Horndeski in the Cosmic Linear
Anisotropy Solving System
Einstein-Boltzmann 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 scalar-tensor theory described by second-order equations of motion, and contains many well known models, including (but by no means limited to) covariant Galileons, Brans-Dicke, f(R), chameleons, k-essence 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, CMB-LSS correlations and ultra-large scales in Horndeski's theory
J. Renk, M. Zumalacarregui, F. Montanari
JCAP 1607 (2016) 040
- The Observational Future of Cosmological Scalar-Tensor 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 Einstein-Boltzmann 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 Einstein-Boltzmann 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 next-generation 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, CMB-LSS correlations and ultra-large 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 Scalar-Tensor 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 Einstein-Boltzmann 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 α-attractors: phenomenology and observational constraints C. García-García, E. Linder, P. Ruíz-Lapuente, M. Zumalacárregui
JCAP 1808 (2018) 022
- Investigating scalar-tensor-gravity with statistics of the cosmic large-scale 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 Multi-Messenger Gravitational-Wave 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 scalar-tensor gravity J. Noller, A. Nicola
1811.12928
- KiDS+GAMA: Constraints on Horndeski gravity from combined large-scale 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
- Alpha-attractor dark energy in view of next-generation cosmological surveys C. Garcia-Garcia 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 scalar-tensor cosmologies: Thawing quintessence C. Garcia-Garcia, 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 fine-tuned 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 Cruz-Dombriz
2005.00418
- Information entropy in cosmological inference problems A. Pinho, R. Reischke, M. Teich, B. Malte Schäfer
2005.02035
- Cross-bispectra 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 Scalar-Tensor Modified Gravity with Gravitational Waves and Large Scale Structure Surveys T. Baker, I. Harrison
2007.13791
- Scalar-tensor 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 scalar-tensor cosmologies: Shift-symmetric Horndeski models D. Traykova, E. Bellini, P. G. Ferreira, C. García-García, J. Noller, M. Zumalacárregui
2103.11195
- Fully relativistic predictions in Horndeski gravity from standard Newtonian N-body 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