Physics of the Dark Universe最新文献

{"title":"Imprints of electric charge on the stability of compact stellar models: A comparison between GR and f(R,T) gravity","authors":"Tayyab Naseer ,&nbsp;M. Sharif ,&nbsp;Fatima Chand","doi":"10.1016/j.dark.2024.101783","DOIUrl":"10.1016/j.dark.2024.101783","url":null,"abstract":"<div><div>In the framework of <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></mrow></math></span> theory, this paper develops two unique non-singular interior models that describe anisotropic spherical structures in the presence of an electromagnetic field. The modified Einstein–Maxwell field equations are formulated in conjunction with a static charged interior geometry. After that, the field equations are solved by applying two distinct forms of the radial metric potential that make the system easier to solve. Using particular types of anisotropic pressure, we obtain two different models. We come across differential equations in both cases, and their solutions contain constants of integration which are found through matching conditions of an inner and the outer Reissner–Nordström line elements at the spherical boundary. In this context, the assumption of zero radial pressure at the interface is also utilized. Next, we investigate certain conditions that, when satisfied, result in physically existing compact models. We consider the observed data of a star, LMC X-4, together with several parametric values in order to graphically evaluate the developed solutions. Our results show that, for chosen values of charge andmodel parameter, both models fit the physically existing conditions in this modified theory.</div></div>","PeriodicalId":48774,"journal":{"name":"Physics of the Dark Universe","volume":"47 ","pages":"Article 101783"},"PeriodicalIF":5.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143100221","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":"Periodic orbits and their gravitational wave radiations around the Schwarzschild-MOG black hole","authors":"Oreeda Shabbir ,&nbsp;Mubasher Jamil ,&nbsp;Mustapha Azreg-Aïnou","doi":"10.1016/j.dark.2025.101816","DOIUrl":"10.1016/j.dark.2025.101816","url":null,"abstract":"<div><div>This article explores the motion of massive particles in the gravitational field of a modified gravity (MOG) black hole (BH), characterized by the parameter <span><math><mi>α</mi></math></span>. Using the Hamiltonian formalism, the geodesic equations and the effective potential governing particle trajectories are derived. Key features, including the innermost stable circular orbit (ISCO) and the innermost bound circular orbit (IBCO), are analyzed, revealing their dependence on the particle’s energy, angular momentum, and the MOG parameter. In the extremal case, where <span><math><mrow><mi>α</mi><mo>=</mo><mo>−</mo><mn>1</mn></mrow></math></span>, the event horizon merges with the Cauchy horizon, forming a distinctive BH configuration. Numerical methods are employed to compute periodic orbits in this spacetime, with a comparison drawn to the Schwarzschild BH. The findings indicate that for <span><math><mrow><mi>α</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>, periodic orbits around Schwarzschild-MOG BH exhibit lower energy requirements than those in Schwarzschild spacetime, whereas for <span><math><mrow><mo>−</mo><mn>1</mn><mo>&lt;</mo><mi>α</mi><mo>&lt;</mo><mn>0</mn></mrow></math></span>, the energy requirements are higher. Precessing orbits near periodic trajectories are also examined, offering insights into their complex dynamical behavior. Finally, the gravitational wave (GW) radiation from the periodic orbits of a test particle around the Schwarzschild-MOG BH is examined, generating intricate waveforms that provide insights into the gravitational structure of the system.</div></div>","PeriodicalId":48774,"journal":{"name":"Physics of the Dark Universe","volume":"47 ","pages":"Article 101816"},"PeriodicalIF":5.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143100686","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":"Probing the regular spacetime with an asymptotically Minkowski core by precessing motion","authors":"Bo Yang ,&nbsp;Yi Xie ,&nbsp;Wenbin Lin","doi":"10.1016/j.dark.2024.101770","DOIUrl":"10.1016/j.dark.2024.101770","url":null,"abstract":"<div><div>Following the works of Rahaman et al. (2018) and Chen et al. (2024) in which the dyon black holes and covariant loop quantum black holes were respectively taken as effective descriptions of the exterior field of the Sun and tested by the motion of planets of the Solar System, we hypothesize that the exterior solution of a regular black hole with an asymptotically Minkowski core might be adopted to describe the external field of a spherical celestial body featuring a suppression parameter <span><math><mi>ℓ</mi></math></span> and constrain such a parameter. We calculate the first-order post-Newtonian relativistic periastron advance of a timelike particle in this spacetime. We then test this model in the five binary pulsars and Solar System, determining its upper limits as <span><math><mrow><mi>ℓ</mi><mo>∼</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><mspace></mspace><mi>m</mi></mrow></math></span>. Compared with the result of <span><math><mrow><mi>ℓ</mi><mo>∼</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>8</mn></mrow></msup><mspace></mspace><mi>m</mi></mrow></math></span> obtained from the shadow of Sgr A*, our result is improved by 10 orders of magnitude.</div></div>","PeriodicalId":48774,"journal":{"name":"Physics of the Dark Universe","volume":"47 ","pages":"Article 101770"},"PeriodicalIF":5.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143095536","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":"Construction of wormhole under embedded approach through dark matter halos in F(T,TG) gravity","authors":"Asifa Ashraf ,&nbsp;Wen-Xiu Ma ,&nbsp;Faisal Javed ,&nbsp;S.K. Maurya ,&nbsp;Farruh Atamurotov ,&nbsp;Abdelmalek Bouzenada ,&nbsp;Magda Abd El-Rahman","doi":"10.1016/j.dark.2024.101777","DOIUrl":"10.1016/j.dark.2024.101777","url":null,"abstract":"<div><div>In this study, we explore generalized Ellis–Bronnikov and embedded wormhole solutions within the context of <span><math><mrow><mi>F</mi><mrow><mo>(</mo><mi>T</mi><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span> gravity with an anisotropic matter source. To achieve the necessary conditions for wormhole formation, we investigate the energy conditions within <span><math><mrow><mi>F</mi><mrow><mo>(</mo><mi>T</mi><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span> gravity. Our analysis includes various matter distributions, particularly dark matter halos, using observational data from the <span><math><mrow><mi>M</mi><mn>87</mn></mrow></math></span> galaxy. We also explore the results in the framework of <span><math><mrow><mi>F</mi><mrow><mo>(</mo><mi>T</mi><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span> gravity, considering three different dark matter halo distributions. For each case, the violation of energy conditions proves the presence of strange matter, say exotic matter, which is a necessary condition for wormhole existence in this gravitational model when dark matter halos are present. We investigate the effect of physical parameters on the stable configurations of the generated thin-shell surrounding the wormhole structure. In the first scenario, we can see that the shape function parameters have a significant impact on the shell’s stable regions. In addition, the considered black hole contributes significantly to the shell’s stability.</div></div>","PeriodicalId":48774,"journal":{"name":"Physics of the Dark Universe","volume":"47 ","pages":"Article 101777"},"PeriodicalIF":5.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143099710","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":"Tsallis holographic dark energy model in an anisotropic universe with linearly varying deceleration parameter and its correspondence with phantom","authors":"Chandra Rekha Mahanta,&nbsp;Dibyajyoti Das","doi":"10.1016/j.dark.2024.101755","DOIUrl":"10.1016/j.dark.2024.101755","url":null,"abstract":"<div><div>In this paper, we investigate a spatially homogeneous and anisotropic Bianchi type-I universe filled with cold dark matter and Tsallis holographic dark energy within the framework of General Relativity. We assume the cold dark matter and the Tsallis holographic dark energy to be non-interacting and obtain exact solutions of the Einstein field equations by considering a linearly varying deceleration parameter. The physical and kinematical properties of the resulting model are explored through different parameters of cosmological importance such as the Hubble parameter, the anisotropy parameter, the equation of state parameter, the jerk parameter, the snap parameter, the lerk parameter etc. The validation or violation of the four energy conditions are also checked. We find that the Weak and Dominant Energy Conditions are fulfilled but the Null and Strong Energy Conditions are violated at late time which supports the accelerated expansion of the universe. In addition, we establish the correspondence between phantom scalar field model and Tsallis holographic dark energy model.</div></div>","PeriodicalId":48774,"journal":{"name":"Physics of the Dark Universe","volume":"47 ","pages":"Article 101755"},"PeriodicalIF":5.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143100012","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":"Quantum and thermal pressures from light scalar fields","authors":"Hauke Fischer,&nbsp;Christian Käding,&nbsp;Mario Pitschmann","doi":"10.1016/j.dark.2024.101756","DOIUrl":"10.1016/j.dark.2024.101756","url":null,"abstract":"<div><div>Light scalar fields play a variety of roles in modern physics, especially in cosmology and modified theories of gravity. For this reason, there is a zoo of experiments actively trying to find evidence for many scalar field models that have been proposed in theoretical considerations. Among those are setups in which the pressures expected to be induced by light scalar fields between two parallel plates are studied, for example, Casimir force experiments. While it is known that classical and quantum pressures caused by light scalar fields could have significant impacts on such experiments, in this article, we show that this can also be the case for thermal pressure. More specifically, we derive expressions for the quantum and thermal pressures induced by exchanges of light scalar field fluctuations between two thin parallel plates. As particular examples, we then look at screened scalar fields. For chameleon, symmetron and environment-dependent dilaton models, we find large regions in their parameter spaces that allow for thermal pressures to equal or exceed the quantum pressures. By comparing with earlier constraints from quantum pressure calculations, we conclude that thermal pressures induced by chameleons are actually of experimental significance.</div></div>","PeriodicalId":48774,"journal":{"name":"Physics of the Dark Universe","volume":"47 ","pages":"Article 101756"},"PeriodicalIF":5.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143100014","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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":"Impact of DESI BAO Data on Inflationary Parameters: Stability against late-time new physics","authors":"Simony Santos da Costa","doi":"10.1016/j.dark.2024.101791","DOIUrl":"10.1016/j.dark.2024.101791","url":null,"abstract":"<div><div>In this work, I investigate the impact of Dark Energy Spectroscopic Instrument (DESI) Baryonic Acoustic Oscillations (BAO) data on cosmological parameters, focusing on the inflationary spectral index <span><math><msub><mrow><mi>n</mi></mrow><mrow><mi>s</mi></mrow></msub></math></span>, the amplitude of scalar perturbations <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>s</mi></mrow></msub></math></span>, and the matter density parameter <span><math><msub><mrow><mi>ω</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span>. By examining different models of late-time new physics, the inflationary parameters were revealed to be stable when compared with the baseline dataset that used the earlier BAO data from the SDSS collaboration. When combined with Cosmic Microwave Background (CMB) and type Ia supernovae (SNeIa), DESI BAO data leads to a slight reduction in <span><math><msub><mrow><mi>ω</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span> (less than 2%) and modest changes in <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>s</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>n</mi></mrow><mrow><mi>s</mi></mrow></msub></math></span>, if compared with the same combination but using SDSS BAO data instead, suggesting a subtle shift in matter clustering. These effects may be attributed to a higher expansion rate from dynamical dark energy, changes in the recombination period, or modifications to the matter–radiation equality time. Further analyses of models with dynamical dark energy and free curvature show a consistent trend of reduced <span><math><msub><mrow><mi>ω</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span>, accompanied by slight increases in both <span><math><msub><mrow><mi>n</mi></mrow><mrow><mi>s</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>. The results emphasize the importance of the DESI BAO data in refining cosmological parameter estimates and highlight the stability of inflationary parameters across different late-time cosmological models.</div></div>","PeriodicalId":48774,"journal":{"name":"Physics of the Dark Universe","volume":"47 ","pages":"Article 101791"},"PeriodicalIF":5.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143100215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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":"An opacity-free method of testing the cosmic distance duality relation using strongly lensed gravitational wave signals","authors":"Shun-Jia Huang ,&nbsp;En-Kun Li ,&nbsp;Jian-dong Zhang ,&nbsp;Xian Chen ,&nbsp;Zucheng Gao ,&nbsp;Xin-yi Lin ,&nbsp;Yi-Ming Hu","doi":"10.1016/j.dark.2025.101810","DOIUrl":"10.1016/j.dark.2025.101810","url":null,"abstract":"<div><div>The cosmic distance duality relation (CDDR), expressed as <span><math><mrow><msub><mrow><mi>D</mi></mrow><mrow><mi>L</mi></mrow></msub><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo>=</mo><msup><mrow><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>z</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><msub><mrow><mi>D</mi></mrow><mrow><mi>A</mi></mrow></msub><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow></mrow></math></span>, plays an important role in modern cosmology. In this paper, we propose a new method of testing CDDR using strongly lensed gravitational wave (SLGW) signals. Under the geometric optics approximation, we calculate the gravitational lens effects of two lens models, the point mass and singular isothermal sphere. We use functions of <span><math><mrow><msub><mrow><mi>η</mi></mrow><mrow><mn>1</mn></mrow></msub><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo>=</mo><mn>1</mn><mo>+</mo><msub><mrow><mi>η</mi></mrow><mrow><mn>0</mn></mrow></msub><mi>z</mi></mrow></math></span> and <span><math><mrow><msub><mrow><mi>η</mi></mrow><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo>=</mo><mn>1</mn><mo>+</mo><msub><mrow><mi>η</mi></mrow><mrow><mn>0</mn></mrow></msub><mi>z</mi><mo>/</mo><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>z</mi><mo>)</mo></mrow></mrow></math></span> to parameterize the deviation of CDDR. By reparameterizing the SLGW waveform with CDDR and the distance-redshift relation, we include the deviation parameters <span><math><msub><mrow><mi>η</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> of CDDR as waveform parameters. We evaluate the ability of this method by calculating the parameter estimation of simulated SLGW signals from massive binary black holes. We apply the Fisher information matrix and Markov Chain Monte Carlo methods to calculate parameter estimation. We find that with only one SLGW signal, the measurement precision of <span><math><msub><mrow><mi>η</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> can reach a considerable level of 0.5-1.3% for <span><math><mrow><msub><mrow><mi>η</mi></mrow><mrow><mn>1</mn></mrow></msub><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow></mrow></math></span> and 1.1-2.6% for <span><math><mrow><msub><mrow><mi>η</mi></mrow><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow></mrow></math></span>, depending on the lens model and parameters.</div></div>","PeriodicalId":48774,"journal":{"name":"Physics of the Dark Universe","volume":"47 ","pages":"Article 101810"},"PeriodicalIF":5.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143100224","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":"Traversable wormholes satisfying the Karmarkar condition in f(R) gravity with deflection angle of light","authors":"Nayan Sarkar ,&nbsp;Susmita Sarkar ,&nbsp;Moumita Sarkar ,&nbsp;Farook Rahaman","doi":"10.1016/j.dark.2025.101828","DOIUrl":"10.1016/j.dark.2025.101828","url":null,"abstract":"<div><div>In this present work, we introduce a completely new wormhole shape function satisfying the Karmarkar condition that constructs static, spherically symmetric wormhole solutions in the framework of modified <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> gravity. The proposed shape function generating wormholes are asymptotically flat by satisfying the essential conditions. Here, we consider two well-known <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> gravity models, namely the exponential <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> gravity model, and the Tsujikawa <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> gravity model, interestingly, the reported shape function generating wormholes are static, and spherically symmetric structures in the circumstances of the non-existence theorem and supported by the non-exotic matter in those <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> gravity models corresponding to the suitable values of free parameters. Moreover, the non-exotic matter supporting wormholes are in the equilibrium state by satisfying the ToV-equation in both the considered <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> gravity models. We also study the weak gravitational lensing in the spacetime of the present wormhole structures and estimate the deflection angle of light that decreases for increasing values of the impact parameter.</div></div>","PeriodicalId":48774,"journal":{"name":"Physics of the Dark Universe","volume":"47 ","pages":"Article 101828"},"PeriodicalIF":5.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143100227","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":"Third-order corrections to the slow-roll expansion: Calculation and constraints with Planck, ACT, SPT, and BICEP/Keck","authors":"Mario Ballardini ,&nbsp;Alessandro Davoli,&nbsp;Salvatore Samuele Sirletti","doi":"10.1016/j.dark.2025.101813","DOIUrl":"10.1016/j.dark.2025.101813","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We investigate the primordial power spectra (PPS) of scalar and tensor perturbations, derived through the slow-roll approximation. By solving the Mukhanov-Sasaki equation and the tensor perturbation equation with Green’s function techniques, we extend the PPS calculations to third-order corrections, providing a comprehensive expansion in terms of slow-roll parameters with an independent approach to the solution of the integrals compared to the one previously presented in the literature. We investigate the accuracy of the analytic predictions starting from first-order corrections up to third-order ones with the numerical solutions of the perturbation equations for a selection of single-field slow-roll inflationary models. We derive the constraints on the Hubble flow functions &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; from &lt;em&gt;Planck&lt;/em&gt;, ACT, SPT, and BICEP/Keck data. We find an upper bound &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;≲&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;002&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; at 95% CL dominated by BICEP/Keck data and robust to all the different combination of datasets. We derive the constraint &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;≃&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;031&lt;/mn&gt;&lt;mo&gt;±&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;004&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; at 68% confidence level (CL) from the combination of &lt;em&gt;Planck&lt;/em&gt; data and late-time probes such as baryon acoustic oscillations, redshift space distortions, and supernovae data at first order in the slow-roll expansion. The uncertainty on &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; gets larger including second- and third-order corrections, allowing for a non-vanishing running and running of the running respectively, leading to &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;≃&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;034&lt;/mn&gt;&lt;mo&gt;±&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;007&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; at 68% CL. We find &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;≃&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;±&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; at 95% CL both at second and at third order in the slow-roll expansion of the spectra. &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; remains always unconstrained. The combination of &lt;em&gt;Planck&lt;/em&gt; and SPT data, compatible among each others, leads to slightly tighter constraints on &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;. On the contrary, the combination of &lt;em&gt;Planck&lt;/em&gt; data with ACT measurements, which point to higher values of the scalar spectral index compared to &lt;em&gt;Planck&lt;/em&gt; findings, leads to shifts in the means and maximum likelihood values for ","PeriodicalId":48774,"journal":{"name":"Physics of the Dark Universe","volume":"47 ","pages":"Article 101813"},"PeriodicalIF":5.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143100230","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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}