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Imprints of cosmological tensions in reconstructed gravity


There has been substantial interest in modifications of the standard Λ cold dark matter (ΛCDM, where Λ is the cosmological constant) cosmological model prompted by tensions between certain datasets, most notably the Hubble tension. The late-time modifications of the ΛCDM model can be parameterized by three time-dependent functions describing the expansion history of the Universe and gravitational effects on light and matter in the large-scale structure. We perform a joint Bayesian reconstruction of these three functions from a combination of recent cosmological observations, utilizing a theory-informed prior built on the general Horndeski class of scalar–tensor theories. This reconstruction is interpreted in light of the well-known Hubble constant, clustering amplitude S8 and lensing amplitude AL tensions. We identify the phenomenological features that alternative theories would need to have to ease some of these tensions, and deduce important constraints on broad classes of modified gravity models. Among other things, our findings suggest that late-time dynamical dark energy and modifications of gravity are not likely to offer a solution to the Hubble tension, or simultaneously solve the AL and S8 tensions.

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Fig. 1: Reconstructed functions.
Fig. 2: Reconstructed Σ.
Fig. 3: The impact on cosmological tensions.
Fig. 4: Illustration of the Hubble tension.

Data availability

The observational data used in this work are publicly available and referenced in the Article. Our work involves a lot of intermediate stages and different types of data, sharing it all is not feasible. Nevertheless, the data that support the plots within this Article and other findings of this study are available from the corresponding author upon reasonable request.

Code availability

An earlier version of the code used in our work, MGCosmoMC, is publicly available33,34,48. The updated version is available from the corresponding author upon reasonable request.


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L.P. is supported by the National Sciences and Engineering Research Council (NSERC) of Canada, and by the Chinese Academy of Sciences President’s International Fellowship Initiative, under grant number 2020VMA0020. M.R. is supported in part by NASA ATP grant number NNH17ZDA001N and by funds provided by the Center for Particle Cosmology. K.K. was supported by the European Research Council under the European Union’s Horizon 2020 programme (grant agreement number 646702 ‘CosTesGrav’). K.K. is also supported by the UK STFC grant numbers ST/S000550/1 and ST/W001225/1. M.M. has received support from a fellowship from ‘la Caixa’ Foundation (ID 100010434), with fellowship code LCF/BQ/PI19/11690015, the Spanish Agencia Estatal de Investigacion through the ‘IFT Centro de Excelencia Severo Ochoa SEV-2016-0599’ grant and the Agenzia Spaziale Italiana (ASI) under agreement number 2018-23-HH.0. A.S. acknowledges support from the NWO and the Dutch Ministry of Education, Culture and Science (OCW) (grant number VI.Vidi.192.069). G.-B.Z. is supported by the National Key Basic Research and Development Program of China (grant number 2018YFA0404503), NSFC grant numbers 11925303, 11720101004 and 11890691, a grant from the CAS Interdisciplinary Innovation Team and science research grants from the China Manned Space Project under grant number CMS-CSST-2021-B01. We gratefully acknowledge the use of GetDist50. This research was enabled in part by support provided by WestGrid (, Compute Canada Calcul Canada ( and by the University of Chicago Research Computing Center through the Kavli Institute for Cosmological Physics at the University of Chicago.

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Authors and Affiliations



L.P. co-initiated the project, helped develop the theoretical framework and numerical tools, tested the code and Markov chain Monte Carlo runs, performed part of the data analysis, drafted the manuscript and wrote a significant part of the text. M.R. co-initiated the project, helped develop the theoretical framework and numerical tools, helped with testing the code, performed a significant part of the data analysis, made most of the plots and tables, and contributed to writing the Article. K.K. co-initiated the project, helped develop the theoretical framework and contributed to writing the manuscript text. M.M. co-initiated the project, helped develop and test the numerical tools, performed part of the data analysis and contributed to writing the manuscript text. A.S. co-initiated the project, helped develop the theoretical framework and contributed to writing the manuscript text. G.-B.Z. co-initiated the project, helped develop the theoretical framework and numerical tools, helped with testing the code and contributed to writing the manuscript text. J.L. implemented most of the modifications of MGCAMB and MGCosmoMC required for this work. S.P. helped develop the numerical tools and performed some of the test Markov chain Monte Carlo runs at early stages of the project. A.Z. helped with the implementation of modifications of MGCAMB and MGCosmoMC.

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Correspondence to Levon Pogosian.

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Supplementary Figs. 1–7, Tables 1–3, Sections 1–5 and references.

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Pogosian, L., Raveri, M., Koyama, K. et al. Imprints of cosmological tensions in reconstructed gravity. Nat Astron (2022).

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