Tommaso Antonelli, Andrea Giusti, Roberto Casadio, Lavinia Heisenberg
{"title":"Quasinormal Modes for Coherent Quantum Black Holes","authors":"Tommaso Antonelli, Andrea Giusti, Roberto Casadio, Lavinia Heisenberg","doi":"10.1002/prop.70093","DOIUrl":"10.1002/prop.70093","url":null,"abstract":"<p>Coherent quantum black holes are quantum geometries obtained by means of a mean-field-like approach to the gravitational interaction. This procedure attenuates the classical spacetime singularities of general relativity by replacing them with integrable singularities in the quantum-corrected geometry. After discussing some relevant observables for a novel geometry for spherically symmetric black holes, we investigate the quasinormal modes spectrum of scalar, electromagnetic, and gravitational fields for the proposed model. The results indicate potential deviations from general relativity, the magnitude of which is gauged by the value of the ultraviolet regulator of the model (physically identifiable as a matter core). Observations of the ringdown phase in black hole mergers could help detect such deviations.</p>","PeriodicalId":55150,"journal":{"name":"Fortschritte Der Physik-Progress of Physics","volume":"74 3","pages":""},"PeriodicalIF":7.8,"publicationDate":"2026-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/prop.70093","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147585036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Asad Ali, Hamid Arian Zad, Muhammad Irtiza Hussain, Saif Al-Kuwari, Hashir Kuniyil, Muhammad Talha Rahim, Michal Jaščur, Saeed Haddadi
{"title":"Quantum Mpemba Effect in a Four-Site Bose–Hubbard Model","authors":"Asad Ali, Hamid Arian Zad, Muhammad Irtiza Hussain, Saif Al-Kuwari, Hashir Kuniyil, Muhammad Talha Rahim, Michal Jaščur, Saeed Haddadi","doi":"10.1002/prop.70089","DOIUrl":"https://doi.org/10.1002/prop.70089","url":null,"abstract":"<div>\u0000 \u0000 <p>We investigate relaxation-order inversion, known as the quantum Mpemba effect (QME), in a minimal open many-body system called a one-dimensional four-site Bose–Hubbard chain governed by Lindblad dynamics with local number dephasing. Families of thermal initial states are prepared at a fixed temperature and evolved under a common reference Liouvillian toward the same stationary state. Relaxation is characterized using four complementary diagnostics: trace distance, quantum relative entropy, symmetry-projected entropy imbalance (entanglement asymmetry), and the <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>ℓ</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <annotation>$ell _{1}$</annotation>\u0000 </semantics></math>-norm of coherence in the Fock basis. We find that QME emerges robustly in -the clean interacting regime, where on-site interactions redistribute the overlaps of initial states with slow Liouvillian decay modes, enabling states initially farther from equilibrium to converge faster at late times. In contrast, the noninteracting limit exhibits a monotonic relaxation hierarchy across all metrics. Introducing a linear Stark potential or random on-site disorder suppresses relaxation and eliminates QME signatures by inhibiting transport-assisted mixing and enhancing the dominance of slow modes. Within the explored parameter regime, the Stark field induces significantly stronger retardation than disorder. We further show that symmetry-projected entropy imbalance is particularly sensitive to charge-sector decoherence in reduced subsystems and provides a stringent probe of QME in bosonic platforms. Our results elucidate the essential role of interactions in enabling anomalous relaxation in open lattice systems and connect the suppression of QME under spatial inhomogeneity to localization phenomena in tilted and disordered Bose–Hubbard chains.</p></div>","PeriodicalId":55150,"journal":{"name":"Fortschritte Der Physik-Progress of Physics","volume":"74 3","pages":""},"PeriodicalIF":7.8,"publicationDate":"2026-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147567868","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Asad Ali, Hamid Arian Zad, Muhammad Irtiza Hussain, Saif Al-Kuwari, Hashir Kuniyil, Muhammad Talha Rahim, Michal Jaščur, Saeed Haddadi
{"title":"Quantum Mpemba Effect in a Four-Site Bose–Hubbard Model","authors":"Asad Ali, Hamid Arian Zad, Muhammad Irtiza Hussain, Saif Al-Kuwari, Hashir Kuniyil, Muhammad Talha Rahim, Michal Jaščur, Saeed Haddadi","doi":"10.1002/prop.70089","DOIUrl":"https://doi.org/10.1002/prop.70089","url":null,"abstract":"<div>\u0000 \u0000 <p>We investigate relaxation-order inversion, known as the quantum Mpemba effect (QME), in a minimal open many-body system called a one-dimensional four-site Bose–Hubbard chain governed by Lindblad dynamics with local number dephasing. Families of thermal initial states are prepared at a fixed temperature and evolved under a common reference Liouvillian toward the same stationary state. Relaxation is characterized using four complementary diagnostics: trace distance, quantum relative entropy, symmetry-projected entropy imbalance (entanglement asymmetry), and the <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>ℓ</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <annotation>$ell _{1}$</annotation>\u0000 </semantics></math>-norm of coherence in the Fock basis. We find that QME emerges robustly in -the clean interacting regime, where on-site interactions redistribute the overlaps of initial states with slow Liouvillian decay modes, enabling states initially farther from equilibrium to converge faster at late times. In contrast, the noninteracting limit exhibits a monotonic relaxation hierarchy across all metrics. Introducing a linear Stark potential or random on-site disorder suppresses relaxation and eliminates QME signatures by inhibiting transport-assisted mixing and enhancing the dominance of slow modes. Within the explored parameter regime, the Stark field induces significantly stronger retardation than disorder. We further show that symmetry-projected entropy imbalance is particularly sensitive to charge-sector decoherence in reduced subsystems and provides a stringent probe of QME in bosonic platforms. Our results elucidate the essential role of interactions in enabling anomalous relaxation in open lattice systems and connect the suppression of QME under spatial inhomogeneity to localization phenomena in tilted and disordered Bose–Hubbard chains.</p></div>","PeriodicalId":55150,"journal":{"name":"Fortschritte Der Physik-Progress of Physics","volume":"74 3","pages":""},"PeriodicalIF":7.8,"publicationDate":"2026-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147567867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dark Energy Models in Coasting Cosmology Based on Generalized Entropies","authors":"Yunliang Ren, Xiaofeng Yang, Xuwei Zhang, Shuangnan Chen, Yangjun Shi, Cheng Cheng, Xiaolong He, Hoernisa Iminniyaz","doi":"10.1002/prop.70091","DOIUrl":"https://doi.org/10.1002/prop.70091","url":null,"abstract":"<div>\u0000 \u0000 <p>In this work, we investigate a class of coasting cosmology models constrained by modified entropies within the framework of the holographic principle. Using the Hubble horizon as the infrared cutoff, we explore the feasibility of five distinct modified entropy forms in coasting cosmology. In this framework, dark energy and matter are assumed to evolve independently without interaction. We further constrain these models using the latest observational data from the PantheonPLUS, the Dark Energy Survey Supernova 5-Year Results (DES-SN5YR), the Dark Energy Spectroscopic Instrument (DESI), and the Cosmic Microwave Background (CMB) distance priors from Planck 2018, and obtain best-fit parameter distributions consistent with observational requirements. By comparing the fitted results with theoretical expectations, we analyze the applicability of different modified entropies in this class of models. Furthermore, we calculate the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC), and the Deviance Information Criterion (DIC), and contrast these results with those of the standard cosmological model (<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Λ</mi>\u0000 <mi>CDM</mi>\u0000 </mrow>\u0000 <annotation>$Lambda{rm CDM}$</annotation>\u0000 </semantics></math>) to assess both the quality of fit and the comparative performance of the various modified entropy models.</p></div>","PeriodicalId":55150,"journal":{"name":"Fortschritte Der Physik-Progress of Physics","volume":"74 3","pages":""},"PeriodicalIF":7.8,"publicationDate":"2026-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147567214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dark Energy Models in Coasting Cosmology Based on Generalized Entropies","authors":"Yunliang Ren, Xiaofeng Yang, Xuwei Zhang, Shuangnan Chen, Yangjun Shi, Cheng Cheng, Xiaolong He, Hoernisa Iminniyaz","doi":"10.1002/prop.70091","DOIUrl":"https://doi.org/10.1002/prop.70091","url":null,"abstract":"<div>\u0000 \u0000 <p>In this work, we investigate a class of coasting cosmology models constrained by modified entropies within the framework of the holographic principle. Using the Hubble horizon as the infrared cutoff, we explore the feasibility of five distinct modified entropy forms in coasting cosmology. In this framework, dark energy and matter are assumed to evolve independently without interaction. We further constrain these models using the latest observational data from the PantheonPLUS, the Dark Energy Survey Supernova 5-Year Results (DES-SN5YR), the Dark Energy Spectroscopic Instrument (DESI), and the Cosmic Microwave Background (CMB) distance priors from Planck 2018, and obtain best-fit parameter distributions consistent with observational requirements. By comparing the fitted results with theoretical expectations, we analyze the applicability of different modified entropies in this class of models. Furthermore, we calculate the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC), and the Deviance Information Criterion (DIC), and contrast these results with those of the standard cosmological model (<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Λ</mi>\u0000 <mi>CDM</mi>\u0000 </mrow>\u0000 <annotation>$Lambda{rm CDM}$</annotation>\u0000 </semantics></math>) to assess both the quality of fit and the comparative performance of the various modified entropy models.</p></div>","PeriodicalId":55150,"journal":{"name":"Fortschritte Der Physik-Progress of Physics","volume":"74 3","pages":""},"PeriodicalIF":7.8,"publicationDate":"2026-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147567702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Monopoles, Clarified","authors":"Aviral Aggarwal, Subhroneel Chakrabarti, Madhusudhan Raman","doi":"10.1002/prop.70090","DOIUrl":"https://doi.org/10.1002/prop.70090","url":null,"abstract":"<p>We propose a manifestly duality-invariant, Lorentz-invariant, and local action to describe quantum electrodynamics in the presence of magnetic monopoles that derives from Sen's formalism. By employing field strengths as the dynamical variables, rather than potentials, this formalism resolves longstanding ambiguities in prior frameworks. Our analysis finds consistent outcomes at both tree and loop levels using the established principles of quantum field theory, obviating the need for external assumptions or amendments. We clarify the mechanisms of charge renormalization and demonstrate the renormalization group invariance of the charge quantization condition. Our approach can be useful for phenomenological studies and in quantum field theories with strong–weak dualities.</p>","PeriodicalId":55150,"journal":{"name":"Fortschritte Der Physik-Progress of Physics","volume":"74 3","pages":""},"PeriodicalIF":7.8,"publicationDate":"2026-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/prop.70090","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147566887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sameer Ahmad Mir, Arshid Shabir, Swatantra Kumar Tiwari, Mir Faizal
{"title":"Geometric Baryogenesis With Chiral-Time Equivalence","authors":"Sameer Ahmad Mir, Arshid Shabir, Swatantra Kumar Tiwari, Mir Faizal","doi":"10.1002/prop.70088","DOIUrl":"https://doi.org/10.1002/prop.70088","url":null,"abstract":"<div>\u0000 \u0000 <p>The asymmetry between matter and antimatter demands a cause, as simple as it is profound. Here, we show that a single geometric principle chiral-time equivalence (CTE)-suffices to generate and correlate the required CP violation with the time orientation of the cosmos. Promoting the Immirzi parameter to a pseudoscalar Nambu–Goldstone field <span></span><math>\u0000 <semantics>\u0000 <mi>Φ</mi>\u0000 <annotation>$Phi$</annotation>\u0000 </semantics></math>, CTE fixes the leading operators: a shift-symmetric derivative portal <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>∂</mi>\u0000 <mi>μ</mi>\u0000 </msub>\u0000 <mi>Φ</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <msubsup>\u0000 <mi>J</mi>\u0000 <mrow>\u0000 <mi>B</mi>\u0000 <mo>−</mo>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mi>μ</mi>\u0000 </msubsup>\u0000 <mo>/</mo>\u0000 <msub>\u0000 <mi>M</mi>\u0000 <mo>∗</mo>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$((partial _mu Phi)J^mu _{B-L}/M_*)$</annotation>\u0000 </semantics></math> that acts as a dynamical chemical potential in FRW, and a topological term <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>Φ</mi>\u0000 <mspace></mspace>\u0000 <mi>R</mi>\u0000 <mover>\u0000 <mi>R</mi>\u0000 <mo>∼</mo>\u0000 </mover>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(Phi ,Rtilde{R})$</annotation>\u0000 </semantics></math> that imprints parity on tensor modes. In thermal equilibrium this structure produces gravity-assisted leptogenesis, whose magnitude is set at the decoupling temperature by susceptibilities, rather than by tuned departures from equilibrium. A fully flavored Boltzmann network with curvature sources captures flavor transfer and washout, while slow-roll and resonant regimes are established via thermodynamic and Kubo formulas. Consistency is secured by an EFT analysis (stability, perturbative unitarity, and BBN safety), and by explicit elimination of EC torsion and control of dynamical Chern-Simons (dCS) birefringence in the small-coupling domain. The most striking prediction is a sign locking among <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>η</mi>\u0000 <mi>B</mi>\u0000 </msub>\u0000 <annotation>$eta _B$</annotation>\u0000 </semantics></math>","PeriodicalId":55150,"journal":{"name":"Fortschritte Der Physik-Progress of Physics","volume":"74 3","pages":""},"PeriodicalIF":7.8,"publicationDate":"2026-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147566891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sameer Ahmad Mir, Arshid Shabir, Swatantra Kumar Tiwari, Mir Faizal
{"title":"Geometric Baryogenesis With Chiral-Time Equivalence","authors":"Sameer Ahmad Mir, Arshid Shabir, Swatantra Kumar Tiwari, Mir Faizal","doi":"10.1002/prop.70088","DOIUrl":"https://doi.org/10.1002/prop.70088","url":null,"abstract":"<div>\u0000 \u0000 <p>The asymmetry between matter and antimatter demands a cause, as simple as it is profound. Here, we show that a single geometric principle chiral-time equivalence (CTE)-suffices to generate and correlate the required CP violation with the time orientation of the cosmos. Promoting the Immirzi parameter to a pseudoscalar Nambu–Goldstone field <span></span><math>\u0000 <semantics>\u0000 <mi>Φ</mi>\u0000 <annotation>$Phi$</annotation>\u0000 </semantics></math>, CTE fixes the leading operators: a shift-symmetric derivative portal <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>∂</mi>\u0000 <mi>μ</mi>\u0000 </msub>\u0000 <mi>Φ</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <msubsup>\u0000 <mi>J</mi>\u0000 <mrow>\u0000 <mi>B</mi>\u0000 <mo>−</mo>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mi>μ</mi>\u0000 </msubsup>\u0000 <mo>/</mo>\u0000 <msub>\u0000 <mi>M</mi>\u0000 <mo>∗</mo>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$((partial _mu Phi)J^mu _{B-L}/M_*)$</annotation>\u0000 </semantics></math> that acts as a dynamical chemical potential in FRW, and a topological term <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>Φ</mi>\u0000 <mspace></mspace>\u0000 <mi>R</mi>\u0000 <mover>\u0000 <mi>R</mi>\u0000 <mo>∼</mo>\u0000 </mover>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(Phi ,Rtilde{R})$</annotation>\u0000 </semantics></math> that imprints parity on tensor modes. In thermal equilibrium this structure produces gravity-assisted leptogenesis, whose magnitude is set at the decoupling temperature by susceptibilities, rather than by tuned departures from equilibrium. A fully flavored Boltzmann network with curvature sources captures flavor transfer and washout, while slow-roll and resonant regimes are established via thermodynamic and Kubo formulas. Consistency is secured by an EFT analysis (stability, perturbative unitarity, and BBN safety), and by explicit elimination of EC torsion and control of dynamical Chern-Simons (dCS) birefringence in the small-coupling domain. The most striking prediction is a sign locking among <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>η</mi>\u0000 <mi>B</mi>\u0000 </msub>\u0000 <annotation>$eta _B$</annotation>\u0000 </semantics></math>","PeriodicalId":55150,"journal":{"name":"Fortschritte Der Physik-Progress of Physics","volume":"74 3","pages":""},"PeriodicalIF":7.8,"publicationDate":"2026-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147566827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Monopoles, Clarified","authors":"Aviral Aggarwal, Subhroneel Chakrabarti, Madhusudhan Raman","doi":"10.1002/prop.70090","DOIUrl":"https://doi.org/10.1002/prop.70090","url":null,"abstract":"<p>We propose a manifestly duality-invariant, Lorentz-invariant, and local action to describe quantum electrodynamics in the presence of magnetic monopoles that derives from Sen's formalism. By employing field strengths as the dynamical variables, rather than potentials, this formalism resolves longstanding ambiguities in prior frameworks. Our analysis finds consistent outcomes at both tree and loop levels using the established principles of quantum field theory, obviating the need for external assumptions or amendments. We clarify the mechanisms of charge renormalization and demonstrate the renormalization group invariance of the charge quantization condition. Our approach can be useful for phenomenological studies and in quantum field theories with strong–weak dualities.</p>","PeriodicalId":55150,"journal":{"name":"Fortschritte Der Physik-Progress of Physics","volume":"74 3","pages":""},"PeriodicalIF":7.8,"publicationDate":"2026-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/prop.70090","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147566886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Re-Examination of Foundational Elements of Cosmology","authors":"Lavinia Heisenberg","doi":"10.1002/prop.70084","DOIUrl":"https://doi.org/10.1002/prop.70084","url":null,"abstract":"<p>This paper undertakes a conceptual re-examination of several foundational elements of cosmology through the lens of spacetime symmetries. A new derivation of the Friedmann–Lemaître–Robertson–Walker metric is obtained by a careful conceptual examination of rotations and translations on generic manifolds, followed by solving the rotational and translational Killing equations, yielding both the metric <i>and</i> its translational generators for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mo>∈</mo>\u0000 <mo>{</mo>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>}</mo>\u0000 </mrow>\u0000 <annotation>$kin lbrace -1,0,1rbrace$</annotation>\u0000 </semantics></math> without any further assumptions. We then analyze how continuous symmetries are inherited by the Einstein tensor and the Hilbert energy–momentum tensor, proving two general propositions. Furthermore, we use the Maxwell and Kalb–Ramond fields to show that a homogeneous and isotropic energy–momentum tensor, in general, does <i>not</i> give rise to field configurations which share these symmetries. In particular, the Kalb–Ramond field we derive is significantly more general than what is usually encountered in the cosmological context. Finally, we provide a rigorous but accessible, elementary, and transparent derivation of the scalar–vector–tensor decomposition from the linearized Einstein equations. Together, these results highlight the value of multiple complementary formulations of the same cosmological physics.</p>","PeriodicalId":55150,"journal":{"name":"Fortschritte Der Physik-Progress of Physics","volume":"74 3","pages":""},"PeriodicalIF":7.8,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/prop.70084","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147566497","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}