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We discuss flat Friedmann-Lemaître-Robertson-Walker (FLRW) metric-affine cosmology where the metric and connection as well as the matter energy-momentum and hypermomentum all obey the symmetry of spatial homogeneity and isotropy. In particular, we outline a scenario where a dark dust fluid carries spin hypermomentum which makes its effective equation of state dynamical and might relate to the DESI DR2 data.

We prove that ideals in amenable second-countable non-Hausdorff étale groupoid \\(C^*\\)-algebras are determined by their isotropy fibres. As an application, we characterise when the singular functions in Connes' algebra are dense in the singular ideal in terms of a property of explicit ideals in the isotropy group \\(C^*\\)-algebras. We then show this density property holds for all \\(C^*\\)-algebras of groupoids with finite-by-nilpotent isotropy groups.

A promising energy range to look for angular correlations between cosmic rays of extragalactic origin and their sources is at the highest energies, above a few tens of EeV (1 EeV ≡ 1018 eV). Despite the flux of these particles being extremely low, the area of ∼3000 km2 covered at the Pierre Auger Observatory, and the 17 yr data-taking period of the Phase 1 of its operations, have enabled us to measure the arrival directions of more than 2600 ultra-high-energy cosmic rays above 32 EeV. We publish this data set, the largest available at such energies from an integrated exposure of 122,000 km2 sr yr, and search it for anisotropies over the 3.4π steradians covered with the Observatory. Evidence for a deviation in excess of isotropy at intermediate angular scales, with ∼15° Gaussian spread or ∼25° top-hat radius, is obtained at the 4σ significance level for cosmic-ray energies above ∼40 EeV.

In this paper, we study \\(6\\)-dimensional GKM manifolds with \\(4\\) fixed points. We classify all possible GKM graphs, and for each type of graph we construct a manifold, proving the existence. We show that six types occur. (P1) complex projective space \\(C P^3\\) with standard complex structure (P2) blow up of \\(S^6\\) at a fixed point, diffeomorphic to \\(C P^3\\) (P3) \\(C P^3\\) as the homogeneous space \\(Sp(2)/(U(1) Sp(1))\\) with non-standard almost complex structure (Q1) complex quadric \\(Q_3\\) with standard complex structure (Q2) blow up of \\(S^6\\) along isotropy \\(2\\)-sphere, diffeomorphic to \\(Q_3\\) (S) \\(S^2 S^4\\), obtained as equivariant gluing along orbits of two \\(S^6\\)'s

The purpose of this note is to show that, in contrast to the \\( F_p\\)-case (proven in [7]), the \\(p\\)-primary and \\(p\\)-adic cases of the Isotropy Conjecture, claiming that the isotropic Chow groups with \\( Z/p^r\\), \\(r>1\\), respectively, with \\( Z_p\\)-coefficients over a flexible field coincide with the numerical ones, don't hold. We show that the \\(BP\\)-theory with \\(I(ınfty)\\)-primary, respectively, \\(I(ınfty)\\)-adic coefficients may serve as a regular substitute for \\(p\\)-primary, respectively, \\(p\\)-adic Chow groups, which permits to extend the results of [6] to arbitrary primes.

Hundreds of millions of supermassive black hole binaries are expected to contribute to the gravitational-wave signal in the nanohertz frequency band. Their signal is often approximated either as an isotropic Gaussian stochastic background with a power-law spectrum or as an individual source corresponding to the brightest binary. In reality, the signal is best described as a combination of a stochastic background and a few of the brightest binaries modeled individually. We present a method that uses this approach to efficiently create realistic pulsar timing array data sets using synthetic catalogs of binaries based on the Illustris cosmological hydrodynamic simulation. We explore three different properties of such realistic backgrounds that could help distinguish them from those formed in the early universe: (i) their characteristic strain spectrum, (ii) their statistical isotropy, and (iii) the variance of their spatial correlations. We also investigate how the presence of confusion noise from a stochastic background affects detection prospects of individual binaries. We calculate signal-to-noise ratios of the brightest binaries in different realizations for a simulated pulsar timing array based on the NANOGrav 12.5 yr data set extended to a time span of 15 yr. We find that ∼6% of the realizations produce systems with signal-to-noise ratios larger than 5, suggesting that individual systems might soon be detected (the fraction increases to ∼41% at 20 yr). These can be taken as a pessimistic prediction for the upcoming NANOGrav 15 yr data set, since it does not include the effect of potentially improved timing solutions and newly added pulsars.

We prove that ideals in amenable second-countable non-Hausdorff étale groupoid \\(C^*\\)-algebras are determined by their isotropy fibres. As an application, we characterise when the singular functions in Connes' algebra are dense in the singular ideal in terms of a property of explicit ideals in the isotropy group \\(C^*\\)-algebras.

This paper leverages the first released catalog from the FAST All Sky H i Survey (FASHI) to examine the hypothesis of cosmic isotropy in the local Universe. Given the design of the overall FAST survey, the inhomogeneous detection sensitivity of FASHI is likely to introduce significant biases in the statistical properties of the catalog. To mitigate the potential influence of spurious clustering effects due to these sensitivity variations, we focus on extragalactic H i sources within the sensitivity range of [0.65, 1.0]. This refined subsample is divided into 10 distinct sky regions, for which we compute the two-point angular correlation functions (2PACF) over angular scales of 0 .° 5 < θ < 10°. We apply the Markov Chain Monte Carlo method to fit these 2PACFs with a power-law model and assess the statistical significance of the best-fit parameters for the 10 FASHI sky regions by comparing them against results from mock catalogs generated under the assumptions of homogeneity and isotropy. Our findings indicate that the local Universe, as traced by the H i sources in the FASHI survey, aligns with the cosmic isotropy hypothesis within a 2σ confidence level. We do not detect any statistically significant deviations from cosmic isotropy in the FASHI survey data.

Field‐line curvature scattering (FLCS) is believed to be the primary mechanism forming electron isotropy boundaries (IB) and can rapidly scatter relativistic electrons from the outer radiation belt. However, its direct and quantitative impact on controlling outer belt electron lifetimes has never been directly assessed. Using simultaneous observations of IBs from low‐altitude satellites and in situ electron fluxes from equatorial satellites, we report IBs intruding into the outer belt (reaching L ∼ 4.5), closely synchronized with sharp flux radial gradients near IBs, caused by significant electron loss outside IBs during a 4‐day storm recovery period. By combining observations with simulations, we provide the first direct and quantitative evidence that FLCS‐induced electron loss outside the IB dominantly controls the outer belt electron lifetimes. Our findings reveal that this simple yet fundamental physical process, which has been historically neglected in global radiation belt models, can explain the outer electron belt configuration.

During substorms, Earth's magnetotail undergoes rapid dipolarization, driving Earthward plasma flows that decelerate and dissipate energy upon encountering the dipole magnetic field in the nightside transition region. This region mediates the interaction between the magnetotail, inner magnetosphere, and the ionospheric auroral zone, though significant mapping uncertainties obscure the precise link and particle acceleration processes. Using data from THEMIS, TREx, and ELFIN, we analyze a storm‐time substorm on 4 September 2022, establishing a relationship, that is, not a causation, between magnetospheric and ionospheric dynamics. Following a dipolarization, the auroral bulge overlapped with the footprints of the electron isotropy boundary (IB) and the outer radiation belt. Notably, the precipitating electron energies reached at least 2 MeV in the bulge, exceeding previous reports. By comparing the latitudes of the electron IB with respect to the auroral bulge, we deduce that the sources of both auroral and relativistic precipitation were confined in the dipolarized region.