Cosmologies

Cosmology Specifications

This page describes the specification of the Cosmologies and the CLASS parameters that they define. The CLASS parameter files and resulting power spectra and transfer functions are available in the AbacusSummit/Cosmologies directory.

We have given the cosmologies numbers, so that the simulations will refer to c123.

There are various sets of cosmologies in this list:

• The primary cosmology (c000) is a Planck2018 LCDM version, specifically the mean of base_plikHM_TTTEEE_lowl_lowE_lensing. This cosmology has 25 base boxes, plus other mass resolution options. Planck, and AbacusSummit, include a massive neutrino in this cosmology.

• c009 is the same cosmology, but with massless neutrinos, at fixed omega_cb, H0, and sigma_cb. c019 and c020 have two and zero 60 meV neutrino species, at fixed omega_cb, theta_CMB, and sigma_cb.

• There are 4 secondary cosmologies (c001-4), each with 6 base boxes. There is a low-omega_c choice based on WMAP7, a wCDM choice, a high-Neff choice, and a low-sigma8 choice.

• There are ten reference cosmologies (c010, c012-c018, c021-022) that match the choices employed in flagship runs from other groups, so as to ease comparisons between code bases. Note that most of these have massless neutrinos. c011 was not run.

• There is a linear derivative grid (c100-c116) that provides 8 matched pairs, with small positive and negative steps in an 8-dimensional parameter space, plus one additional simulation that is the high-sigma8 partner to the low-sigma8 secondary cosmology. Another set of ten simulations (c117-c126) are pairs with smaller spacing.

• There is a larger unstructured emulator grid (c130-c181) that provides a wider coverage of this 8-dimensional space.

Further details are below the table.

All cosmologies use tau=0.0544. Most use 60 meV neutrinos (also the choice of the Planck 2018 baseline cosmology), omega_nu = 0.00064420, scaling from z = 1. We use HyRec, rather than RecFast.

CLASS is run with the pk_ref.pre precision choices, unless the name ends with _fast, in which case we use the defaults. There was one case where CLASS underflowed an integration tolerance with the pk_ref precisions; we reverted to pk_permille.pre for this.

Remember that Omega_m = (omega_b+omega_cdm+omega_ncdm)/h^2.

We output five redshifts from CLASS, z = 0.0, 1.0, 3.0, 7.0, and 49, which are called z1,z2,z3,z4,z5.

We use the CDM+Baryon power spectrum at z = 1 (z2_pk_cb) and scale back by the ratio of growth factors $$D(z_\mathrm{init})/D(1)$$ to define our matter-dominated CDM-only simulation IC. The growth function includes the neutrinos as a smooth component.

Cosmologies Table

Download the cosmologies table here. However, in analysis applications, users are encouraged to use the cosmological parameters stored as in the header field of the ASDF data product files (which is loaded into the meta field of Astropy tables, or the header field of CompaSOHaloCatalog objects) rather than referencing the cosmologies table.

Note

The following table is wide, you may have to scroll to the right to see all the columns.

root

notes

omega_b

omega_cdm

h

A_s

n_s

alpha_s

N_ur

N_ncdm

omega_ncdm

w0_fld

wa_fld

sigma8_m

sigma8_cb

abacus_cosm000

Baseline LCDM, Planck 2018 base_plikHM_TTTEEE_lowl_lowE_lensing mean

0.02237

0.1200

0.6736

2.0830e-9

0.9649

0.0

2.0328

1

0.00064420

-1.0

0.0

0.807952

0.811355

abacus_cosm001

WMAP9+ACT+SPT LCDM, Calabrese++ 2017

0.02242

0.1134

0.7030

2.0376e-9

0.9638

0.0

2.0328

1

0.00064420

-1.0

0.0

0.776779

0.780222

abacus_cosm002

wCDM with thawing model w0 = -0.7, wa = -0.5

0.02237

0.1200

0.6278

2.3140e-09

0.9649

0.0

2.0328

1

0.00064420

-0.7

-0.5

0.808189

0.811577

abacus_cosm003

Neff=3.70, from base_nnu_plikHM_TT_lowl_lowE_Riess18_post_BAO

0.02260

0.1291

0.7160

2.2438e-9

0.9876

0.0

2.6868

1

0.00064420

-1.0

0.0

0.855190

0.858583

abacus_cosm004

Low sigma8_matter = 0.75, otherwise Baseline LCDM

0.02237

0.1200

0.6736

1.7949e-9

0.9649

0.0

2.0328

1

0.00064420

-1.0

0.0

0.749999

0.753159

abacus_cosm009

Baseline LCDM with massless neutrinos matching omega_cb & sigma8_cb

0.02237

0.1200

0.6736

2.0417e-9

0.9649

0.0

3.046

0

0.0

-1.0

0.0

0.811362

0.811362

abacus_cosm010

AbacusCosmos Planck LCDM cosmology

0.02222

0.1199

0.6726

2.100e-9

0.9652

0.0

3.04

0

0.0

-1.0

0.0

0.823630

0.823630

abacus_cosm011

AbacusCosmos Planck LCDM cosmology +10% in sigma8

0.02222

0.1199

0.6726

2.541e-9

0.9652

0.0

3.04

0

0.0

-1.0

0.0

0.905993

0.905993

abacus_cosm012

Euclid Flagship1 LCDM, sigma8_m=0.8279

0.02200

0.1212

0.6700

2.1000e-9

0.9600

0.0

3.046

0

0.0

-1.0

0.0

0.827899

0.827899

abacus_cosm013

Euclid Flagship2 LCDM, sigma8_m=0.813715, sigma8_cb=0.817135

0.02200

0.1206

0.6700

2.1000e-9

0.9600

0.0

2.0328

1

0.00064420

-1.0

0.0

0.813715

0.817135

abacus_cosm014

OuterRim LCDM, sigma8=0.80

0.02258

0.1109

0.7100

2.1591e-9

0.9630

0.0

3.046

0

0.0

-1.0

0.0

0.800000

0.800000

abacus_cosm015

DarkSky LCDM, sigma8=0.835

0.02215

0.1175

0.6880

2.1852e-9

0.9688

0.0

3.046

0

0.0

-1.0

0.0

0.835005

0.835005

abacus_cosm016

Horizon Run 4 LCDM, sigma8=0.7937

0.02281

0.1120

0.7200

2.0996e-9

0.9600

0.0

3.046

0

0.0

-1.0

0.0

0.793693

0.793693

abacus_cosm017

IllustrisTNG LCDM, sigma8=0.8159

0.02230

0.1194

0.6774

2.0671e-9

0.9667

0.0

3.046

0

0.0

-1.0

0.0

0.815903

0.815903

abacus_cosm018

MultiDark Planck LCDM, sigma8=0.8228

0.02214

0.1189

0.6777

2.1022e-9

0.9600

0.0

3.046

0

0.0

-1.0

0.0

0.819708

0.819708

abacus_cosm019

Baseline LCDM with two 0.06 eV neutrinos

0.02237

0.1200

0.6683

2.1353e-09

0.9649

0.0

1.0196

2

0.00064420,0.00064420

-1.0

0.0

0.805050

0.811826

abacus_cosm020

Baseline LCDM w/ massless neutrinos matching theta_star & sigma8_cb

0.02237

0.1200

0.6790

2.0342e-09

0.9649

0.0

3.046

0

0.0

-1.0

0.0

0.811350

0.811350

abacus_cosm021

MassiveNUs massless base

0.02254

0.12446

0.700

2.1000e-09

0.9700

0.0

3.046

0

0.0

-1.0

0.0

0.849842

0.849842

abacus_cosm022

MassiveNUs with one 0.1 eV massive neutrino species

0.02254

0.12339

0.700

2.1000e-09

0.9700

0.0

2.0328

1

0.001074

-1.0

0.0

0.824961

0.830296

abacus_cosm100

Baseline +2% ln(omega_b)

0.02282

0.1200

0.6777

2.0934e-09

0.9649

0.0

2.0328

1

0.00064420

-1.0

0.0

0.808181

0.811575

abacus_cosm101

Baseline -2% ln(omega_b)

0.02193

0.1200

0.6696

2.0751e-09

0.9649

0.0

2.0328

1

0.00064420

-1.0

0.0

0.808156

0.811570

abacus_cosm102

Baseline +3.3% ln(omega_c)

0.02237

0.1240

0.6597

2.0205e-09

0.9649

0.0

2.0328

1

0.00064420

-1.0

0.0

0.808270

0.811574

abacus_cosm103

Baseline -3.3% ln(omega_c)

0.02237

0.1161

0.6877

2.1541e-09

0.9649

0.0

2.0328

1

0.00064420

-1.0

0.0

0.808075

0.811582

abacus_cosm104

Baseline +0.01 n_s

0.02237

0.1200

0.6736

2.0684e-09

0.9749

0.0

2.0328

1

0.00064420

-1.0

0.0

0.808166

0.811572

abacus_cosm105

Baseline -0.01 n_s

0.02237

0.1200

0.6736

2.0999e-09

0.9549

0.0

2.0328

1

0.00064420

-1.0

0.0

0.808177

0.811580

abacus_cosm106

Baseline +0.02 nrun

0.02237

0.1200

0.6736

2.0638e-09

0.9649

0.02

2.0328

1

0.00064420

-1.0

0.0

0.808181

0.811586

abacus_cosm107

Baseline -0.02 nrun

0.02237

0.1200

0.6736

2.1045e-09

0.9649

-0.02

2.0328

1

0.00064420

-1.0

0.0

0.808168

0.811571

abacus_cosm108

Baseline +0.1 w0

0.02237

0.1200

0.6444

2.2390e-09

0.9649

0.0

2.0328

1

0.00064420

-0.9

0.0

0.808177

0.811570

abacus_cosm109

Baseline -0.1 w0

0.02237

0.1200

0.7037

1.9465e-09

0.9649

0.0

2.0328

1

0.00064420

-1.1

0.0

0.808161

0.811576

abacus_cosm110

Baseline +0.4 wa, -0.1 w0

0.02237

0.1200

0.6698

2.1219e-09

0.9649

0.0

2.0328

1

0.00064420

-1.1

0.4

0.808170

0.811572

abacus_cosm111

Baseline -0.4 wa, +0.1 w0

0.02237

0.1200

0.6752

2.0639e-09

0.9649

0.0

2.0328

1

0.00064420

-0.9

-0.4

0.808179

0.811584

abacus_cosm112

Baseline +2% sigma8

0.02237

0.1200

0.6736

2.1672e-9

0.9649

0.0

2.0328

1

0.00064420

-1.0

0.0

0.824120

0.827591

abacus_cosm113

Baseline -2% sigma8

0.02237

0.1200

0.6736

2.0021e-9

0.9649

0.0

2.0328

1

0.00064420

-1.0

0.0

0.792107

0.795443

abacus_cosm114

Baseline +0.3 nnu, +3.3% ln(omega_c), +0.01 n_s

0.02237

0.1240

0.6947

2.0463e-09

0.9749

0.0

2.3328

1

0.00064420

-1.0

0.0

0.808245

0.811563

abacus_cosm115

Baseline -0.3 nnu, -3.3% ln(omega_c), -0.01 n_s

0.02237

0.1161

0.6517

2.1211e-09

0.9549

0.0

1.7328

1

0.00064420

-1.0

0.0

0.808089

0.811582

abacus_cosm116

Emulator grid around baseline cosmology

0.02237

0.1200

0.6736

2.3938e-09

0.9649

0.000

2.0328

1

0.00064420

-1.000

0.000

0.866133

0.869782

abacus_cosm117

Baseline +0.83% ln(omega_c)

0.02237

0.1210

0.6701

2.0675e-09

0.9649

0.0

2.0328

1

0.00064420

-1.0

0.0

0.808205

0.811584

abacus_cosm118

Baseline -0.83% ln(omega_c)

0.02237

0.1190

0.6771

2.1014e-09

0.9649

0.0

2.0328

1

0.00064420

-1.0

0.0

0.808152

0.811582

abacus_cosm119

Baseline +0.003 n_s

0.02237

0.1200

0.6736

2.0794e-09

0.9679

0.0

2.0328

1

0.00064420

-1.0

0.0

0.808168

0.811573

abacus_cosm120

Baseline -0.003 n_s

0.02237

0.1200

0.6736

2.0889e-09

0.9619

0.0

2.0328

1

0.00064420

-1.0

0.0

0.808181

0.811585

abacus_cosm121

Baseline +0.025 w0

0.02237

0.1200

0.6662

2.1211e-09

0.9649

0.0

2.0328

1

0.00064420

-0.975

0.0

0.808169

0.811571

abacus_cosm122

Baseline -0.025 w0

0.02237

0.1200

0.6810

2.0483e-09

0.9649

0.0

2.0328

1

0.00064420

-1.025

0.0

0.808170

0.811577

abacus_cosm123

Baseline +0.1 wa, -0.025 w0

0.02237

0.1200

0.6729

2.0915e-09

0.9649

0.0

2.0328

1

0.00064420

-1.025

0.1

0.808176

0.811580

abacus_cosm124

Baseline -0.1 wa, +0.025 w0

0.02237

0.1200

0.6742

2.0778e-09

0.9649

0.0

2.0328

1

0.00064420

-0.975

-0.1

0.808175

0.811580

abacus_cosm125

Baseline +0.5% sigma8

0.02237

0.1200

0.6736

2.1039e-09

0.9649

0.0

2.0328

1

0.00064420

-1.0

0.0

0.811995

0.815415

abacus_cosm126

Baseline -0.5% sigma8

0.02237

0.1200

0.6736

2.0622e-09

0.9649

0.0

2.0328

1

0.00064420

-1.0

0.0

0.803908

0.807294

abacus_cosm130

Emulator grid around baseline cosmology

0.02237

0.1200

0.6736

1.6140e-09

0.9649

0.000

2.0328

1

0.00064420

-1.000

0.000

0.711201

0.714197

abacus_cosm131

Emulator grid around baseline cosmology

0.02237

0.1086

0.7165

2.3146e-09

0.9649

0.000

2.0328

1

0.00064420

-1.000

0.000

0.807866

0.811587

abacus_cosm132

Emulator grid around baseline cosmology

0.02237

0.1200

0.6736

2.1791e-09

0.9049

0.000

2.0328

1

0.00064420

-1.000

0.000

0.808189

0.811584

abacus_cosm133

Emulator grid around baseline cosmology

0.02237

0.1200

0.6736

2.6144e-09

0.9649

0.000

2.0328

1

0.00064420

-1.000

0.000

0.905163

0.908976

abacus_cosm134

Emulator grid around baseline cosmology

0.02237

0.1326

0.6319

1.9066e-09

0.9649

0.000

2.0328

1

0.00064420

-1.000

0.000

0.808458

0.811566

abacus_cosm135

Emulator grid around baseline cosmology

0.02237

0.1200

0.6736

1.9904e-09

1.0249

0.000

2.0328

1

0.00064420

-1.000

0.000

0.808160

0.811573

abacus_cosm136

Emulator grid around baseline cosmology

0.02073

0.1192

0.6618

2.5239e-09

0.9303

0.000

2.0328

1

0.00064420

-1.000

0.000

0.882475

0.886249

abacus_cosm137

Emulator grid around baseline cosmology

0.02212

0.1271

0.6472

1.6540e-09

0.9252

0.000

2.0328

1

0.00064420

-1.000

0.000

0.729693

0.732609

abacus_cosm138

Emulator grid around baseline cosmology

0.02108

0.1138

0.6847

2.2282e-09

0.9723

0.000

2.0328

1

0.00064420

-1.000

0.000

0.821432

0.825095

abacus_cosm139

Emulator grid around baseline cosmology

0.02416

0.1128

0.7164

2.1681e-09

0.9732

0.000

2.0328

1

0.00064420

-1.000

0.000

0.793003

0.796493

abacus_cosm140

Emulator grid around baseline cosmology

0.02096

0.1221

0.6536

1.8126e-09

0.9893

0.000

2.0328

1

0.00064420

-1.000

0.000

0.772033

0.775267

abacus_cosm141

Emulator grid around baseline cosmology

0.02381

0.1272

0.6623

1.9945e-09

0.9384

0.000

2.0328

1

0.00064420

-1.000

0.000

0.799575

0.802737

abacus_cosm142

Emulator grid around baseline cosmology

0.02287

0.1130

0.7038

1.6701e-09

0.9927

0.000

2.0328

1

0.00064420

-1.000

0.000

0.707082

0.710219

abacus_cosm143

Emulator grid around baseline cosmology

0.02206

0.1278

0.6443

2.1084e-09

0.9952

0.000

2.0328

1

0.00064420

-1.000

0.000

0.847522

0.850903

abacus_cosm144

Emulator grid around baseline cosmology

0.02210

0.1130

0.6968

2.7653e-09

0.9279

0.000

2.0328

1

0.00064420

-1.000

0.000

0.891360

0.895324

abacus_cosm145

Emulator grid around baseline cosmology

0.02428

0.1186

0.6961

2.1634e-09

0.9347

0.000

2.0328

1

0.00064420

-1.000

0.000

0.801404

0.804769

abacus_cosm146

Emulator grid around baseline cosmology

0.02097

0.1180

0.6682

1.9020e-09

0.9351

0.000

2.0328

1

0.00064420

-1.000

0.000

0.762696

0.765984

abacus_cosm147

Emulator grid around baseline cosmology

0.02113

0.1215

0.6498

1.9081e-09

0.9587

0.000

2.0328

1

0.00064420

-0.809

-0.628

0.777157

0.780416

abacus_cosm148

Emulator grid around baseline cosmology

0.02289

0.1201

0.6199

1.9629e-09

0.9380

0.000

2.0328

1

0.00064420

-0.925

0.393

0.714913

0.717888

abacus_cosm149

Emulator grid around baseline cosmology

0.02188

0.1200

0.6688

2.1521e-09

0.9913

0.000

2.0328

1

0.00064420

-1.174

0.613

0.824854

0.828343

abacus_cosm150

Emulator grid around baseline cosmology

0.02248

0.1216

0.7224

2.5099e-09

0.9355

0.000

2.0328

1

0.00064420

-1.090

-0.373

0.937655

0.941570

abacus_cosm151

Emulator grid around baseline cosmology

0.02315

0.1254

0.6582

2.2686e-09

0.9757

0.000

2.0328

1

0.00064420

-0.826

-0.615

0.860820

0.864288

abacus_cosm152

Emulator grid around baseline cosmology

0.02165

0.1148

0.6204

1.7965e-09

0.9541

0.000

2.0328

1

0.00064420

-0.732

-0.187

0.677885

0.680849

abacus_cosm153

Emulator grid around baseline cosmology

0.02192

0.1199

0.6092

2.2946e-09

0.9917

0.000

2.0328

1

0.00064420

-0.735

-0.172

0.794389

0.797729

abacus_cosm154

Emulator grid around baseline cosmology

0.02158

0.1148

0.7426

2.0689e-09

0.9538

0.000

2.0328

1

0.00064420

-1.076

-0.395

0.838698

0.842413

abacus_cosm155

Emulator grid around baseline cosmology

0.02369

0.1184

0.6247

2.0723e-09

0.9713

0.000

2.0328

1

0.00064420

-0.727

-0.184

0.735302

0.738388

abacus_cosm156

Emulator grid around baseline cosmology

0.02202

0.1261

0.6499

1.9738e-09

0.9678

0.000

2.0328

1

0.00064420

-1.176

0.621

0.801974

0.805210

abacus_cosm157

Emulator grid around baseline cosmology

0.02247

0.1214

0.6668

2.5108e-09

0.9356

0.000

2.0328

1

0.00064420

-1.167

0.616

0.872315

0.875941

abacus_cosm158

Emulator grid around baseline cosmology

0.02201

0.1262

0.6958

1.8626e-09

0.9667

0.000

2.0328

1

0.00064420

-1.082

-0.392

0.829816

0.833179

abacus_cosm159

Emulator grid around baseline cosmology

0.02206

0.1261

0.5967

1.7977e-09

0.9673

0.000

2.0328

1

0.00064420

-0.726

-0.220

0.718521

0.721402

abacus_cosm160

Emulator grid around baseline cosmology

0.02223

0.1185

0.7456

2.0963e-09

0.9942

0.000

2.0328

1

0.00064420

-1.271

0.217

0.876756

0.880523

abacus_cosm161

Emulator grid around baseline cosmology

0.02282

0.1274

0.7330

1.9688e-09

0.9649

0.026

2.7283

1

0.00064420

-1.000

0.000

0.793066

0.796247

abacus_cosm162

Emulator grid around baseline cosmology

0.02136

0.1048

0.6383

2.1592e-09

0.9297

-0.026

1.3521

1

0.00064420

-1.000

0.000

0.779589

0.783285

abacus_cosm163

Emulator grid around baseline cosmology

0.02135

0.1290

0.7280

2.1689e-09

0.9922

-0.018

2.8575

1

0.00064420

-1.000

0.000

0.838824

0.842187

abacus_cosm164

Emulator grid around baseline cosmology

0.02173

0.1091

0.6042

2.0003e-09

0.9211

0.016

1.1769

1

0.00064420

-1.000

0.000

0.774159

0.777681

abacus_cosm165

Emulator grid around baseline cosmology

0.02225

0.1278

0.7293

2.0676e-09

1.0241

0.026

2.7558

1

0.00064420

-1.000

0.000

0.835954

0.839319

abacus_cosm166

Emulator grid around baseline cosmology

0.02306

0.1151

0.6826

2.2779e-09

0.9691

0.038

1.9089

1

0.00064420

-1.000

0.000

0.837463

0.841106

abacus_cosm167

Emulator grid around baseline cosmology

0.02248

0.1400

0.7050

1.7321e-09

0.9715

-0.017

2.8889

1

0.00064420

-1.000

0.000

0.768419

0.771255

abacus_cosm168

Emulator grid around baseline cosmology

0.02157

0.1084

0.6070

2.5378e-09

0.9275

0.016

1.1911

1

0.00064420

-1.000

0.000

0.871407

0.875401

abacus_cosm169

Emulator grid around baseline cosmology

0.02189

0.1222

0.6474

1.8067e-09

0.9898

0.038

1.9109

1

0.00064420

-1.000

0.000

0.777925

0.781158

abacus_cosm170

Emulator grid around baseline cosmology

0.02319

0.1076

0.6418

1.7994e-09

0.9387

-0.026

1.3411

1

0.00064420

-1.000

0.000

0.716059

0.719332

abacus_cosm171

Emulator grid around baseline cosmology

0.02348

0.1272

0.6733

2.2585e-09

0.9762

-0.038

2.1543

1

0.00064420

-1.000

0.000

0.852878

0.856267

abacus_cosm172

Emulator grid around baseline cosmology

0.02282

0.1032

0.6369

2.1259e-09

0.9012

0.017

1.1954

1

0.00064420

-1.000

0.000

0.765650

0.769278

abacus_cosm173

Emulator grid around baseline cosmology

0.02322

0.1161

0.6800

1.8904e-09

0.9628

0.038

1.9049

1

0.00064420

-1.000

0.000

0.763962

0.767255

abacus_cosm174

Emulator grid around baseline cosmology

0.02302

0.1064

0.6427

2.4889e-09

0.9437

-0.026

1.3242

1

0.00064420

-1.000

0.000

0.840113

0.843996

abacus_cosm175

Emulator grid around baseline cosmology

0.02173

0.1336

0.6432

1.7429e-09

0.9898

-0.003

2.7456

1

0.00064420

-0.911

0.350

0.708760

0.711484

abacus_cosm176

Emulator grid around baseline cosmology

0.02238

0.1199

0.6972

2.3120e-09

0.9459

0.036

1.9043

1

0.00064420

-1.222

0.339

0.892483

0.896318

abacus_cosm177

Emulator grid around baseline cosmology

0.02239

0.1344

0.6820

2.0641e-09

1.0002

0.007

2.8643

1

0.00064420

-0.757

-0.443

0.806026

0.809110

abacus_cosm178

Emulator grid around baseline cosmology

0.02234

0.1204

0.6542

1.9665e-09

0.9424

0.037

1.8987

1

0.00064420

-0.874

-0.455

0.791239

0.794555

abacus_cosm179

Emulator grid around baseline cosmology

0.02240

0.1067

0.5881

2.2365e-09

0.9308

-0.003

1.1884

1

0.00064420

-0.755

-0.435

0.775969

0.779541

abacus_cosm180

Emulator grid around baseline cosmology

0.02258

0.1209

0.7451

2.2790e-09

0.9796

-0.034

2.1722

1

0.00064420

-1.108

-0.274

0.894071

0.897833

abacus_cosm181

Emulator grid around baseline cosmology

0.02169

0.1112

0.5745

2.0651e-09

0.9336

-0.013

1.4059

1

0.00064420

-0.910

0.350

0.730036

0.733292

Running CLASS

We used this fork of CLASS with N-body gauge support: https://github.com/wullm/class_public. Specifically, we used git hash 6cf8e3.

The CLASS outputs stored in AbacusSummit/Cosmologies can be reproduced by running this code passing both the CLASS.ini file for a given cosmology and the abacus_base.pre or abacus_base_fast.pre file. For example:

$cd AbacusSummit/Cosmologies/abacus_cosm000$ <path to class executable> CLASS.ini ../abacus_base.pre


Beyond the Planck2018 LCDM primary cosmology, we chose 4 other secondary cosmologies. One was WMAP7, to have a large change in omega_m, H0, and sigma8. Others were one wCDM, one high Neff, and one low S8.

wCDM: Chose w0=-0.7, wa=-0.5 to be an extreme thawing model.

Neff=3.70 cosmology: Took the chains from base_nnu_plikHM_TT_lowl_lowE_Riess18_post_BAO and averaged those in 3.595 < nnu < 3.90, chosen so that the weighted mean was 3.70. Also standardized As to tau=0.0544.

Low sigma8: Opted to drop the amplitude by about 7.7%, to make sigma8(matter)=0.75. This is a sizeable shift, but there’s lots of ways to damp power.

Then we are doing a large grid of cosmologies to provide control of first and second derivatives around the primary LCDM model.

For the grid of positive/negative excursions for linear derivatives around the baseline LCDM, we opted for the simplicity of rectalinear derivatives in ln(omega_b), ln(omega_c), ns, nrun, sigma8_m, w0. Note that we treat sigma8_m, not As, as the independent variable, in the expectation that this will keep large-scale structure closer to constant. For wa, we opt to hold w(z=0.333)=w0+0.25*wa fixed, close to the mirage model. For Neff, the Planck chains suggested substantial degeneracies with omegac and ns, so we opt to move these two along with Neff to stay close to the CMB degeneracy direction.

We added one extra simulation to be the paired opposite to the low-sigma8 secondary cosmology.

For the broader emulator set, we construct the unstructured grid as follows: We place points on the surface of an 8-dimensional unit sphere, denoting these v0..v7, then map them into the 8-dimensional parameter space by:

• sigma8cb = 0.811355 (1 + 0.12 v0 - 0.125 v4 + 0.06 u0), where u0 is another random number, uniform in [-1,1].

• omega_c = 0.1200 exp(0.100 v1 + 0.165 v6)

• ns = 0.9649 + 0.06 v2 + 0.05 v6

• omegab = 0.02237 exp(0.10 v3)

• w0 = -1.0 + 0.3 v4 -0.2 v5

• wa = 0.8 v5

• Nur = 2.0328 + 1.2 v6

• alpha_s = 0.05 v7

These parameter ranges were chosen to be relatively large (5-8 sigma) beyond today’s CMB+LSS constraints, but it is important to note that most of an 8-d sphere is not close to the extreme in any one parameter, but rather 1/sqrt(8) of that extreme.

We have continued to have omega_c and ns vary with Nur, and w0 to vary with wa (so that variations in wa hold w(z=0.333) constant). In addition, we opted to have sigma8 vary with w(0.333), not as much as a pure wCDM fit to the CMB would imply, but to partially track that behavior.

Finally, we add extra +-6% scatter to sigma8. Note that if we were holding the amplitude of the CMB anisotropies fixed (and fixed tau), then our parameter variations would vary sigma8 quite a lot. But we have not varied tau or neutrino mass, so we want to allow some scatter in sigma8.

Next, we have to specify the distribution of points on the 8-d unit sphere. We want to keep the points well separated, but also impose some constraints. We seek to have some of the points sit in subspaces, so that one doesn’t have to be using the entire 8-dimensional space in all fits. And we want to avoid most antipodal points, as these provide only redundant information about second derivatives (since we already have the linear derivative set). We also want to mildly exceed the number of simulations needed to constrain the second derivatives, so that there is some ability to drop simulations for cross-validation.

We use 49 antipodal pairs of points on the sphere. These are subject to the constraints below, but otherwise are evolved from their random start to an electrostatic glass, resulting in a well dispersed set of points. The constraints:

a) The first 3 pairs are forced to be at the unit vectors in the v0, v1, and v2 directions, which will map to individual extremal excursions in sigma8cb, omega_c, and ns. We retain both points of each pair in the grid, as these are particularly important directions. In all cases below, we keep only the first point of each pair.

b) The next 11 pairs sample only the v0..v3 directions and are constrained to have v4..v7 = 0, so that they will only sample sigma8cb, omega_c, ns, and omega_b. We note that the 4-dimensional space has 10 second derivatives, for which we’re 17 simulations (and 14 non-antipodal).

c) The next 14 pairs sample the v0..v5 directions, holding v6..v7 = 0. These will add w0, wa to the space. This introduces 11 new second derivatives.

d) The next 14 pairs sample the v0..v3 + v6..7 directions, holding v4..v5 = 0. These will add Nur and alpha_s to the LCDM space. Again, this introduces 11 new second derivatives.

e) The last 7 pairs sample the full space, and hence have excursions in w0, wa, Nur, and alpha_s. This last subspace has 4 new second derivatives to measure.

The randomness of the starting point was subjected to some patterns on the sign of certain coordinates in order to encourage a glass with better balance in 2-d projections. This was judged simply by eye.