A data-driven reconstruction of Horndeski gravity via the Gaussian processes. (English) Zbl 1486.83063


83C56 Dark matter and dark energy
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
81V35 Nuclear physics
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
76Q05 Hydro- and aero-acoustics
83E05 Geometrodynamics and the holographic principle
70H45 Constrained dynamics, Dirac’s theory of constraints
Full Text: DOI arXiv


[1] Supernova Search Team Collaboration; Riess, Adam G., Observational evidence from supernovae for an accelerating universe and a cosmological constant, Astron. J., 116, 1009-1038 (1998)
[2] Supernova Cosmology Project Collaboration; Perlmutter, S., Measurements of Ω and Λ from 42 high redshift supernovae, Astrophys. J., 517, 565-586 (1999) · Zbl 1368.85002
[3] S. Dodelson, Modern Cosmology, Academic Press, (2003).
[4] Clifton, Timothy; Ferreira, Pedro G.; Padilla, Antonio; Skordis, Constantinos, Modified Gravity and Cosmology, Phys. Rept., 513, 1-189 (2012)
[5] Weinberg, Steven; Hsu, Jong-Ping; Fine, D., The Cosmological Constant Problem, Rev. Mod. Phys., 61, 1-23 (1989) · Zbl 1129.83361
[6] Bull, Philip, Beyond ΛCDM: Problems, solutions, and the road ahead, Phys. Dark Univ., 12, 56-99 (2016)
[7] Sahni, Varun; Starobinsky, Alexei A., The Case for a positive cosmological Lambda term, Int. J. Mod. Phys. D, 9, 373-444 (2000)
[8] Sahni, Varun; Starobinsky, Alexei, Reconstructing Dark Energy, Int. J. Mod. Phys. D, 15, 2105-2132 (2006) · Zbl 1118.83001
[9] Copeland, Edmund J.; Sami, M.; Tsujikawa, Shinji, Dynamics of dark energy, Int. J. Mod. Phys. D, 15, 1753-1936 (2006) · Zbl 1203.83061
[10] Capozziello, Salvatore; De Laurentis, Mariafelicia, Extended Theories of Gravity, Phys. Rept., 509, 167-321 (2011)
[11] Di Valentino, Eleonora, Snowmass2021 - Letter of interest cosmology intertwined II: The hubble constant tension, Astropart. Phys., 131 (2021)
[12] Di Valentino, Eleonora, Cosmology intertwined III: fσ_8 and S_8, Astropart. Phys., 131 (2021)
[13] Planck Collaboration; Aghanim, N., Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys., 641, A6 (2020)
[14] Bernal, Jose Luis; Verde, Licia; Riess, Adam G., The trouble with H_0, JCAP, 10 (2016)
[15] Riess, Adam G.; Casertano, Stefano; Yuan, Wenlong; Macri, Lucas M.; Scolnic, Dan, Large Magellanic Cloud Cepheid Standards Provide a 1
[16] Wong, Kenneth C., H0LiCOW - XIII. A 2.4 per cent measurement of H0 from lensed quasars: 5.3σ tension between early- and late-Universe probes, Mon. Not. Roy. Astron. Soc., 498, 1420-1439 (2020)
[17] Planck Collaboration; Ade, P. A. R., Planck 2015 results. XIII. Cosmological parameters, Astron. Astrophys., 594, A13 (2016)
[18] Riess, Adam G., The Expansion of the Universe is Faster than Expected, Nature Rev. Phys., 2, 10-12 (2019)
[19] Pesce, D. W., The Megamaser Cosmology Project. XIII. Combined Hubble constant constraints, Astrophys. J. Lett., 891, L1 (2020)
[20] de Jaeger, T.; Stahl, B. E.; Zheng, W.; Filippenko, A. V.; Riess, A. G.; Galbany, L., A measurement of the Hubble constant from Type II supernovae, Mon. Not. Roy. Astron. Soc., 496, 3402-3411 (2020)
[21] Di Valentino, Eleonora; Melchiorri, Alessandro; Silk, Joseph, Planck evidence for a closed Universe and a possible crisis for cosmology, Nature Astron., 4, 196-203 (2019)
[22] Handley, Will, Curvature tension: evidence for a closed universe, Phys. Rev. D, 103 (2021)
[23] Horndeski, Gregory Walter, Second-order scalar-tensor field equations in a four-dimensional space, Int. J. Theor. Phys., 10, 363-384 (1974)
[24] Sotiriou, Thomas P.; Faraoni, Valerio, f(R) Theories Of Gravity, Rev. Mod. Phys., 82, 451-497 (2010) · Zbl 1205.83006
[25] De Felice, Antonio; Tsujikawa, Shinji, f(R) theories, Living Rev. Rel., 13, 3 (2010) · Zbl 1215.83005
[26] Nojiri, Shin’ichi; Odintsov, Sergei D., Modified f(R) gravity consistent with realistic cosmology: From matter dominated epoch to dark energy universe, Phys. Rev. D, 74 (2006) · Zbl 1105.83021
[27] Hu, Wayne; Sawicki, Ignacy, Models of f(R) Cosmic Acceleration that Evade Solar-System Tests, Phys. Rev. D, 76 (2007)
[28] Appleby, Stephen A.; Battye, Richard A., Do consistent F(R) models mimic General Relativity plus Λ?, Phys. Lett. B, 654, 7-12 (2007) · Zbl 1246.83160
[29] Starobinsky, Alexei A., Disappearing cosmological constant in f(R) gravity, JETP Lett., 86, 157-163 (2007)
[30] Appleby, Stephen A.; Battye, Richard A.; Starobinsky, Alexei A., Curing singularities in cosmological evolution of F(R) gravity, JCAP, 06 (2010)
[31] Sotiriou, Thomas P.; Stergioulas, N.; Tsagas, C., 6+1 lessons from f(R) gravity, J. Phys. Conf. Ser., 189 (2009)
[32] LIGO Scientific, Virgo Collaboration; Abbott, B. P., GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral, Phys. Rev. Lett., 119 (2017)
[33] Ezquiaga, Jose María; Zumalacárregui, Miguel, Dark Energy in light of Multi-Messenger Gravitational-Wave astronomy, Front. Astron. Space Sci., 5, 44 (2018)
[34] Nicolis, Alberto; Rattazzi, Riccardo; Trincherini, Enrico, The Galileon as a local modification of gravity, Phys. Rev. D, 79 (2009)
[35] Deffayet, C.; Esposito-Farese, Gilles; Vikman, A., Covariant Galileon, Phys. Rev. D, 79 (2009)
[36] Martin-Moruno, Prado; Nunes, Nelson J.; Lobo, Francisco S. N., Horndeski theories self-tuning to a de Sitter vacuum, Phys. Rev. D, 91 (2015)
[37] Charmousis, Christos; Copeland, Edmund J.; Padilla, Antonio; Saffin, Paul M., General second order scalar-tensor theory, self tuning, and the Fab Four, Phys. Rev. Lett., 108 (2012)
[38] Gubitosi, Giulia; Linder, Eric V., Purely Kinetic Coupled Gravity, Phys. Lett. B, 703, 113-118 (2011)
[39] Krssak, M.; van den Hoogen, R. J.; Pereira, J. G.; Böhmer, C. G.; Coley, A. A., Teleparallel theories of gravity: illuminating a fully invariant approach, Class. Quant. Grav., 36 (2019) · Zbl 1478.83205
[40] Bahamonde, Sebastian; Dialektopoulos, Konstantinos F.; Levi Said, Jackson, Can Horndeski Theory be recast using Teleparallel Gravity?, Phys. Rev. D, 100 (2019)
[41] Bahamonde, Sebastian; Dialektopoulos, Konstantinos F.; Hohmann, Manuel; Levi Said, Jackson, Post-Newtonian limit of Teleparallel Horndeski gravity, Class. Quant. Grav., 38 (2020) · Zbl 1479.83194
[42] Bahamonde, Sebastian; Dialektopoulos, Konstantinos F.; Gakis, Viktor; Levi Said, Jackson, Reviving Horndeski theory using teleparallel gravity after GW170817, Phys. Rev. D, 101 (2020)
[43] Seikel, Marina; Clarkson, Chris; Smith, Mathew, Reconstruction of dark energy and expansion dynamics using Gaussian processes, JCAP, 06 (2012)
[44] Shafieloo, Arman; Kim, Alex G.; Linder, Eric V., Gaussian Process Cosmography, Phys. Rev. D, 85 (2012)
[45] Seikel, Marina; Clarkson, Chris, Optimising Gaussian processes for reconstructing dark energy dynamics from supernovae (2013)
[46] Yennapureddy, Manoj K.; Melia, Fulvio, Reconstruction of the HII Galaxy Hubble Diagram using Gaussian Processes, JCAP, 11 (2017)
[47] Gómez-Valent, Adrià; Amendola, Luca, H_0 from cosmic chronometers and Type Ia supernovae, with Gaussian Processes and the novel Weighted Polynomial Regression method, JCAP, 04 (2018)
[48] Li, En-Kun; Du, Minghui; Zhou, Zhi-Huan; Zhang, Hongchao; Xu, Lixin, Testing the effect of H_0 on fσ_8 tension using a Gaussian process method, Mon. Not. Roy. Astron. Soc., 501, 4452-4463 (2021)
[49] Liao, Kai; Shafieloo, Arman; Keeley, Ryan E.; Linder, Eric V., A model-independent determination of the Hubble constant from lensed quasars and supernovae using Gaussian process regression, Astrophys. J. Lett., 886, L23 (2019)
[50] Keeley, Ryan E.; Shafieloo, Arman; Zhao, Gong-Bo; Vazquez, Jose Alberto; Koo, Hanwool, Reconstructing the Universe: Testing the Mutual Consistency of the Pantheon and SDSS/eBOSS BAO Data Sets with Gaussian Processes, Astron. J., 161, 151 (2021)
[51] Renzi, Fabrizio; Silvestri, Alessandra, A look at the Hubble speed from first principles (2020)
[52] Colgáin, Eoinó; Sheikh-Jabbari, M. M., Elucidating cosmological model dependence with H_0 (2021)
[53] Benisty, David, Quantifying the S_8 tension with the Redshift Space Distortion data set, Phys. Dark Univ., 31 (2021)
[54] Belgacem, Enis; Foffa, Stefano; Maggiore, Michele; Yang, Tao, Gaussian processes reconstruction of modified gravitational wave propagation, Phys. Rev. D, 101 (2020)
[55] Moore, Christopher J.; Berry, Christopher P. L.; Chua, Alvin J. K.; Gair, Jonathan R., Improving gravitational-wave parameter estimation using Gaussian process regression, Phys. Rev. D, 93 (2016)
[56] Cañas-Herrera, Guadalupe; Contigiani, Omar; Vardanyan, Valeri, Learning How to Surf: Reconstructing the Propagation and Origin of Gravitational Waves with Gaussian Processes, Astrophys. J., 918, 20 (2021)
[57] Briffa, Rebecca; Capozziello, Salvatore; Levi Said, Jackson; Mifsud, Jurgen; Saridakis, Emmanuel N., Constraining teleparallel gravity through Gaussian processes, Class. Quant. Grav., 38 (2020) · Zbl 1480.83063
[58] Cai, Yi-Fu; Khurshudyan, Martiros; Saridakis, Emmanuel N., Model-independent reconstruction of f(T) gravity from Gaussian Processes, Astrophys. J., 888, 62 (2020)
[59] Ren, Xin; Wong, Thomas Hong Tsun; Cai, Yi-Fu; Saridakis, Emmanuel N., Data-driven Reconstruction of the Late-time Cosmic Acceleration with f(T) Gravity, Phys. Dark Univ., 32 (2021)
[60] Levi Said, Jackson; Mifsud, Jurgen; Sultana, Joseph; Adami, Kristian Zarb, Reconstructing teleparallel gravity with cosmic structure growth and expansion rate data, JCAP, 06 (2021) · Zbl 1485.83058
[61] Yang, Tao; Guo, Zong-Kuan; Cai, Rong-Gen, Reconstructing the interaction between dark energy and dark matter using Gaussian Processes, Phys. Rev. D, 91 (2015)
[62] Reyes, Mauricio; Escamilla-Rivera, Celia, Improving data-driven model-independent reconstructions and updated constraints on dark energy models from Horndeski cosmology, JCAP, 07 (2021) · Zbl 1485.83056
[63] Lovelock, D., The Einstein tensor and its generalizations, J. Math. Phys., 12, 498-501 (1971) · Zbl 0213.48801
[64] Kobayashi, Tsutomu, Horndeski theory and beyond: a review, Rept. Prog. Phys., 82 (2019)
[65] Hou, Shaoqi; Gong, Yungui; Liu, Yunqi, Polarizations of Gravitational Waves in Horndeski Theory, Eur. Phys. J. C, 78, 378 (2018)
[66] Brans, C.; Dicke, R. H.; Hsu, Jong-Ping; Fine, D., Mach’s principle and a relativistic theory of gravitation, Phys. Rev., 124, 925-935 (1961) · Zbl 0103.21402
[67] Goldstein, A., An Ordinary Short Gamma-Ray Burst with Extraordinary Implications: Fermi-GBM Detection of GRB 170817A, Astrophys. J. Lett., 848, L14 (2017)
[68] Ezquiaga, Jose María; Zumalacárregui, Miguel, Dark Energy After GW170817: Dead Ends and the Road Ahead, Phys. Rev. Lett., 119 (2017)
[69] Tsamis, N. C.; Woodard, R. P., Nonperturbative models for the quantum gravitational back reaction on inflation, Annals Phys., 267, 145-192 (1998) · Zbl 0914.53065
[70] Deffayet, Cedric; Pujolas, Oriol; Sawicki, Ignacy; Vikman, Alexander, Imperfect Dark Energy from Kinetic Gravity Braiding, JCAP, 10 (2010) · Zbl 1306.83080
[71] Kobayashi, Tsutomu; Yamaguchi, Masahide; Yokoyama, Jun’ichi, Generalized G-inflation: Inflation with the most general second-order field equations, Prog. Theor. Phys., 126, 511-529 (2011) · Zbl 1243.83080
[72] Kase, Ryotaro; Tsujikawa, Shinji, Dark energy in Horndeski theories after GW170817: A review, Int. J. Mod. Phys. D, 28 (2019) · Zbl 1423.83058
[73] Arjona, Rubén; Cardona, Wilmar; Nesseris, Savvas, Designing Horndeski and the effective fluid approach, Phys. Rev. D, 100 (2019) · Zbl 1485.83127
[74] Bernardo, Reginald Christian; Vega, Ian, Tailoring cosmologies in cubic shift-symmetric Horndeski gravity, JCAP, 10 (2019)
[75] D.J.C. MacKay, Information Theory, Inference amp; Learning Algorithms, Cambridge University Press, U.S.A. (2002).
[76] C.E. Rasmussen and C.K.I. Williams, Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning), The MIT Press, (2005).
[77] Wang, Deng; Meng, Xin-He, Improved constraints on the dark energy equation of state using Gaussian processes, Phys. Rev. D, 95 (2017)
[78] Zhang, Ming-Jian; Li, Hong, Gaussian processes reconstruction of dark energy from observational data, Eur. Phys. J. C, 78, 460 (2018)
[79] Mukherjee, Purba; Banerjee, Narayan, Revisiting a non-parametric reconstruction of the deceleration parameter from observational data (2020)
[80] Aljaf, Muhsin; Gregoris, Daniele; Khurshudyan, Martiros, Constraints on interacting dark energy models through cosmic chronometers and Gaussian process, Eur. Phys. J. C, 81, 544 (2021)
[81] Busti, Vinicius C.; Clarkson, Chris; Seikel, Marina; Heavens, Alan; Starck, Jean-Luc; Krone-Martins, Alberto, The Value of H_0 from Gaussian Processes, IAU Symp., 306, 25-27 (2014)
[82] Cai, Rong-Gen; Guo, Zong-Kuan; Yang, Tao, Null test of the cosmic curvature using H(z) and supernovae data, Phys. Rev. D, 93 (2016)
[83] Bernardo, Reginald Christian; Levi Said, Jackson, Towards a model-independent reconstruction approach for late-time Hubble data, JCAP, 08 (2021)
[84] F. Pedregosa et al., Scikit-learn: Machine learning in Python, J. Mach. Learn. Res.12 (2011) 2825. · Zbl 1280.68189
[85] Torrado, Jesus; Lewis, Antony, Cobaya: Code for Bayesian Analysis of hierarchical physical models, JCAP, 05 (2021)
[86] Lewis, Antony, GetDist: a Python package for analysing Monte Carlo samples (2019)
[87] Harris, Charles R., Array programming with NumPy, Nature, 585, 357-362 (2020)
[88] P. Virtanen et al., SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python, Nature Meth.17 (2020) 261.
[89] M.L. Waskom, seaborn: statistical data visualization, J. Open Source Softw.6 (2021) 3021.
[90] Hunter, John D., Matplotlib: A 2D Graphics Environment, Comput. Sci. Eng., 9, 90-95 (2007)
[91] T. Kluyver et al., Jupyter notebooks — a publishing format for reproducible computational workflows, in Positioning and Power in Academic Publishing: Players, Agents and Agendas, F. Loizides and B. Scmidt, eds., (Netherlands), pp. 87-90, IOS Press, (2016), https://eprints.soton.ac.uk/403913/.
[92] R. Bernardo, Reggiebernardo/notebooks: dark energy research notebooks, 10.5281/zenodo.4810864, (2021).
[93] Freedman, Wendy L., The Carnegie-Chicago Hubble Program. VIII. An Independent Determination of the Hubble Constant Based on the Tip of the Red Giant Branch (2019)
[94] Moresco, Michele; Pozzetti, Lucia; Cimatti, Andrea; Jimenez, Raul; Maraston, Claudia; Verde, Licia, A 6
[95] Moresco, Michele, Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z ∼ 2, Mon. Not. Roy. Astron. Soc., 450, L16-L20 (2015)
[96] Zhang, Cong; Zhang, Han; Yuan, Shuo; Zhang, Tong-Jie; Sun, Yan-Chun, Four new observational H(z) data from luminous red galaxies in the Sloan Digital Sky Survey data release seven, Res. Astron. Astrophys., 14, 1221-1233 (2014)
[97] Stern, Daniel; Jimenez, Raul; Verde, Licia; Kamionkowski, Marc; Stanford, S. Adam, Cosmic Chronometers: Constraining the Equation of State of Dark Energy. I: H(z) Measurements, JCAP, 02 (2010)
[98] Moresco, M., Improved constraints on the expansion rate of the Universe up to z 1.1 from the spectroscopic evolution of cosmic chronometers, JCAP, 08 (2012)
[99] Scolnic, D. M., The Complete Light-curve Sample of Spectroscopically Confirmed SNe Ia from Pan-STARRS1 and Cosmological Constraints from the Combined Pantheon Sample, Astrophys. J., 859, 101 (2018)
[100] Riess, Adam G., Type Ia Supernova Distances at Redshift > 1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate, Astrophys. J., 853, 126 (2018)
[101] BOSS Collaboration; Alam, Shadab, The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample, Mon. Not. Roy. Astron. Soc., 470, 2617-2652 (2017)
[102] Bautista, Julian E., The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: measurement of the BAO and growth rate of structure of the luminous red galaxy sample from the anisotropic correlation function between redshifts 0.6 and 1, Mon. Not. Roy. Astron. Soc., 500, 736-762 (2020)
[103] Gil-Marin, Hector, The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: measurement of the BAO and growth rate of structure of the luminous red galaxy sample from the anisotropic power spectrum between redshifts 0.6 and 1.0, Mon. Not. Roy. Astron. Soc., 498, 2492-2531 (2020)
[104] Tamone, Amélie, The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Growth rate of structure measurement from anisotropic clustering analysis in configuration space between redshift 0.6 and 1.1 for the Emission Line Galaxy sample, Mon. Not. Roy. Astron. Soc., 499, 5527-5546 (2020)
[105] de Mattia, Arnaud, The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: measurement of the BAO and growth rate of structure of the emission line galaxy sample from the anisotropic power spectrum between redshift 0.6 and 1.1, Mon. Not. Roy. Astron. Soc., 501, 5616-5645 (2021)
[106] Neveux, Richard, The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: BAO and RSD measurements from the anisotropic power spectrum of the quasar sample between redshift 0.8 and 2.2, Mon. Not. Roy. Astron. Soc., 499, 210-229 (2020)
[107] Hou, Jiamin, The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: BAO and RSD measurements from anisotropic clustering analysis of the Quasar Sample in configuration space between redshift 0.8 and 2.2, Mon. Not. Roy. Astron. Soc., 500, 1201-1221 (2020)
[108] de Sainte Agathe, Victoria, Baryon acoustic oscillations at z = 2.34 from the correlations of Lyα absorption in eBOSS DR14, Astron. Astrophys., 629, A85 (2019)
[109] Blomqvist, Michael, Baryon acoustic oscillations from the cross-correlation of Lyα absorption and quasars in eBOSS DR14, Astron. Astrophys., 629, A86 (2019)
[110] Banerjee, Aritra; Cai, Haiying; Heisenberg, Lavinia; Colgáin, Eoin Ó.; Sheikh-Jabbari, M. M.; Yang, Tao, Hubble sinks in the low-redshift swampland, Phys. Rev. D, 103 (2021)
[111] Ben Achour, Jibril; Crisostomi, Marco; Koyama, Kazuya; Langlois, David; Noui, Karim; Tasinato, Gianmassimo, Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order, JHEP, 12, 100 (2016) · Zbl 1390.83249
[112] De Felice, Antonio; Heisenberg, Lavinia; Kase, Ryotaro; Mukohyama, Shinji; Tsujikawa, Shinji; Zhang, Ying-li, Cosmology in generalized Proca theories, JCAP, 06 (2016) · Zbl 1398.83077
[113] De Felice, Antonio; Heisenberg, Lavinia; Kase, Ryotaro; Mukohyama, Shinji; Tsujikawa, Shinji; Zhang, Ying-li, Effective gravitational couplings for cosmological perturbations in generalized Proca theories, Phys. Rev. D, 94 (2016)
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