Horndeski in the Cosmic Linear
Anisotropy Solving System
EinsteinBoltzmann solver for dark energy and modified gravity
The Science
hi_class implements Horndeski's theory in the modern Cosmic Linear Anisotropy Solving System. It can be used to compute any linear cosmological observable in seconds, including FRW distances, CMB, matter power and number count spectra.
hi_class can be readily interfaced with Monte Python to test Gravity and Dark Energy models.
Horndeski is the most general scalartensor theory described by secondorder equations of motion, and contains many well known models, including (but by no means limited to) covariant Galileons, BransDicke, f(R), chameleons, kessence and quintesssence. hi_class relies on a reformulation of the Effective Field Theory for Dark Energy developed by E. Bellini and I. Sawicki (see JCAP 1407 (2014) 050).
The publicly available version (hi_class v2.0) is presented and described in:
 hi_class: Horndeski in the Cosmic Linear Anisotropy Solving System
M. Zumalacarregui, E. Bellini, I. Sawicki, J. Lesgourgues, P. Ferreira
JCAP 1708 (2017) no.08, 019
 hi_class: Background Evolution, Initial Conditions and Approximation Schemes
E. Bellini, I. Sawicki, M. Zumalacarregui
JCAP 2002 (2020) no.02, 008
hi_class has been used to obtain results in a number of publications, including
 Nonlinear evolution of the BAO scale in alternative theories of gravity
E. Bellini, M. Zumalacarregui
PRD92 (2015) 063522
 Constraints on deviations from LCDM within Horndeski gravity
E. Bellini, A. Cuesta, R. Jimenez, L. Verde
JCAP 1602 (2016) 053
 Gravity at the horizon: on relativistic effects, CMBLSS correlations and ultralarge scales in Horndeski's theory
J. Renk, M. Zumalacarregui, F. Montanari
JCAP 1607 (2016) 040
 The Observational Future of Cosmological ScalarTensor Theories
D. Alonso, E. Bellini, P. G. Ferreira, M. Zumalacarregui
PRD95 (2017) 063502
 Galileon Gravity in Light of ISW, CMB, BAO and H0 data
J. Renk, M. Zumalacarregui, F. Montanari, A. Barreira
JCAP 1710 (2017) 020
 A comparison of EinsteinBoltzmann solvers for testing General Relativity
E. Bellini et al.
PRD97 (2018) 023520
See the full list below (if your article is not listed, please contact us).
The Code
hi_class computes the cosmological predictions of alternative theories of gravity. The code solves the linear equations starting deep in the radiation era, and can compute any cosmological observable, including (but not limited to) cosmological distances, the matter power spectrum, Cosmic Microwave Background temperature and polarization, as well as their correlation with the matter distribution. The publicly available version incorporates parameterized models based on the Effective Field Theory of Dark Energy.
hi_class has been tested for a range of models against several codes in a dedicated paper
A comparison of EinsteinBoltzmann solvers for testing General Relativity . The codes validated include EFTCAMB , COOP and the Galileon code developed by Barreira et al. (based on CAMB). The results agree within 0.1% for CMB and matter power spectra, as good as for base CLASS/CAMB using default precision parameters (at low multipoles the agreement is within 0.5%, well within cosmic variance). The achieved precision is sufficient for tests of gravity with nextgeneration surveys.
Download
hi_class is freely available to the scientific community. If you use it in a publication/preprint please cite at least the original CLASS paper and
 hi_class: Horndeski in the Cosmic Linear Anisotropy Solving System
M. Zumalacarregui, E. Bellini, I. Sawicki, J. Lesgourgues, P. Ferreira
JCAP 1708 (2017) 019
 hi_class: Background Evolution, Initial Conditions and Approximation Schemes
E. Bellini, I. Sawicki, M. Zumalacarregui
1909.01828
The code can be cloned from the GitHub repository
or downloaded as a compressed file. To get started and find detailed information on the available models and code functionality please read the hi_class.ini file.
hi_class is being developed by
We are very grateful to Thomas Tram for his invaluable advice and the many users who have offered suggestions, found bugs and contributed to improve the code.
If you are interested in using a beta version or for other inquiries about hi_class please contact emilio  bellini  physics.ox.ac.uk or miguelzuma  berkeley.edu
hi_class has been used to obtain results in the following publications:
 Nonlinear evolution of the BAO scale in alternative theories of gravity
E. Bellini, M. Zumalacarregui
PRD92 (2015) 063522
 Constraints on deviations from LCDM within Horndeski gravity
E. Bellini, A. Cuesta, R. Jimenez, L. Verde
JCAP 1602 (2016) 053
 Gravity at the horizon: on relativistic effects, CMBLSS correlations and ultralarge scales in Horndeski's theory
J. Renk, M. Zumalacarregui, F. Montanari
JCAP 1607 (2016) 040
 hi_class: Horndeski in the Cosmic Linear Anisotropy Solving System
M. Zumalacarregui, E. Bellini, I. Sawicki, J. Lesgourgues, P. Ferreira
JCAP 1708 (2017) 019
 The Observational Future of Cosmological ScalarTensor Theories
D. Alonso, E. Bellini, P. G. Ferreira, M. Zumalacarregui
PRD95 (2017) 063502
 Galileon Gravity in Light of ISW, CMB, BAO and H0 data
J. Renk, M. Zumalacarregui, F. Montanari, A. Barreira
JCAP 1710 (2017) 020
 A comparison of EinsteinBoltzmann solvers for testing General Relativity
E. Bellini et al.
PRD97 (2018) 023520
 The impact of relativistic effects on cosmological parameter estimation
C. Lorenz, D. Alonso, P. Ferreira
PRD97 (2018) 023537
 Dark Energy after GW170817: Dead Ends and the Road Ahead
J. M. Ezquiaga, M. Zumalacarregui
Phys.Rev.Lett. 119 251304
(see Physics Viewpoint )
 Testing (modified) gravity with 3D and tomographic cosmic shear A. Spurio Mancini, R. Reischke, V. Pettorino, B.M. Schaefer, M. Zumalacarregui
MNRAS 480 (2018) 3725
 Dark energy from αattractors: phenomenology and observational constraints C. GarcíaGarcía, E. Linder, P. RuízLapuente, M. Zumalacárregui
JCAP 1808 (2018) 022
 Investigating scalartensorgravity with statistics of the cosmic largescale structure R. Reischke, A. Spurio Mancini, B. Malte Schäfer, P. Merkel
1804.02441
 Testing Horndeski gravity as dark matter with hi_class A. Casalino, M. Rinaldi
1807.01995
 Dark Energy in light of MultiMessenger GravitationalWave astronomy JM Ezquiaga, M. Zumalacárregui
1807.09241
 Gravity's Islands: Parametrizing Horndeski Stability M. Denissenya, E. Linder
1808.00013
 No Slip CMB M. Brush, E. Linder, M. Zumalacarregui
1810.12337
 Radiative stability and observational constraints on dark energy and modified gravity J. Noller, A. Nicola
1811.03082
 Cosmological parameter constraints for Horndeski scalartensor gravity J. Noller, A. Nicola
1811.12928
 KiDS+GAMA: Constraints on Horndeski gravity from combined largescale structure probes A Spurio Mancini et al.
1901.03686
 The phenomenology of beyond Horndeski gravity D. Traykova, E. Bellini, P. Ferreira
1902.10687
 Positivity in the sky S. Melville J. Noller
1904.05874
 Designing Horndeski and the effective fluid approach R. Arjona, W. Cardona, S. Nesseris
1904.06294
 Modified Gravity Away from a ΛCDM Background G. Brando et al.
1904.12903
 Alphaattractor dark energy in view of nextgeneration cosmological surveys C. GarciaGarcia et al.
1905.03753
 Dark sector evolution in Horndeski models F. Pace et al.
1905.06795
 The Shape Dependence of Vainshtein Screening in the Cosmic Matter Bispectrum C. Burrage, J. Dombrowski, D. Saadeh
1905.06260
 Testing modified gravity at cosmological distances with LISA standard sirens LISA Cosmology Working Group
1906.01593
 hi_class: Background Evolution, Initial Conditions and Approximation Schemes
E. Bellini, I. Sawicki, M. Zumalacarregui
1909.01828
 Theoretical priors in scalartensor cosmologies: Thawing quintessence C. GarciaGarcia, E. Bellini, P. Ferreira, D. Traykova, M. Zumalacarregui
1911.02868
 Cosmological constraints on dark energy in light of gravitational wave bounds J. Noller
2001.05469
 Gravity in the Era of Equality: Towards solutions to the Hubble problem without finetuned initial conditions M. Zumalacarregui
2003.06396
 The H0 tension: ΔG_N vs. ΔN_eff G. Ballesteros, A. Notari, F. Rompineve 2004.05049
 A larger value for H0 by an evolving gravitational constant Matteo Braglia et al.
2004.11161
 Improvements in cosmological constraints from breaking growth degeneracy L. Perenon, S. Ilic, R. Maartens, A. de la CruzDombriz
2005.00418
 Information entropy in cosmological inference problems A. Pinho, R. Reischke, M. Teich, B. Malte Schäfer
2005.02035
 Crossbispectra Constraints on Modified Gravity Theories from Nancy Grace Roman Space Telescope and Rubin Observatory Legacy Survey of Space and Time C. Heinrich, O. Doré
2006.03138
 Relativistic Corrections to the Growth of Structure in Modified Gravity G. Brando, K. Koyama, D. Wands
2006.11019
 Constraining ScalarTensor Modified Gravity with Gravitational Waves and Large Scale Structure Surveys T. Baker, I. Harrison
2007.13791
 Scalartensor cosmologies without screening J. Noller, L. Santoni, E. Trincherini, L. Trombetta
2008.08649
 Early modified gravity in light of the $H_0$ tension and LSS data M. Braglia, M. Ballardini, F. Finelli and K. Koyama
2011.12934
 Can Conformally Invariant Modified Gravity Solve The Hubble Tension? T. Abadi and E. Kovetz
2011.13853
 Positivity Bounds on Dark Energy: When Matter Matters C. de Rham, S. Melville and J. Noller
2103.06855
 Testing modified (Horndeski) gravity by combining intrinsic galaxy alignments with cosmic shear R. Reischke, V. Bosca, T. Tugendhat, B. Malte Schäfer
2103.01657
 Theoretical priors in scalartensor cosmologies: Shiftsymmetric Horndeski models D. Traykova, E. Bellini, P. G. Ferreira, C. GarcíaGarcía, J. Noller, M. Zumalacárregui
2103.11195
 Fully relativistic predictions in Horndeski gravity from standard Newtonian Nbody simulations G. Brando, K. Koyama, D. Wands, M. Zumalacárregui, I. Sawicki, E. Bellini
2105.04491
 On tachyonic stability priors for dark energy R. Gsponer, J. Noller
2107.01044
 Positivity bounds from multiple vacua and their cosmological consequences S. Melville, J. Noller
2202.01222
 Enabling matter power spectrum emulation in beyondΛCDM cosmologies with COLA G. Brando, B. Fiorini, K. Koyama, H. Winther
2203.11120
 Neutrino mass and kinetic gravity braiding degeneracies G. GarciaArroyo, J. L. CervantesCota, U. Nucamendi
2205.05755
 A Forecast for Large Scale Structure Constraints on Horndeski Gravity with Line Intensity Mapping B. Scott, K. Karkare, S. Bird,
2209.13029
 Testing gravity with gravitational wave friction and gravitational slip I. Matos, E. Bellini, M. Calvão, M. Kunz,
2210.12174

Revisiting Vainshtein Screening for fast Nbody simulations G. Brando, K. Koyama, H. Winther,
2303.09549
 Probing Dark Energy and Modifications of Gravity with GroundBased MillimeterWavelength Line Intensity Mapping A. Moradinezhad Dizgah, E. Bellini, G. Keating,
2304.08471
 Machine learning unveils the linear matter power spectrum of modified gravity J. B. OrjuelaQuintana, S. Nesseris, D. Sapone,
2307.03643
 Probing Early Modification of Gravity with Planck, ACT and SPT G. F. Abellán, M. Braglia, M. Ballardini, F. Finelli, V. Poulin,
2308.12345
 Constraining dark energy with the integrated SachsWolfe effect E. Seraille, J. Noller, B. Sherwin,
2401.06221
 A simple prediction of the nonlinear matter power spectrum in BransDicke gravity from linear theory H. Sletmoen, H. Winther,
2403.03786
 Modified gravity interpretation of the evolving dark energy in light of DESI data A. Chudaykin, M. Kunz,
2407.02558
 Scant evidence for thawing quintessence W. Wolf, C. GarcíaGarcía, D. Bartlett, P. Ferreira
2408.17318
 Constraints on dark energy and modified gravity from the BOSS FullShape and DESI BAO data P. Taule, M. Marinucci, G. Biselli, M. Pietroni, F. Vernizzi
2409.08971
 Fast radio bursts as a probe of gravity on cosmological scales D. Neumann, R. Reischke, S. Hagstotz, H. Hildebrandt
2409.11163