Physics of the Dark Universe最新文献

{"title":"Time delay of pulsar signals in astrophysical black hole spacetimes","authors":"Parth Bambhaniya ,&nbsp;Viraj Kalsariya ,&nbsp;Saurabh ,&nbsp;Elisabete M. de Gouveia Dal Pino ,&nbsp;Ivan De Martino ,&nbsp;Riccardo Della Monica ,&nbsp;Mariafelicia De Laurentis","doi":"10.1016/j.dark.2025.102036","DOIUrl":"10.1016/j.dark.2025.102036","url":null,"abstract":"<div><div>In this paper, we investigate the fully relativistic time delay of pulsar signals propagating in the vicinity of a rotating black hole and its potential mimickers, including a deformed Kerr black hole and the Janis–Newman–Winicour naked singularity. We aim to compute and compare the pulsar time delays caused by different spacetime geometries to explore possible observational signatures that distinguish between black holes and their alternatives. We begin by solving the equations of motion for null geodesics in these background geometries. Subsequently, we address the emitter-observer problem to compute the time delay of pulsar signals in Kerr, deformed Kerr, and JNW spacetimes. A comparative analysis between Schwarzschild and Kerr black holes allows us to observe the effect of spin on propagation delay in pulsar timing. Further, we examine the impact of the deformation parameter in the deformed Kerr black hole and the influence of the scalar field on the rotating JNW spacetime. Our study considers both direct and indirect photons emitted by a source in the equatorial circular orbit. We find that the variations in the spin parameter show very small but detectable changes when we compare the time delay cases of a Kerr black hole with deformed Kerr and rotating JNW spacetimes. Our pulsar time delay results suggest a potential observable distinguishing feature of these astrophysical black hole geometries which could be useful for the forthcoming observational facilities such as Square Kilometer Array Observatory, Five-hundred-meter Aperture Spherical Telescope and Event Horizon Telescope.</div></div>","PeriodicalId":48774,"journal":{"name":"Physics of the Dark Universe","volume":"49 ","pages":"Article 102036"},"PeriodicalIF":6.4,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144738922","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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":"Van der Waals black holes: Universality, quantum corrections, and topological classifications","authors":"Ankit Anand ,&nbsp;Saeed Noori Gashti","doi":"10.1016/j.dark.2025.102018","DOIUrl":"10.1016/j.dark.2025.102018","url":null,"abstract":"<div><div>In this paper, we investigate the universal extremality relation and thermodynamic topology of Van der Waals (VdW) black holes-solutions of Einstein’s equations whose thermodynamic behavior closely resembles that of Van der Waals fluids. In the classical case, the black hole entropy obeys the Bekenstein–Hawking area law and satisfies the standard universality relation. We then incorporate quantum corrections using three distinct frameworks: the Generalized Uncertainty Principle (GUP), the Extended Uncertainty Principle (EUP), and Rainbow Gravity. While these corrections modify the entropy law, we find that a generalized form of the universal extremality relation still holds. Next, we explore the thermodynamic topology of VdW black holes, focusing on the distribution of topological charges. Our analysis reveals that variations in the black hole and model parameters lead to significant changes in topological classifications and stability, as quantified by winding numbers. In the GUP-corrected case, topological charge distributions exhibit robustness against parameter variations, suggesting classification stability. For EUP-corrected black holes, we identify two distinct topological classes, with some configurations displaying three non-zero topological charges and others maintaining a total charge of zero, despite changes in individual charge counts. The Rainbow Gravity-corrected scenario shows similar consistency in topological behavior.</div></div>","PeriodicalId":48774,"journal":{"name":"Physics of the Dark Universe","volume":"49 ","pages":"Article 102018"},"PeriodicalIF":6.4,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144721967","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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":"Imprints of electric charge and Rastall’s non-conservation phenomenon on dynamical properties of anisotropic compact stellar models","authors":"Tayyab Naseer ,&nbsp;M. Sharif ,&nbsp;Hammad Afzal ,&nbsp;Mohamed R. Eid ,&nbsp;Reem Altuijri","doi":"10.1016/j.dark.2025.102024","DOIUrl":"10.1016/j.dark.2025.102024","url":null,"abstract":"<div><div>Within the framework of Rastall gravity, this study constructs two novel non-singular interior solutions for anisotropic compact objects coupled with an electromagnetic field. The modified Einstein–Maxwell field equations are obtained to initiate our analysis that describe a static charged inner spacetime configuration. These equations are subsequently solved by implementing two expressions for the radial metric potential and anisotropic pressure by keeping in mind their acceptability criteria. Differential equations are appeared in both scenarios whose solutions involve integration constants which are fixed by applying continuity requirements between the interior and exterior Reissner–Nordström geometries at the interface. In this context, the requirement of zero radial pressure at the junction is also enforced. Afterwards, our analysis incorporates observational data from two stars, namely LMC X-4 and 4U 1820-30 along with certain parametric values to graphically validate the obtained solutions. We deduce that for specific charge and model parameter values, both configurations satisfy the physical validity criteria within this non-conserved theoretical framework.</div></div>","PeriodicalId":48774,"journal":{"name":"Physics of the Dark Universe","volume":"49 ","pages":"Article 102024"},"PeriodicalIF":5.0,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144714101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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":"Relativistic structure of a supermassive black hole embedded in the dark matter halo of NGC 4649 (M60)","authors":"Francisco S.N. Lobo ,&nbsp;Jorde A.A. Ramos ,&nbsp;Manuel E. Rodrigues","doi":"10.1016/j.dark.2025.102026","DOIUrl":"10.1016/j.dark.2025.102026","url":null,"abstract":"<div><div>We construct a static, spherically symmetric black hole (BH) solution embedded within a dark matter (DM) halo, formulated as a non-vacuum extension of the Schwarzschild spacetime. The DM distribution is modeled via an empirical density profile calibrated to observations of the elliptical galaxy NGC 4649 (M60), incorporating Hubble Space Telescope (HST) imaging, stellar velocity dispersion data, and globular cluster dynamics. The resultant spacetime metric depends on three independent parameters: the black hole mass <span><math><mi>M</mi></math></span>, the asymptotic circular velocity <span><math><msub><mrow><mi>V</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span>, and the halo scale radius <span><math><mi>a</mi></math></span>, and smoothly reduces to the Schwarzschild limit as <span><math><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>→</mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mi>a</mi><mo>→</mo><mn>0</mn></mrow></math></span>. We analyze the influence of the halo on key geometric and physical quantities, including the event horizon radius, photon sphere, shadow size, and curvature invariants. The Kretschmann scalar exhibits an enhanced sensitivity to halo-induced modifications, particularly in the near-horizon regime. Thermodynamic properties of the solution are also examined. In the extremal limit, characterized by a vanishing surface gravity, the model supports a finite tangential pressure, implying a non-trivial extension of standard black hole thermodynamics. These results highlight the relevance of incorporating astrophysical environments into BH modeling and offer new avenues for testing strong-field gravity through precision observational data.</div></div>","PeriodicalId":48774,"journal":{"name":"Physics of the Dark Universe","volume":"49 ","pages":"Article 102026"},"PeriodicalIF":6.4,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144721969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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":"Anisotropic cosmology using observational datasets: Exploring via machine learning approaches","authors":"Vinod Kumar Bhardwaj ,&nbsp;Manish Kalra ,&nbsp;Priyanka Garg ,&nbsp;Saibal Ray","doi":"10.1016/j.dark.2025.102012","DOIUrl":"10.1016/j.dark.2025.102012","url":null,"abstract":"<div><div>In the current study, we present the observational data constraints on the parameters space for an anisotropic cosmological model of Bianchi I type spacetime in general relativity (GR). For the analysis, we consider observational datasets of Cosmic Chronometers (CC), Baryon Acoustic Oscillation (BAO), and Cosmic Microwave Background Radiation (CMBR) peak parameters. The Markov chain Monte Carlo (MCMC) technique is utilized to constrain the best-fit values of the model parameters. For this purpose, we use the publicly available Python code from CosmoMC and have developed the contour plots with different constraint limits. For the joint dataset of CC, BAO, and CMBR, the parameter’s best-fit values for the derived model are estimated as <span><math><mrow><msub><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><mn>69</mn><mo>.</mo><mn>9</mn><mo>±</mo><mn>1</mn><mo>.</mo><mn>4</mn></mrow></math></span> km/s/Mpc, <span><math><mrow><msub><mrow><mi>Ω</mi></mrow><mrow><mi>m</mi><mn>0</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>27</mn><msubsup><mrow><mn>7</mn></mrow><mrow><mo>−</mo><mn>0</mn><mo>.</mo><mn>015</mn></mrow><mrow><mo>+</mo><mn>0</mn><mo>.</mo><mn>017</mn></mrow></msubsup></mrow></math></span>, <span><math><mrow><msub><mrow><mi>Ω</mi></mrow><mrow><mi>Λ</mi><mn>0</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>72</mn><msubsup><mrow><mn>2</mn></mrow><mrow><mo>−</mo><mn>0</mn><mo>.</mo><mn>017</mn></mrow><mrow><mo>+</mo><mn>0</mn><mo>.</mo><mn>015</mn></mrow></msubsup></mrow></math></span>, and <span><math><mrow><msub><mrow><mi>Ω</mi></mrow><mrow><mi>σ</mi><mn>0</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>0009</mn><mo>±</mo><mn>0</mn><mo>.</mo><mn>0001</mn></mrow></math></span>. To estimate <span><math><mrow><mi>H</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow></mrow></math></span>, we explore machine learning (ML) techniques like linear regression, Artificial Neural Network (ANN), and polynomial regression and thereafter analyze the results with the theoretically developed <span><math><mrow><mi>H</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow></mrow></math></span> for the proposed model. Among these ML techniques, the polynomial regression exceeds the performance compared to other techniques. Further, we also note that larger dataset provides a better understanding of the cosmological scenario in terms of ML view point.</div></div>","PeriodicalId":48774,"journal":{"name":"Physics of the Dark Universe","volume":"49 ","pages":"Article 102012"},"PeriodicalIF":5.0,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144703142","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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":"Universal relations with the non-extensive entropy perspective","authors":"Ankit Anand ,&nbsp;Saeed Noori Gashti","doi":"10.1016/j.dark.2025.102015","DOIUrl":"10.1016/j.dark.2025.102015","url":null,"abstract":"<div><div>Recent advancements in black hole thermodynamics have introduced corrections to elucidate the relationship between entropy and extremality bound of black holes. Traditionally, this relationship has been studied in the context of black holes characterized by Bekenstein–Hawking entropy. However, this study extends the investigation to encompass non-extensive generalizations of entropy. We introduce a minor constant correction, denoted as <span><math><mrow><mo>(</mo><mi>ɛ</mi><mo>)</mo></mrow></math></span>, and examine the universal relations for a charged Anti-de Sitter (AdS) black hole. Our findings indicate that these universal relations do not hold for the charged AdS black hole when described by the non-extensive generalizations of entropy. Of course, with some adjustments, the universality relations are met. In contrast, the universal relations remain compatible when the black hole is described by Bekenstein–Hawking entropy.</div></div>","PeriodicalId":48774,"journal":{"name":"Physics of the Dark Universe","volume":"49 ","pages":"Article 102015"},"PeriodicalIF":5.0,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144694798","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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":"Cosmological model with Gong-Zong parametrization in f(R,Lm) gravity","authors":"Romanshu Garg ,&nbsp;Tanmoy Chowdhury ,&nbsp;G.P. Singh ,&nbsp;Farook Rahaman","doi":"10.1016/j.dark.2025.102025","DOIUrl":"10.1016/j.dark.2025.102025","url":null,"abstract":"<div><div>We present the cosmic expansion scenarios in the <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>R</mi><mo>,</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span> gravity studied by using the dark energy equation of state (EoS) parameters. We proceed with the specific form of <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>R</mi><mo>,</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span> gravity termed as <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>R</mi><mo>,</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>+</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mi>m</mi></mrow><mrow><mi>α</mi></mrow></msubsup></mrow></math></span>. We derive the expansion rate in terms of the red-shift for two different forms of EoS parameter. In first model, EoS parameter varies inversely with the redshift and in second model, it involves the exponential form with the redshift. By using the Bayesian methods based on the <span><math><msup><mrow><mi>χ</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-minimization technique, the median values of model parameters are determined for the cosmic chronometer(CC) and Joint (CC+Pantheon) data sets. The behavior of fundamental cosmological parameters such as the deceleration parameter, energy density and pressure are thoroughly examined. Additionally, the nature of Statefinder diagnostics and the present age of universe exemplifies the compatibility with the late-time astronomical observations.</div></div>","PeriodicalId":48774,"journal":{"name":"Physics of the Dark Universe","volume":"49 ","pages":"Article 102025"},"PeriodicalIF":5.0,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144703097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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":"Wormhole solutions in dRGT gravity via Ultra-Diffuse Galaxies and Navarro–Frenk–White Dark halos using galactic rotation curve","authors":"Sourav Chaudhary ,&nbsp;S.K. Maurya ,&nbsp;Jitendra Kumar","doi":"10.1016/j.dark.2025.102019","DOIUrl":"10.1016/j.dark.2025.102019","url":null,"abstract":"<div><div>This work explores wormhole formation in galactic halos using dRGT gravity, considering two dark matter profiles: Ultra-Diffuse Galaxies (UDG) and the Navarro–Frenk–White (NFW) model. Inspired by Rahaman et al. [ <span><span>Can. J. Phys. 97, no.3, 241-247 (2019)</span><svg><path></path></svg></span>], this work presents a detailed graphical investigation of the nature of exotic matter in the wormhole framework, alongside a condition-based energy assessment of the content of the matter. The derived shape functions of the wormhole geometry meet the necessary criteria in both cases. Our study presents a novel wormhole solution supported by dark matter, with the redshift and shape functions constructed from the UDG and NFW density profiles along with the corresponding rotational velocity. We observe that in Model I, NEC is violated in the region surrounding the wormhole throat, whereas in Model II, the violation is present throughout the entire wormhole configuration. In addition, we analyze the forces that maintain equilibrium in the system and use embedding diagrams to visualize the geometry of the wormhole. This study also investigates the properties of dimensionless anisotropy and exoticity. Our results suggest that dark matter may help sustain these structures, offering new perspectives on its influence in galactic dynamics.</div></div>","PeriodicalId":48774,"journal":{"name":"Physics of the Dark Universe","volume":"49 ","pages":"Article 102019"},"PeriodicalIF":5.0,"publicationDate":"2025-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144694797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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":"Exploring gravastar models in f(R, T) gravity with Heintzmann geometry","authors":"Arfa Waseem ,&nbsp;A. Eid ,&nbsp;Salma Yaqoob ,&nbsp;Faisal Javed","doi":"10.1016/j.dark.2025.102006","DOIUrl":"10.1016/j.dark.2025.102006","url":null,"abstract":"<div><div>Gravastars have gained significant attention as a viable alternative to black holes, providing a resolution to the singularity problem while maintaining a strong theoretical foundation. In this work, we construct a gravastar model within the f(R, <span><math><mi>T</mi></math></span>) framework, employing the Mazur Mottola formalism and utilizing the temporal component of the Heintzmann spacetime to characterize the interior structure. The model comprises three distinct regions: a core with negative energy density, an intermediate thin shell of ultra-relativistic stiff fluid, and an exterior assumed to be de Sitter spacetime which can be governed by the Schwarzschild solution. Under this specification, we derive a set of exact and singularity-free solutions of the gravastar and a comprehensive analysis of the shell’s fundamental attributes, including its geometric thickness, energy content, entropy, surface pressure, density, and equation of state parameter, is conducted. Through rigorous graphical evaluation, we establish the dynamical stability of the proposed configuration, reinforcing the viability of gravastars as astrophysical entities within the broader framework of modified gravity.</div></div>","PeriodicalId":48774,"journal":{"name":"Physics of the Dark Universe","volume":"49 ","pages":"Article 102006"},"PeriodicalIF":5.0,"publicationDate":"2025-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144714102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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":"Effective equation of state oscillations at matter–radiation equality and primordial gravitational waves","authors":"S.D. Odintsov ,&nbsp;V.K. Oikonomou","doi":"10.1016/j.dark.2025.102016","DOIUrl":"10.1016/j.dark.2025.102016","url":null,"abstract":"<div><div>The theory controlling the Universe’s evolution in the classical regime has to be motivated by particle physics reasoning and should also generate inflation and dark energy eras in a unified way. One such framework is <span><math><mrow><mi>F</mi><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> gravity. In this work we examine a class of exponential deformations of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> gravity motivated by fundamental physics of scalaron evolution in a de Sitter background. As we show this class of models describe both inflation and the dark energy era in a viable way compatible with the Planck constraints on inflation and the cosmological parameters. Regarding the inflationary era, the exponentially deformed <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> model also yields a rescaled Einstein–Hilbert term which remarkably does not affect the dynamics and the inflationary evolution is identical to that of an <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> model. The dark energy era is also found to be viable and mimics the <span><math><mi>Λ</mi></math></span>-Cold-Dark-Matter model. More importantly, this class of <span><math><mrow><mi>F</mi><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> gravity exponential <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> deformations also has an important characteristic, and specifically it yields total equation of state oscillations deeply in the matter domination era, for redshifts <span><math><mrow><mi>z</mi><mo>∼</mo><mn>3400</mn></mrow></math></span>, so near the matter–radiation equality. These total equation of state deformations at such a large redshift may directly affect the energy spectrum of the primordial gravitational waves. Indeed as we show, the effect is measurable and it leads to an enhancement of the tensor perturbations energy spectrum for low frequencies probed by the future LiteBIRD mission. This enhancement might have a measurable effect on the <span><math><mi>B</mi></math></span>-modes of the Cosmic Microwave Background radiation and thus may be detectable by the LiteBIRD mission. Only a handful of theoretical frameworks can generate the gravitational wave pattern generated by the class of exponentially deformed <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> models we presented.</div></div>","PeriodicalId":48774,"journal":{"name":"Physics of the Dark Universe","volume":"49 ","pages":"Article 102016"},"PeriodicalIF":5.0,"publicationDate":"2025-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144694799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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}