>2</mn> <mo>]</mo> </mrow> </mrow> </math> in Kantowski–Sachs (KS) and closed Friedmann–Lemaître–Robertson–Walker (FLRW) metrics are investigated. We use methods from non-linear dynamical systems theory and averaging theory considering a time-dependent perturbation function D. We define a regular dynamical system over a compact phase space, obtaining global results. That is, for KS metric the global late-time attractors of full and time-averaged systems are two anisotropic contracting solutions, which are non-flat locally rotationally symmetric (LRS) Kasner and Taub (flat LRS Kasner) for $$0\le \gamma \le 2$$ <math> <mrow> <mn>0</mn> <mo>≤</mo> <mi>γ</mi> <mo>≤</mo> <mn>2</mn> </mrow> </math> , and flat FLRW matter-dominated universe if $$0\le \gamma \le \frac{2}{3}$$ <math> <mrow> <mn>0</mn> <mo>≤</mo> <mi>γ</mi> <mo>≤</mo> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> </mrow> </math> . For closed FLRW metric late-time attractors of full and averaged systems are a flat matter-dominated FLRW universe for $$0\le \gamma \le \frac{2}{3}$$ <math> <mrow> <mn>0</mn> <mo>≤</mo> <mi>γ</mi> <mo>≤</mo> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> </mrow> </math> as in KS and Einstein–de Sitter solution for $$0\le \gamma &lt;1$$ <math> <mrow> <mn>0</mn> <mo>≤</mo> <mi>γ</mi> <mo>&lt;</mo> <mn>1</mn> </mrow> </math> . Therefore, a time-averaged system determines future asymptotics of the full system. Also, oscillations entering the system through Klein–Gordon (KG) equation can be controlled and smoothed out when D goes monotonically to zero, and incidentally for the whole D-range for KS and closed FLRW (if $$0\le \gamma &lt; 1$$ <math> <mrow> <mn>0</mn> <mo>≤</mo> <mi>γ</mi> <mo>&lt;</mo> <mn>1</mn> </mrow> </math> ) too. However, for $$\gamma \ge 1$$ <math> <mrow> <mi>γ</mi> <mo>≥</mo> <mn>1</mn> </mrow> </math> closed FLRW solutions of the full system depart from the solutions of the averaged system as D is large. Our results are supported by numerical simulations.

Averaging generalized scalar-field cosmologies III: Kantowski–Sachs and closed Friedmann–Lemaître–Robertson–Walker models