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We perform a Bayesian analysis of CMB data from the Planck and ACT experiments to constrain the primordial helium mass fraction Y<SUB>He</SUB> and the effective number of relativistic species N<SUB>eff</SUB> in extensions of the standard ΛCDM cosmological model. With Planck 2018 data alone we find no statistically significant departure from Big Bang Nucleosynthesis (BBN) consistency: <mml:math><mml:mrow><mml:msub><mml:mi>Y</mml:mi><mml:mrow><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mi>e</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:msubsup><mml:mn>240</mml:mn><mml:mrow><mml:mo>−</mml:mo><mml:mn>0.013</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo><mml:mn>0.013</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math> (68% CL, free Y<SUB>He</SUB>) is compatible with the BBN-predicted value of <mml:math><mml:mrow><mml:msubsup><mml:mi>Y</mml:mi><mml:mrow><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mi>B</mml:mi><mml:mi>N</mml:mi></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mn>0.24672</mml:mn><mml:mo>±</mml:mo><mml:mn>0.00006</mml:mn></mml:mrow></mml:math> at the 0.4 σ level, and model selection yields a Bayes factor <mml:math><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mstyle><mml:mi>Λ</mml:mi></mml:mstyle><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mi>D</mml:mi><mml:mi>M</mml:mi><mml:mo>,</mml:mo><mml:mspace></mml:mspace><mml:mstyle><mml:mi>Λ</mml:mi></mml:mstyle><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mi>D</mml:mi><mml:mi>M</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mi>Y</mml:mi><mml:mrow><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msub><mml:mo>≃</mml:mo><mml:mn>10.7</mml:mn></mml:mrow></mml:math> in favor of the standard model. When ACT DR6 data are added, a mild ∼ 2 σ tension emerges: the CMB damping tail prefers <mml:math><mml:mrow><mml:msub><mml:mi>Y</mml:mi><mml:mrow><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mi>e</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:msubsup><mml:mn>2256</mml:mn><mml:mrow><mml:mo>−</mml:mo><mml:mn>0.011</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo><mml:mn>0.0095</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math>, appreciably below the BBN-consistent value. In a ΛCDM<mml:math><mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mi>f</mml:mi><mml:mi>f</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> extension the same preference manifests as <mml:math><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mi>f</mml:mi><mml:mi>f</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mo>.</mml:mo><mml:msubsup><mml:mn>75</mml:mn><mml:mrow><mml:mo>−</mml:mo><mml:mn>0.15</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo><mml:mn>0.13</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math>, about 2 σ below the standard value. A joint (Y<SUB>He</SUB>, N<SUB>eff</SUB>) extension recovers N<SUB>eff</SUB> compatible with 3.044 while maintaining the low-Y<SUB>He</SUB> direction. Bayesian model comparison consistently favors the simpler ΛCDM. We discuss possible systematic and physical interpretations of the mild tension, including degenerate BBN with a nonzero lepton asymmetry, a non-standard neutron lifetime, a transient change in Newton's constant during BBN, and variations of other fundamental constants, evaluating their viability against correlated deuterium constraints.

To identify globular clusters (GCs) belonging to Sagittarius, we conducted verification from multiple aspects and carried out a detailed analysis of member GCs and the associated objectives. From the cluster catalog of E. L. Hunt &amp; S. Reffert, we obtain the candidates of Sagittarius through the geometric space with proper motion (μ<SUB>α</SUB>, μ<SUB>δ</SUB>). We conduct further verification to make sure they are genuine members of Sagittarius using parameters such as proper motion, V<SUB>gsr</SUB>, and direction of motion. After three steps of verification, we confirm that 10 GCs belong to Sagittarius. Among them, nine have been reported in previous studies, and our verification further confirms their membership in the Sagittarius system. The remaining one, HSC 61, is a newly identified member. Combining these with 21 credible Sagittarius-associated GCs from D. Minniti et al., our final sample includes 31 Sagittarius-associated GCs. Twenty-six are located in the core, and five are located in the stellar stream. We constructed the metallicity distribution in all of Sagittarius; there is one rich peak in the core, and there is one poor peak in the stream. The reason may be that the outer and poorer GCs of the core were first pulled into the stream. Additionally, we analyze the Sagittarius merger event through energy and angular momentum. Elqui is the most distant stream discovered in the Dark Energy Survey at a distance of 50 kpc, and Malhan thought Elqui belongs to the Sagittarius merger. We present new evidence that Sagittarius and Elqui belong to the same accretion event. Through verification, we have added two new star clusters to this large accretion event of Sagittarius. We found that the Large Magellanic Cloud has a certain influence on the orbits of Elqui and Sagittarius.

Analytical solutions encompassing the so-called Hubble tension problem are revisited through the framework of Weyl--Wigner quantum mechanics and discussed in the context of generalized phase-space scenarios of quantum cosmology. After reviewing the nature of the problem and its recent developments, an extended formulation constructed within the quantum phase-space framework to address the Hubble tension is proposed. For the quantum cosmology described in the minisuperspace framework through (generic) localized phase-space quantum states, when residual quantum corrections to the Einstein--Friedmann equation are analytically derived, quantum effects are shown to suppress the Hubble tension divergence between early- and late-time predictions. Besides addressing the Hubble tension problem within the standard $Λ$CDM cosmological model, our approach encompasses generalized quantum cosmological scenarios that also include curvature and dark sector modifications.