Special Issue on Modified Gravity Approaches to the Tensions of ΛCDM: Goals and Highlights
1. Introduction
The standard cosmological model, known as CDM, has been remarkably successful in providing a coherent and predictive framework for understanding the Universe's evolution, its large-scale structure, and cosmic microwave background (CMB) radiation [[1], [3], [5]]. Central to this model are the cosmological constant , representing dark energy responsible for the accelerated expansion of the Universe, and cold dark matter (CDM), which accounts for the gravitational scaffolding underlying galaxy formation and evolution. Despite its triumphs, the CDM model is not without its challenges [[7]]. In recent years, high-precision cosmological observations have revealed a series of tensions that question the completeness of the CDM paradigm. These tensions—most notably, the discrepancy in the Hubble constant ( ) measurements from local and early Universe observations [[7], [9], [11], [13], [15], [17]], the growth rate of cosmic structures [[19], [21], [23], [25]], and the scale of cosmological anisotropies [[27], [29], [31], [33], [35], [37]]—suggest potential shortcomings in our understanding of the fundamental components and laws governing the Universe.
The emergence of these tensions has spurred a vibrant discourse within the cosmological community, giving rise to the motivation behind this Special Issue on "Modified Gravity Approaches to the Tensions of CDM". These inconsistencies may herald the advent of a new standard cosmological model, one rooted in physics beyond the current paradigm. As we stand on the brink of potentially revolutionary discoveries, it becomes imperative to explore avenues beyond the conventional framework, questioning the validity of general relativity (GR) on cosmological scales and the nature of dark energy and dark matter.
Modified gravity theories offer a well-motivated and generic theoretical framework for extending and potentially supplanting the standard CDM model. These theories, which range from scalar–tensor theories to more exotic formulations such as gravity and non-metricity gravity, propose alterations or extensions to GR that can naturally account for the accelerated expansion of the Universe without resorting to the cosmological constant or elucidating the dynamics of cosmic structure formation in novel ways. Their appeal lies not only in their ability to address the existing tensions [[38], [40], [42], [44], [46], [48], [50], [52], [54], [56]] but also in their potential to enrich our theoretical landscape with new physics that could resolve longstanding puzzles in cosmology [[58], [60], [62], [64], [66], [68]].
This Special Issue aims to delve into the heart of these debates, presenting a collection of cutting-edge research that explores the theoretical viability, empirical implications, and observational constraints of modified gravity theories. Through this collective endeavor, we seek to illuminate the pathways toward a deeper understanding of the cosmos, guided by the principle that the resolution of the CDM tensions could unveil new facets of our Universe and lay the groundwork for a new standard model of cosmology.
2. Overview of the Published Articles
Maria Petronikolou and Emmanuel N. Saridakis's article (contribution 1 [[69]]) delves into scalar–tensor- and bi-scalar–tensor-modified theories of gravity as potential frameworks for alleviating the Hubble tension. By selecting models with a unique shift-symmetric friction term, their work demonstrates how these theories can significantly mitigate the discrepancy between local and early Universe measurements of the Hubble constant, offering new pathways for resolving this longstanding cosmological puzzle.
Ziad Sakr's research (contribution 2 [[70]]) focuses on untangling the discomfort by independently analyzing the matter fluctuation parameter and the growth index . His innovative approach treats as a free parameter, distinct from its traditional derivation, revealing how this separation can lead to more accurate constraints on cosmological parameters and offering a novel perspective on the growth tension within the CDM framework.
Joan Solà Peracaula and colleagues (contribution 3 [[71]]) investigate the Running Vacuum Model (RVM) as a dynamical alternative to the cosmological constant. Their extensive analysis, supported by the latest observational data, showcases the RVM's ability to provide a compelling fit to cosmic phenomena while potentially resolving both the and tensions, marking a significant step towards a dynamic understanding of dark energy.
Christian Böhmer, Erik Jensko, and Ruth Lazkoz (contribution 4 [[72]]) employ dynamical systems analysis to explore gravity's implications for cosmological evolution. Their study elucidates how modifications in the gravity sector can lead to viable cosmological models that offer new insights into the accelerated expansion of the Universe, challenging the conventional CDM model with a fresh theoretical perspective.
Mayukh R. Gangopadhyay and colleagues (contribution 5 [[50]]) present a scenario of large-scale modification of gravity without invoking extra degrees of freedom. Their model, incorporating interactions between baryonic and dark matter, offers a unified framework to address both the late-time acceleration of the Universe and the Hubble tension, suggesting a seamless integration of dark sector phenomena within modified gravity theories.
Filippo Bouché, Salvatore Capozziello, and Vincenzo Salzano (contribution 6 [[73]]) tackle cosmological tensions through the lens of non-local gravity. By revisiting the foundations of gravitational interaction, their work highlights how non-local modifications can reconcile discrepancies in CDM predictions, opening the door to alternative models of dark energy and gravity.
Celia Escamilla-Rivera and Rubén Torres Castillejos (contribution 7 [[74]]) explore the Hubble tension using supermassive black hole shadows data. Their innovative approach leverages high-resolution astrophysical observations to infer , demonstrating the potential of black hole shadows as novel probes in cosmology and offering a fresh avenue for resolving observational tensions.
Denitsa Staicova's contribution (contribution 8 [[75]]) examines dynamical dark energy models in light of combined measurements. By analyzing the multiplication of the Hubble parameter and sound horizon scale as a single parameter, Staicova provides new insights into dark energy dynamics, suggesting that dynamical models could offer a resolution to the Hubble tension.
Savvas Nesseris (contribution 9 [[76]]) reviews the effective fluid approach as a versatile framework for representing a wide array of modified gravity models. By treating modified gravity effects as contributions from an effective dark energy fluid, Nesseris provides a unified analysis tool for comparing theoretical predictions with observational data. This approach not only facilitates the examination of modified gravity's role in cosmic acceleration but also provides a systematic method for confronting these models with the growth rate of structure and the expansion history of the Universe, offering a bridge between theory and observation.
V. K. Oikonomou, Pyotr Tsyba, and Olga Razina (contribution 10 [[77]]) offer a novel perspective by exploring how Earth's geological and climatological history, alongside the shadows of galactic black holes, might reveal insights into our Universe's evolution. Their interdisciplinary approach highlights potential signatures of past pressure singularities and their implications for the early Universe's dynamics. This intriguing exploration underscores the untapped potential of combining astrophysical, geological, and climatological data to inform and constrain cosmological models, opening up new avenues for understanding the Universe's past and the nature of gravity.
Sunny Vagnozzi (contribution 11 [[12]]) presents a compelling argument that early-time physics modifications alone may be insufficient to resolve the Hubble tension. By synthesizing evidence across seven hints derived from cosmological observations and theoretical considerations, Vagnozzi's work critically assesses the landscape of proposed solutions to the Hubble tension. This contribution emphasizes the necessity for a comprehensive approach that accounts for both early- and late-time Universe physics, challenging the cosmological community to broaden the scope of theoretical explorations in search of a more complete resolution to one of modern cosmology's most pressing puzzles.
Together, these eleven contributions exemplify this Special Issue's commitment to exploring the frontiers of modified gravity theories as viable alternatives or extensions to the CDM model. Each article advances the dialogue within the cosmological community, offering fresh insights, innovative methodologies, and compelling arguments that collectively enrich our understanding of the Universe's fundamental nature and its governing laws.
3. Conclusions
The Special Issue "Modified Gravity Approaches to the Tensions of CDM" represents a significant stride toward addressing some of the most perplexing challenges in modern cosmology. Through a diverse collection of contributions, this endeavor has not only contributed to the illumination of the intricacies of the tensions within the CDM model, but has also underscored the potential of modified gravity theories to pave the way for groundbreaking discoveries. Each article, in its unique capacity, has contributed to a deeper understanding of the Universe's fundamental laws, showcasing the richness and vitality of theoretical innovation in the face of empirical puzzles.
The collective progress made through this Special Issue is a testament to the importance of continued exploration and open-mindedness in the scientific quest to understand the cosmos. The detailed examinations of modified gravity theories presented here underscore the necessity of extending our theoretical frameworks beyond the confines of general relativity and the standard cosmological model. These theories offer not just solutions to specific observational tensions, but also a broader perspective on gravity and its role in the evolution of the Universe.
Moreover, this Special Issue stands as a potential milestone in the discovery of new physics. The tensions within the CDM model may indeed signal the limitations of our current understanding, pointing toward an underlying reality that is more complex and nuanced than previously thought. In this context, modified gravity theories emerge not merely as alternatives, but as harbingers of a new standard model of cosmology. They represent the most fundamental approach to addressing the cosmological tensions, weaving together the empirical anomalies with theoretical insights to sketch a more accurate and comprehensive picture of the Universe.
The journey toward resolving the enduring tensions within the CDM model and unveiling the new physics that will undoubtedly reshape our cosmological paradigm is far from over. However, the contributions of this Special Issue mark critical waypoints on this journey. They invite the scientific community to reconsider the foundations of cosmology, to embrace the uncertainties and anomalies, not as mere nuisances, but as beacons guiding us toward a more profound understanding of the Universe.
As we continue to probe the depths of the cosmos with ever more sophisticated tools and technologies, the insights gleaned from modified gravity theories will undoubtedly play a special role. They offer a promising path forward, one that harmonizes the elegance of theoretical physics with the empirical realities of the Universe we strive to understand. In this endeavor, the Special Issue "Modified Gravity Approaches to the Tensions of CDM" stands as both a milestone and a beacon, illuminating the path towards the next standard model of cosmology and the new physics that will underpin it.
Conflicts of Interest
The authors declare no conflicts of interest.
[
Footnotes
1
Disclaimer/Publisher's Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.
]
[
References
Aghanim, N. et al. [Planck Collaboration]. Planck 2018 results. VI. Cosmological parameters. Astron. Astrophys. 2020; 641: A6Erratum in Astron. Astrophys.2021, 652, C4. 10.1051/0004-6361/201833910
2
Qu F.J., Sherwin B.D., Madhavacheril M.S., Han D., Crowley K.T., Abril-Cabezas I., Ade P.A.R., Aiola S., Alford T., Amiri M. The Atacama Cosmology Telescope: A Measurement of the DR6 CMB Lensing Power Spectrum and Its Implications for Structure Growth. Astrophys. J. 2024; 962: 112. 10.3847/1538-4357/acfe06
3
Balkenhol, L. et al. [SPT-3G Collaboration]. Measurement of the CMB temperature power spectrum and constraints on cosmology from the SPT-3G 2018 TT, TE, and EE dataset. Phys. Rev. D. 2023; 108: 023510. 10.1103/PhysRevD.108.023510
4
Alam S., Aubert M., Avila S., Balland C., Bautista J.E., Bershady M.A., Bizyaev D., Blanton M.R., Bolton A.S., Bovy J. Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Cosmological implications from two decades of spectroscopic surveys at the Apache Point Observatory. Phys. Rev. D. 2021; 103: 083533. 10.1103/PhysRevD.103.083533
5
Asgari, M. et al. [KiDS Collaboration]. KiDS-1000 Cosmology: Cosmic shear constraints and comparison between two point statistics. Astron. Astrophys. 2021; 645: A104. 10.1051/0004-6361/202039070
6
Abbott, T.M.C. et al. [DES Collaboration]. Dark Energy Survey Year 3 results: Cosmological constraints from galaxy clustering and weak lensing. Phys. Rev. D. 2022; 105: 023520. 10.1103/PhysRevD.105.023520
7
Perivolaropoulos L., Skara F. Challenges for ΛCDM: An update. New Astron. Rev. 2022; 95: 101659. 10.1016/j.newar.2022.101659
8
Abdalla E., Abellán G.F., Aboubrahim A., Agnello A., Akarsu Ö., Akrami Y., Alestas G., Aloni D., Amendola L., Anchordoqui L.A. Cosmology intertwined: A review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies. J. High Energy Astrophys. 2022; 34: 49-211. 10.1016/j.jheap.2022.04.002
9
Verde L., Treu T., Riess A.G. Tensions between the Early and the Late Universe. Nat. Astron. 2019; 3: 891. 10.1038/s41550-019-0902-0
Di Valentino E., Anchordoqui L.A., Akarsu Ö., Ali-Haimoud Y., Amendola L., Arendse N., Asgari M., Ballardini M., Basilakos S., Battistelli E. Snowmass2021—Letter of interest cosmology intertwined II: The hubble constant tension. Astropart. Phys. 2021; 131: 102605. 10.1016/j.astropartphys.2021.102605
Di Valentino E., Mena O., Pan S., Visinelli L., Yang W., Melchiorri A., Mota D.F., Riess A.G., Silk J. In the realm of the Hubble tension—A review of solutions. Class. Quant. Grav. 2021; 38: 153001. 10.1088/1361-6382/ac086d
Vagnozzi S. Seven Hints That Early-Time New Physics Alone Is Not Sufficient to Solve the Hubble Tension. Universe. 2023; 9393. 10.3390/universe9090393
Dainotti M., De Simone B., Montani G., Schiavone T., Lambiase G. The Hubble constant tension: Current status and future perspectives through new cosmological probes. PoS. 2023; CORFU2022: 235. 10.22323/1.436.0235
Akarsu O., Colgáin E.O., Sen A.A., Sheikh-Jabbari M.M. ΛCDM Tensions: Localising Missing Physics through Consistency Checks. arXiv. 2024. 2402.04767
Kamionkowski M., Riess A.G. The Hubble Tension and Early Dark Energy. Ann. Rev. Nucl. Part. Sci. 2023; 73: 153-180. 10.1146/annurev-nucl-111422-024107
Dainotti M.G., De Simone B., Schiavone T., Montani G., Rinaldi E., Lambiase G. On the Hubble constant tension in the SNe Ia Pantheon sample. Astrophys. J. 2021; 912: 150. 10.3847/1538-4357/abeb73
Jedamzik K., Pogosian L., Zhao G.B. Why reducing the cosmic sound horizon alone can not fully resolve the Hubble tension. Commun. Phys. 2021; 4: 123. 10.1038/s42005-021-00628-x
Vagnozzi S., Pacucci F., Loeb A. Implications for the Hubble tension from the ages of the oldest astrophysical objects. J. High Energy Astrophys. 2022; 36: 27-35. 10.1016/j.jheap.2022.07.004
Di Valentino E., Anchordoqui L.A., Akarsu Ö., Ali-Haimoud Y., Amendola L., Arendse N., Asgari M., Ballardini M., Basilakos S., Battistelli E. Cosmology Intertwined III: fσ8 and S8. Astropart. Phys. 2021; 131: 102604. 10.1016/j.astropartphys.2021.102604
Philcox O.H.E., Ivanov M.M. BOSS DR12 full-shape cosmology: ΛCDM constraints from the large-scale galaxy power spectrum and bispectrum monopole. Phys. Rev. D. 2022; 105: 043517. 10.1103/PhysRevD.105.043517
Heisenberg L., Villarrubia-Rojo H., Zosso J. Can late-time extensions solve the H0 and σ8 tensions?. Phys. Rev. D. 2022; 106: 043503. 10.1103/PhysRevD.106.043503
Benisty D. Quantifying the S8 tension with the Redshift Space Distortion data set. Phys. Dark Univ. 2021; 31: 100766. 10.1016/j.dark.2020.100766
Abbott, T.M.C. et al. [Dark Energy Survey and Kilo-Degree Survey Collaboration]. DES Y3 + KiDS-1000: Consistent cosmology combining cosmic shear surveys. Open J. Astrophys. 2023; 6: 1-40. 10.21105/astro.2305.17173
Tröster, T. et al. [KiDS Collaboration]. KiDS-1000 Cosmology: Constraints beyond flat ΛCDM. Astron. Astrophys. 2021; 649: A88. 10.1051/0004-6361/202039805
Joudaki S., Hildebrandt H., Traykova D., Chisari N.E., Heymans C., Kannawadi A., Kuijken K., Wright A.H., Asgari M., Erben T. KiDS+VIKING-450 and DES-Y1 combined: Cosmology with cosmic shear. Astron. Astrophys. 2020; 638: L1. 10.1051/0004-6361/201936154
Tröster T., Sánchez A.G., Asgari M., Blake C., Crocce M., Heymans C., Hildebrandt H., Joachimi B., Joudaki S., Kannawadi A. Cosmology from large-scale structure: Constraining ΛCDM with BOSS. Astron. Astrophys. 2020; 633: L10. 10.1051/0004-6361/201936772
Aluri P.K., Cea P., Chingangbam P., Chu M.C., Clowes R.G., Hutsemékers D., Kochappan J.P., Lopez A.M., Liu L., Martens N.C. Is the observable Universe consistent with the cosmological principle?. Class. Quant. Grav. 2023; 40: 094001. 10.1088/1361-6382/acbefc
Secrest N.J., von Hausegger S., Rameez M., Mohayaee R., Sarkar S., Colin J. A Test of the Cosmological Principle with Quasars. Astrophys. J. Lett. 2021; 908: L51. 10.3847/2041-8213/abdd40
Uzan J.P., Clarkson C., Ellis G.F.R. Time drift of cosmological redshifts as a test of the Copernican principle. Phys. Rev. Lett. 2008; 100: 191303. 10.1103/PhysRevLett.100.191303
Mc Conville R., Colgáin E.O. Anisotropic distance ladder in Pantheon+supernovae. Phys. Rev. D. 2023; 108: 123533. 10.1103/PhysRevD.108.123533
Watkins R., Allen T., Bradford C.J., Ramon A., Walker A., Feldman H.A., Cionitti R., Al-Shorman Y., Kourkchi E., Tully R.B. Analysing the large-scale bulk flow using cosmicflows4: Increasing tension with the standard cosmological model. Mon. Not. R. Astron. Soc. 2023; 524: 1885-1892. 10.1093/mnras/stad1984
Cowell J.A., Dhawan S., Macpherson H.J. Potential signature of a quadrupolar hubble expansion in Pantheon+supernovae. Mon. Not. R. Astron. Soc. 2023; 526: 1482-1494. 10.1093/mnras/stad2788
Dam L., Lewis G.F., Brewer B.J. Testing the cosmological principle with CatWISE quasars: A bayesian analysis of the number-count dipole. Mon. Not. R. Astron. Soc. 2023; 525: 231-245. 10.1093/mnras/stad2322
Krishnan C., Mondol R., Sheikh-Jabbari M.M. Dipole cosmology: The Copernican paradigm beyond FLRW. J. Cosmol. Astropart. Phys. 2023; 07: 020. 10.1088/1475-7516/2023/07/020
Bengaly C.A.P., Pigozzo C., Alcaniz J.S. Testing the isotropy of cosmic acceleration with Pantheon+SH0ES: A cosmographic analysis. arXiv. 2024. 2402.1774
Ebrahimian E., Krishnan C., Mondol R., Sheikh-Jabbari M.M. Towards A Realistic Dipole Cosmology: The Dipole ΛCDM Model. arXiv. 2023. 2305.16177
Perivolaropoulos L. Isotropy properties of the absolute luminosity magnitudes of SnIa in the Pantheon+ and SH0ES samples. Phys. Rev. D. 2023; 108: 063509. 10.1103/PhysRevD.108.063509
Bahamonde S., Dialektopoulos K.F., Escamilla-Rivera C., Farrugia G., Gakis V., Hendry M., Hohmann M., Levi Said J., Mifsud J., Di Valentino E. Teleparallel gravity: From theory to cosmology. Rept. Prog. Phys. 2023; 86: 026901. 10.1088/1361-6633/ac9cef. 36279849
Adi T., Kovetz E.D. Can conformally coupled modified gravity solve the Hubble tension?. Phys. Rev. D. 2021; 103: 023530. 10.1103/PhysRevD.103.023530
Marra V., Perivolaropoulos L. Rapid transition of Geff at zt≃0.01 as a possible solution of the Hubble and growth tensions. Phys. Rev. D. 2021; 104: L021303. 10.1103/PhysRevD.104.L021303
Odintsov S.D., Sáez-Chillón Gómez D., Sharov G.S. Analyzing the H0 tension in F(R) gravity models. Nucl. Phys. B. 2021; 966: 115377. 10.1016/j.nuclphysb.2021.115377
Ballardini M., Braglia M., Finelli F., Paoletti D., Starobinsky A.A., Umiltà C. Scalar-tensor theories of gravity, neutrino physics, and the H0 tension. J. Cosmol. Astropart. Phys. 2020; 10: 044. 10.1088/1475-7516/2020/10/044
Wang D., Mota D. Can f(T) gravity resolve the H0 tension?. Phys. Rev. D. 2020; 102: 063530. 10.1103/PhysRevD.102.063530
Skara F., Perivolaropoulos L. Tension of the EG statistic and redshift space distortion data with the Planck—ΛCDM model and implications for weakening gravity. Phys. Rev. D. 2020; 101: 063521. 10.1103/PhysRevD.101.063521
Escamilla-Rivera C., Levi Said J. Cosmological viable models in f(T,B) theory as solutions to the H0 tension. Class. Quant. Grav. 2020; 37: 165002. 10.1088/1361-6382/ab939c
Cai Y.F., Khurshudyan M., Saridakis E.N. Model-independent reconstruction of f(T) gravity from Gaussian Processes. Astrophys. J. 2020; 888: 62. 10.3847/1538-4357/ab5a7f
Kazantzidis L., Perivolaropoulos L. σ8 Tension. Is Gravity Getting Weaker at Low z? Observational Evidence and Theoretical Implications. arXiv. 2019. 10.1007/978-3-030-83715-0_33. 1907.03176
Kazantzidis L., Perivolaropoulos L. Evolution of the fσ8 tension with the Planck15/ΛCDM determination and implications for modified gravity theories. Phys. Rev. D. 2018; 97: 103503. 10.1103/PhysRevD.97.103503
Nunes R.C. Structure formation in f(T) gravity and a solution for H0 tension. J. Cosmol. Astropart. Phys. 2018; 05: 052. 10.1088/1475-7516/2018/05/052
Gangopadhyay M.R., Pacif S.K.J., Sami M., Sharma M.K. Generic Modification of Gravity, Late Time Acceleration and Hubble Tension. Universe. 2023; 983. 10.3390/universe9020083
Zumalacarregui M. Gravity in the Era of Equality: Towards solutions to the Hubble problem without fine-tuned initial conditions. Phys. Rev. D. 2020; 102: 023523. 10.1103/PhysRevD.102.023523
Benevento G., Kable J.A., Addison G.E., Bennett C.L. An Exploration of an Early Gravity Transition in Light of Cosmological Tensions. Astrophys. J. 2022; 935: 156. 10.3847/1538-4357/ac80fd
Braglia M., Ballardini M., Finelli F., Koyama K. Early modified gravity in light of the H0 tension and LSS data. Phys. Rev. D. 2021; 103: 043528. 10.1103/PhysRevD.103.043528
Farhang M., Khosravi N. Phenomenological Gravitational Phase Transition: Reconciliation between the Late and Early Universe. Phys. Rev. D. 2021; 103: 083523. 10.1103/PhysRevD.103.083523
Heisenberg L., Villarrubia-Rojo H. Proca in the sky. J. Cosmol. Astropart. Phys. 2021; 03: 032. 10.1088/1475-7516/2021/03/032
Ballesteros G., Notari A., Rompineve F. The H0 tension: ΔGN vs. ΔNeff. J. Cosmol. Astropart. Phys. 2020; 11: 024. 10.1088/1475-7516/2020/11/024
Franco Abellán G., Braglia M., Ballardini M., Finelli F., Poulin V. Probing early modification of gravity with Planck, ACT and SPT. J. Cosmol. Astropart. Phys. 2023; 12: 017. 10.1088/1475-7516/2023/12/017
Akrami Y., Bahamonde S., Luis Blázquez-Salcedo J., Böhmer C., Bonvin C., Bouhmadi-López M., Brax P., Calcagni G., Capozziello S., Casa R. Modified Gravity and Cosmology: An Update by the CANTATA Network; Springer: New York, NY, USA. 2021. 10.1007/978-3-030-83715-0
Langlois D., Saito R., Yamauchi D., Noui K. Scalar-tensor theories and modified gravity in the wake of GW170817. Phys. Rev. D. 2018; 97: 061501. 10.1103/PhysRevD.97.061501
Nojiri S., Odintsov S.D., Oikonomou V.K. Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution. Phys. Rept. 2017; 692: 1-104. 10.1016/j.physrep.2017.06.001
Joyce A., Lombriser L., Schmidt F. Dark Energy Versus Modified Gravity. Ann. Rev. Nucl. Part. Sci. 2016; 66: 95-122. 10.1146/annurev-nucl-102115-044553
Joudaki S., Ferreira P.G., Lima N.A., Winther H.A. Testing gravity on cosmic scales: A case study of Jordan-Brans-Dicke theory. Phys. Rev. D. 2022; 105: 043522. 10.1103/PhysRevD.105.043522
Koyama K. Cosmological Tests of Modified Gravity. Rept. Prog. Phys. 2016; 79: 046902. 10.1088/0034-4885/79/4/046902. 27007681
Kobayashi T. Horndeski theory and beyond: A review. Rept. Prog. Phys. 2019; 82: 086901. 10.1088/1361-6633/ab2429. 31121569
Ishak M. Testing General Relativity in Cosmology. Living Rev. Rel. 2019; 22: 1. 10.1007/s41114-018-0017-4
Sakstein J., Jain B. Implications of the Neutron Star Merger GW170817 for Cosmological Scalar-Tensor Theories. Phys. Rev. Lett. 2017; 119: 251303. 10.1103/PhysRevLett.119.251303. 29303345
Amendola L., Appleby S., Avgoustidis A., Bacon D., Baker T., Baldi M., Bartolo N., Blanchard A., Bonvin C., Borgani S. Cosmology and fundamental physics with the Euclid satellite. Living Rev. Rel. 2018; 21: 2. 10.1007/s41114-017-0010-3
Crisostomi M., Koyama K., Tasinato G. Extended Scalar-Tensor Theories of Gravity. J. Cosmol. Astropart. Phys. 2016; 04: 044. 10.1088/1475-7516/2016/04/044
Petronikolou M., Saridakis E.N. Alleviating the H0 Tension in Scalar–Tensor and Bi-Scalar–Tensor Theories. Universe. 2023; 9397. 10.3390/universe9090397
Sakr Z. Untying the Growth Index to Relieve the σ8 Discomfort. Universe. 2023; 9366. 10.3390/universe9080366
Sola Peracaula J., Gomez-Valent A., de Cruz Perez J., Moreno-Pulido C. Running Vacuum in the Universe: Phenomenological Status in Light of the Latest Observations, and Its Impact on the σ8 and H0 Tensions. Universe. 2023; 9262. 10.3390/universe9060262
Boehmer C.G., Jensko E., Lazkoz R. Dynamical Systems Analysis of f(Q) Gravity. Universe. 2023; 9166. 10.3390/universe9040166
Bouchè F., Capozziello S., Salzano V. Addressing Cosmological Tensions by Non-Local Gravity. Universe. 2023; 927. 10.3390/universe9010027
Escamilla-Rivera C., Torres Castillejos R. H0 Tension on the Light of Supermassive Black Hole Shadows Data. Universe. 2023; 914. 10.3390/universe9010014
Staicova D. DE Models with Combined H0 · rd from BAO and CMB Dataset and Friends. Universe. 2022; 8631. 10.3390/universe8120631
Nesseris S. The Effective Fluid approach for Modified Gravity and its applications. Universe. 2023; 913. 10.3390/universe9010013
Oikonomou V.K., Tsyba P., Razina O. Probing Our Universe's Past Using Earth's Geological and Climatological History and Shadows of Galactic Black Holes. Universe. 2022; 8484. 10.3390/universe8090484
]
By Eleonora Di Valentino; Leandros Perivolaropoulos and Jackson Levi Said
Reported by Author; Author; Author