forked from Alkistis/class_IDE
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathprimordial.c
executable file
·3458 lines (2806 loc) · 130 KB
/
primordial.c
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
/** @file primordial.c Documented primordial module.
*
* Julien Lesgourgues, 24.08.2010
*
* This module computes the primordial spectra. It can be used in different modes:
* simple parametric form, evolving inflaton perturbations, etc. So far only
* the mode corresponding to a simple analytic form in terms of amplitudes, tilts
* and runnings has been developed.
*
* The following functions can be called from other modules:
*
* -# primordial_init() at the beginning (anytime after perturb_init() and before spectra_init())
* -# primordial_spectrum_at_k() at any time for computing P(k) at any k
* -# primordial_free() at the end
*/
#include "primordial.h"
/**
* Primordial spectra for arbitrary argument and for all initial conditions.
*
* This routine evaluates the primordial spectrum at a given value of k by
* interpolating in the pre-computed table.
*
* When k is not in the pre-computed range but the spectrum can be found
* analytically, it finds it. Otherwise returns an error.
*
* Can be called in two modes; linear or logarithmic:
*
* - linear: takes k, returns P(k)
*
* - logarithmic: takes ln(k), return ln(P(k))
*
* One little subtlety: in case of several correlated initial conditions,
* the cross-correlation spectrum can be negative. Then, in logarithmic mode,
* the non-diagonal elements contain the cross-correlation angle \f$ P_{12}/\sqrt{P_{11} P_{22}}\f$
* (from -1 to 1) instead of \f$\ln{P_{12}}\f$
*
* This function can be
* called from whatever module at whatever time, provided that
* primordial_init() has been called before, and primordial_free() has not
* been called yet.
*
* @param ppm Input: pointer to primordial structure containing tabulated primordial spectrum
* @param index_md Input: index of mode (scalar, tensor, ...)
* @param mode Input: linear or logarithmic
* @param input Input: wavenumber in 1/Mpc (linear mode) or its logarithm (logarithmic mode)
* @param output Output: for each pair of initial conditions, primordial spectra P(k) in \f$Mpc^3\f$ (linear mode), or their logarithms and cross-correlation angles (logarithmic mode)
* @return the error status
*/
int primordial_spectrum_at_k(
struct primordial * ppm,
int index_md,
enum linear_or_logarithmic mode,
double input,
double * output /* array with argument output[index_ic1_ic2] (must be already allocated) */
) {
/** Summary: */
/** - define local variables */
int index_ic1,index_ic2,index_ic1_ic2;
double lnk;
int last_index;
/** - infer ln(k) from input. In linear mode, reject negative value of input k value. */
if (mode == linear) {
class_test(input<=0.,
ppm->error_message,
"k = %e",input);
lnk=log(input);
}
else {
lnk = input;
}
/** - if ln(k) is not in the interpolation range, return an error, unless
we are in the case of a analytic spectrum, for which a direct computation is possible */
if ((lnk > ppm->lnk[ppm->lnk_size-1]) || (lnk < ppm->lnk[0])) {
class_test(ppm->primordial_spec_type != analytic_Pk,
ppm->error_message,
"k=%e out of range [%e : %e]",exp(lnk),exp(ppm->lnk[0]),exp(ppm->lnk[ppm->lnk_size-1]));
/* direct computation */
for (index_ic1 = 0; index_ic1 < ppm->ic_size[index_md]; index_ic1++) {
for (index_ic2 = index_ic1; index_ic2 < ppm->ic_size[index_md]; index_ic2++) {
index_ic1_ic2 = index_symmetric_matrix(index_ic1,index_ic2,ppm->ic_size[index_md]);
if (ppm->is_non_zero[index_md][index_ic1_ic2] == _TRUE_) {
class_call(primordial_analytic_spectrum(ppm,
index_md,
index_ic1_ic2,
exp(lnk),
&(output[index_ic1_ic2])),
ppm->error_message,
ppm->error_message);
}
else {
output[index_ic1_ic2] = 0.;
}
}
}
/* if mode==linear, output is already in the correct format. Otherwise, apply necessary transformation. */
if (mode == logarithmic) {
for (index_ic1 = 0; index_ic1 < ppm->ic_size[index_md]; index_ic1++) {
index_ic1_ic2 = index_symmetric_matrix(index_ic1,index_ic1,ppm->ic_size[index_md]);
output[index_ic1_ic2] = log(output[index_ic1_ic2]);
}
for (index_ic1 = 0; index_ic1 < ppm->ic_size[index_md]; index_ic1++) {
for (index_ic2 = index_ic1+1; index_ic2 < ppm->ic_size[index_md]; index_ic2++) {
index_ic1_ic2 = index_symmetric_matrix(index_ic1,index_ic2,ppm->ic_size[index_md]);
if (ppm->is_non_zero[index_md][index_ic1_ic2] == _TRUE_) {
output[index_ic1_ic2] /= sqrt(output[index_symmetric_matrix(index_ic1,index_ic1,ppm->ic_size[index_md])]*
output[index_symmetric_matrix(index_ic2,index_ic2,ppm->ic_size[index_md])]);
}
}
}
}
}
/** - otherwise, interpolate in the pre-computed table */
else {
class_call(array_interpolate_spline(
ppm->lnk,
ppm->lnk_size,
ppm->lnpk[index_md],
ppm->ddlnpk[index_md],
ppm->ic_ic_size[index_md],
lnk,
&last_index,
output,
ppm->ic_ic_size[index_md],
ppm->error_message),
ppm->error_message,
ppm->error_message);
/* if mode==logarithmic, output is already in the correct format. Otherwise, apply necessary transformation. */
if (mode == linear) {
for (index_ic1 = 0; index_ic1 < ppm->ic_size[index_md]; index_ic1++) {
index_ic1_ic2 = index_symmetric_matrix(index_ic1,index_ic1,ppm->ic_size[index_md]);
output[index_ic1_ic2]=exp(output[index_ic1_ic2]);
}
for (index_ic1 = 0; index_ic1 < ppm->ic_size[index_md]; index_ic1++) {
for (index_ic2 = index_ic1+1; index_ic2 < ppm->ic_size[index_md]; index_ic2++) {
index_ic1_ic2 = index_symmetric_matrix(index_ic1,index_ic2,ppm->ic_size[index_md]);
if (ppm->is_non_zero[index_md][index_ic1_ic2] == _TRUE_) {
output[index_ic1_ic2] *= sqrt(output[index_symmetric_matrix(index_ic1,index_ic1,ppm->ic_size[index_md])]*
output[index_symmetric_matrix(index_ic2,index_ic2,ppm->ic_size[index_md])]);
}
else {
output[index_ic1_ic2] = 0.;
}
}
}
}
}
return _SUCCESS_;
}
/**
* This routine initializes the primordial structure (in particular, it computes table of primordial spectrum values)
*
* @param ppr Input: pointer to precision structure (defines method and precision for all computations)
* @param ppt Input: pointer to perturbation structure (useful for knowing k_min, k_max, etc.)
* @param ppm Output: pointer to initialized primordial structure
* @return the error status
*/
int primordial_init(
struct precision * ppr,
struct perturbs * ppt,
struct primordial * ppm
) {
/** Summary: */
/** - define local variables */
double k,k_min,k_max;
int index_md,index_ic1,index_ic2,index_ic1_ic2,index_k;
double pk,pk1,pk2;
double dlnk,lnpk_pivot,lnpk_minus,lnpk_plus,lnpk_minusminus,lnpk_plusplus;
/* uncomment if you use optional test below
(for correlated isocurvature modes) */
//double cos_delta_k;
/** - check that we really need to compute the primordial spectra */
if (ppt->has_perturbations == _FALSE_) {
ppm->lnk_size=0;
if (ppm->primordial_verbose > 0)
printf("No perturbations requested. Primordial module skipped.\n");
return _SUCCESS_;
}
else {
if (ppm->primordial_verbose > 0)
printf("Computing primordial spectra");
}
/** - get kmin and kmax from perturbation structure. Test that they make sense. */
k_min = ppt->k_min; /* first value, inferred from perturbations structure */
k_max = ppt->k_max; /* last value, inferred from perturbations structure */
class_test(k_min <= 0.,
ppm->error_message,
"k_min negative or null: stop to avoid segmentation fault");
class_test(k_max <= 0.,
ppm->error_message,
"k_max negative or null: stop to avoid segmentation fault");
class_test(ppm->k_pivot <= 0.,
ppm->error_message,
"k_pivot negative or null: stop to avoid segmentation fault");
class_test(ppr->k_per_decade_primordial <= 0.,
ppm->error_message,
"k_per_decade_primordial negative or null: stop to avoid segmentation fault");
class_test(ppr->k_per_decade_primordial <= _K_PER_DECADE_PRIMORDIAL_MIN_,
ppm->error_message,
"k_per_decade_primordial = %e: you ask for such a sparse sampling of the primordial spectrum that this is probably a mistake",
ppr->k_per_decade_primordial);
/** - allocate and fill values of \f$ \ln{k}\f$'s */
class_call(primordial_get_lnk_list(ppm,
k_min,
k_max,
ppr->k_per_decade_primordial
),
ppm->error_message,
ppm->error_message);
/** - define indices and allocate tables in primordial structure */
class_call(primordial_indices(ppt,
ppm),
ppm->error_message,
ppm->error_message);
/** - deal with case of analytic primordial spectra (with amplitudes, tilts, runnings, etc.) */
if (ppm->primordial_spec_type == analytic_Pk) {
if (ppm->primordial_verbose > 0)
printf(" (analytic spectrum)\n");
class_call_except(primordial_analytic_spectrum_init(ppt,
ppm),
ppm->error_message,
ppm->error_message,
primordial_free(ppm));
for (index_k = 0; index_k < ppm->lnk_size; index_k++) {
k=exp(ppm->lnk[index_k]);
for (index_md = 0; index_md < ppt->md_size; index_md++) {
for (index_ic1 = 0; index_ic1 < ppm->ic_size[index_md]; index_ic1++) {
for (index_ic2 = index_ic1; index_ic2 < ppm->ic_size[index_md]; index_ic2++) {
index_ic1_ic2 = index_symmetric_matrix(index_ic1,index_ic2,ppm->ic_size[index_md]);
if (ppm->is_non_zero[index_md][index_ic1_ic2] == _TRUE_) {
class_call(primordial_analytic_spectrum(ppm,
index_md,
index_ic1_ic2,
k,
&pk),
ppm->error_message,
ppm->error_message);
if (index_ic1 == index_ic2) {
/* diagonal coefficients: ln[P(k)] */
ppm->lnpk[index_md][index_k*ppm->ic_ic_size[index_md]+index_ic1_ic2] = log(pk);
}
else {
/* non-diagonal coefficients: cosDelta(k) = P(k)_12/sqrt[P(k)_1 P(k)_2] */
class_call(primordial_analytic_spectrum(ppm,
index_md,
index_symmetric_matrix(index_ic1,index_ic1,ppm->ic_size[index_md]),
k,
&pk1),
ppm->error_message,
ppm->error_message);
class_call(primordial_analytic_spectrum(ppm,
index_md,
index_symmetric_matrix(index_ic2,index_ic2,ppm->ic_size[index_md]),
k,
&pk2),
ppm->error_message,
ppm->error_message);
/* either return an error if correlation is too large... */
/*
cos_delta_k = pk/sqrt(pk1*pk2);
class_test_except((cos_delta_k < -1.) || (cos_delta_k > 1.),
ppm->error_message,
primordial_free(ppm),
"correlation angle between IC's takes unphysical values");
ppm->lnpk[index_md][index_k*ppm->ic_ic_size[index_md]+index_ic1_ic2] = cos_delta_k;
*/
/* ... or enforce definite positive correlation matrix */
if (pk > sqrt(pk1*pk2))
ppm->lnpk[index_md][index_k*ppm->ic_ic_size[index_md]+index_ic1_ic2] = 1.;
else if (pk < -sqrt(pk1*pk2))
ppm->lnpk[index_md][index_k*ppm->ic_ic_size[index_md]+index_ic1_ic2] = -1.;
else
ppm->lnpk[index_md][index_k*ppm->ic_ic_size[index_md]+index_ic1_ic2] = pk/sqrt(pk1*pk2);
}
}
else {
/* non-diagonal coefficients when ic's are uncorrelated */
ppm->lnpk[index_md][index_k*ppm->ic_ic_size[index_md]+index_ic1_ic2] = 0.;
}
}
}
}
}
}
/** - deal with case of inflation with given \f$V(\phi)\f$ or \f$H(\phi)\f$ */
else if ((ppm->primordial_spec_type == inflation_V) || (ppm->primordial_spec_type == inflation_H) || (ppm->primordial_spec_type == inflation_V_end)) {
class_call(primordial_inflation_indices(ppm),
ppm->error_message,
ppm->error_message);
if (ppm->primordial_verbose > 0)
printf(" (simulating inflation)\n");
class_call_except(primordial_inflation_solve_inflation(ppt,ppm,ppr),
ppm->error_message,
ppm->error_message,
primordial_free(ppm));
}
/** - deal with the case of external calculation of \f$ P_k \f$*/
else if (ppm->primordial_spec_type == external_Pk) {
class_test(ppt->has_scalars == _FALSE_,
ppm->error_message,
"external Pk module cannot work if you do not ask for scalar modes");
class_test(ppt->has_vectors == _TRUE_,
ppm->error_message,
"external Pk module cannot work if you ask for vector modes");
class_test(ppt->has_bi == _TRUE_ || ppt->has_cdi == _TRUE_ || ppt->has_nid == _TRUE_ || ppt->has_niv == _TRUE_,
ppm->error_message,
"external Pk module cannot work if you ask for isocurvature modes (but that could be implemented easily in the future!)");
if (ppm->primordial_verbose > 0)
printf(" (Pk calculated externally)\n");
class_call_except(primordial_external_spectrum_init(ppt,ppm),
ppm->error_message,
ppm->error_message,
primordial_free(ppm));
}
else {
class_test(0==0,
ppm->error_message,
"primordial spectrum type not recognized");
}
/** - compute second derivative of each \f$ \ln{P_k} \f$ versus lnk with spline, in view of interpolation */
for (index_md = 0; index_md < ppm->md_size; index_md++) {
class_call(array_spline_table_lines(ppm->lnk,
ppm->lnk_size,
ppm->lnpk[index_md],
ppm->ic_ic_size[index_md],
ppm->ddlnpk[index_md],
_SPLINE_EST_DERIV_,
ppm->error_message),
ppm->error_message,
ppm->error_message);
}
/** - derive spectral parameters from numerically computed spectra
(not used by the rest of the code, but useful to keep in memory for several types of investigation) */
if (ppm->primordial_spec_type != analytic_Pk) {
dlnk = log(10.)/ppr->k_per_decade_primordial;
if (ppt->has_scalars == _TRUE_) {
class_call(primordial_spectrum_at_k(ppm,
ppt->index_md_scalars,
logarithmic,
log(ppm->k_pivot),
&lnpk_pivot),
ppm->error_message,
ppm->error_message);
class_call(primordial_spectrum_at_k(ppm,
ppt->index_md_scalars,
logarithmic,
log(ppm->k_pivot)+dlnk,
&lnpk_plus),
ppm->error_message,
ppm->error_message);
class_call(primordial_spectrum_at_k(ppm,
ppt->index_md_scalars,
logarithmic,
log(ppm->k_pivot)-dlnk,
&lnpk_minus),
ppm->error_message,
ppm->error_message);
ppm->A_s = exp(lnpk_pivot);
ppm->n_s = (lnpk_plus-lnpk_minus)/(2.*dlnk)+1.;
ppm->alpha_s = (lnpk_plus-2.*lnpk_pivot+lnpk_minus)/pow(dlnk,2);
/** - expression for alpha_s comes from:
`ns_2 = (lnpk_plus-lnpk_pivot)/(dlnk)+1`
`ns_1 = (lnpk_pivot-lnpk_minus)/(dlnk)+1`
`alpha_s = dns/dlnk = (ns_2-ns_1)/dlnk = (lnpk_plus-lnpk_pivot-lnpk_pivot+lnpk_minus)/(dlnk)/(dlnk)`
**/
class_call(primordial_spectrum_at_k(ppm,
ppt->index_md_scalars,
logarithmic,
log(ppm->k_pivot)+2.*dlnk,
&lnpk_plusplus),
ppm->error_message,
ppm->error_message);
class_call(primordial_spectrum_at_k(ppm,
ppt->index_md_scalars,
logarithmic,
log(ppm->k_pivot)-2.*dlnk,
&lnpk_minusminus),
ppm->error_message,
ppm->error_message);
/** - expression for beta_s:
`ppm->beta_s = (alpha_plus-alpha_minus)/dlnk = (lnpk_plusplus-2.*lnpk_plus+lnpk_pivot -
(lnpk_pivot-2.*lnpk_minus+lnpk_minusminus)/pow(dlnk,3)`
**/
/* Simplification of the beta_s expression: */
ppm->beta_s = (lnpk_plusplus-2.*lnpk_plus+2.*lnpk_minus-lnpk_minusminus)/pow(dlnk,3);
if (ppm->primordial_verbose > 0)
printf(" -> A_s=%g n_s=%g alpha_s=%g\n",ppm->A_s,ppm->n_s,ppm->alpha_s);
}
if (ppt->has_tensors == _TRUE_) {
class_call(primordial_spectrum_at_k(ppm,
ppt->index_md_tensors,
logarithmic,
log(ppm->k_pivot),
&lnpk_pivot),
ppm->error_message,
ppm->error_message);
class_call(primordial_spectrum_at_k(ppm,
ppt->index_md_tensors,
logarithmic,
log(ppm->k_pivot)+dlnk,
&lnpk_plus),
ppm->error_message,
ppm->error_message);
class_call(primordial_spectrum_at_k(ppm,
ppt->index_md_tensors,
logarithmic,
log(ppm->k_pivot)-dlnk,
&lnpk_minus),
ppm->error_message,
ppm->error_message);
ppm->r = exp(lnpk_pivot)/ppm->A_s;
ppm->n_t = (lnpk_plus-lnpk_minus)/(2.*dlnk);
ppm->alpha_t = (lnpk_plus-2.*lnpk_pivot+lnpk_minus)/pow(dlnk,2);
if (ppm->primordial_verbose > 0)
printf(" -> r=%g n_t=%g alpha_t=%g\n",ppm->r,ppm->n_t,ppm->alpha_t);
}
}
return _SUCCESS_;
}
/**
* This routine frees all the memory space allocated by primordial_init().
*
* To be called at the end of each run.
*
* @param ppm Input: pointer to primordial structure (which fields must be freed)
* @return the error status
*/
int primordial_free(
struct primordial * ppm
) {
int index_md;
if (ppm->lnk_size > 0) {
if (ppm->primordial_spec_type == analytic_Pk) {
for (index_md = 0; index_md < ppm->md_size; index_md++) {
free(ppm->amplitude[index_md]);
free(ppm->tilt[index_md]);
free(ppm->running[index_md]);
}
free(ppm->amplitude);
free(ppm->tilt);
free(ppm->running);
}
else if (ppm->primordial_spec_type == external_Pk) {
free(ppm->command);
}
for (index_md = 0; index_md < ppm->md_size; index_md++) {
free(ppm->lnpk[index_md]);
free(ppm->ddlnpk[index_md]);
free(ppm->is_non_zero[index_md]);
}
free(ppm->lnpk);
free(ppm->ddlnpk);
free(ppm->is_non_zero);
free(ppm->ic_size);
free(ppm->ic_ic_size);
free(ppm->lnk);
}
return _SUCCESS_;
}
/**
* This routine defines indices and allocates tables in the primordial structure
*
* @param ppt Input: pointer to perturbation structure
* @param ppm Input/output: pointer to primordial structure
* @return the error status
*/
int primordial_indices(
struct perturbs * ppt,
struct primordial * ppm
) {
int index_md;
ppm->md_size = ppt->md_size;
class_alloc(ppm->lnpk,ppt->md_size*sizeof(double*),ppm->error_message);
class_alloc(ppm->ddlnpk,ppt->md_size*sizeof(double*),ppm->error_message);
class_alloc(ppm->ic_size,ppt->md_size*sizeof(int*),ppm->error_message);
class_alloc(ppm->ic_ic_size,ppt->md_size*sizeof(int*),ppm->error_message);
class_alloc(ppm->is_non_zero,ppm->md_size*sizeof(short *),ppm->error_message);
for (index_md = 0; index_md < ppt->md_size; index_md++) {
ppm->ic_size[index_md] = ppt->ic_size[index_md];
ppm->ic_ic_size[index_md] = (ppm->ic_size[index_md]*(ppm->ic_size[index_md]+1))/2;
class_alloc(ppm->lnpk[index_md],
ppm->lnk_size*ppm->ic_ic_size[index_md]*sizeof(double),
ppm->error_message);
class_alloc(ppm->ddlnpk[index_md],
ppm->lnk_size*ppm->ic_ic_size[index_md]*sizeof(double),
ppm->error_message);
class_alloc(ppm->is_non_zero[index_md],
ppm->ic_ic_size[index_md]*sizeof(short),
ppm->error_message);
}
return _SUCCESS_;
}
/**
* This routine allocates and fills the list of wavenumbers k
*
*
* @param ppm Input/output: pointer to primordial structure
* @param kmin Input: first value
* @param kmax Input: last value that we should encompass
* @param k_per_decade Input: number of k per decade
* @return the error status
*/
int primordial_get_lnk_list(
struct primordial * ppm,
double kmin,
double kmax,
double k_per_decade
) {
int i;
class_test((kmin <= 0.) || (kmax <= kmin),
ppm->error_message,
"inconsistent values of kmin=%e, kmax=%e",kmin,kmax);
ppm->lnk_size = (int)(log(kmax/kmin)/log(10.)*k_per_decade) + 2;
class_alloc(ppm->lnk,ppm->lnk_size*sizeof(double),ppm->error_message);
for (i=0; i<ppm->lnk_size; i++)
ppm->lnk[i]=log(kmin)+i*log(10.)/k_per_decade;
return _SUCCESS_;
}
/**
* This routine interprets and stores in a condensed form the input parameters
* in the case of a simple analytic spectra with amplitudes, tilts, runnings,
* in such way that later on, the spectrum can be obtained by a quick call to
* the routine primordial_analytic_spectrum(()
*
* @param ppt Input: pointer to perturbation structure
* @param ppm Input/output: pointer to primordial structure
* @return the error status
*/
int primordial_analytic_spectrum_init(
struct perturbs * ppt,
struct primordial * ppm
) {
int index_md,index_ic1,index_ic2;
int index_ic1_ic2,index_ic1_ic1,index_ic2_ic2;
double one_amplitude=0.;
double one_tilt=0.;
double one_running=0.;
double one_correlation=0.;
class_alloc(ppm->amplitude,
ppm->md_size*sizeof(double *),
ppm->error_message);
class_alloc(ppm->tilt,
ppm->md_size*sizeof(double *),
ppm->error_message);
class_alloc(ppm->running,
ppm->md_size*sizeof(double *),
ppm->error_message);
for (index_md = 0; index_md < ppm->md_size; index_md++) {
class_alloc(ppm->amplitude[index_md],
ppm->ic_ic_size[index_md]*sizeof(double),
ppm->error_message);
class_alloc(ppm->tilt[index_md],
ppm->ic_ic_size[index_md]*sizeof(double),
ppm->error_message);
class_alloc(ppm->running[index_md],
ppm->ic_ic_size[index_md]*sizeof(double),
ppm->error_message);
}
for (index_md = 0; index_md < ppm->md_size; index_md++) {
/* diagonal coefficients */
for (index_ic1 = 0; index_ic1 < ppm->ic_size[index_md]; index_ic1++) {
if (_scalars_) {
if ((ppt->has_ad == _TRUE_) && (index_ic1 == ppt->index_ic_ad)) {
one_amplitude = ppm->A_s;
one_tilt = ppm->n_s;
one_running = ppm->alpha_s;
}
if ((ppt->has_bi == _TRUE_) && (index_ic1 == ppt->index_ic_bi)) {
one_amplitude = ppm->A_s*ppm->f_bi*ppm->f_bi;
one_tilt = ppm->n_bi;
one_running = ppm->alpha_bi;
}
if ((ppt->has_cdi == _TRUE_) && (index_ic1 == ppt->index_ic_cdi)) {
one_amplitude = ppm->A_s*ppm->f_cdi*ppm->f_cdi;
one_tilt = ppm->n_cdi;
one_running = ppm->alpha_cdi;
}
if ((ppt->has_nid == _TRUE_) && (index_ic1 == ppt->index_ic_nid)) {
one_amplitude = ppm->A_s*ppm->f_nid*ppm->f_nid;
one_tilt = ppm->n_nid;
one_running = ppm->alpha_nid;
}
if ((ppt->has_niv == _TRUE_) && (index_ic1 == ppt->index_ic_niv)) {
one_amplitude = ppm->A_s*ppm->f_niv*ppm->f_niv;
one_tilt = ppm->n_niv;
one_running = ppm->alpha_niv;
}
}
if (_tensors_) {
if (index_ic1 == ppt->index_ic_ten) {
one_amplitude = ppm->A_s*ppm->r;
one_tilt = ppm->n_t+1.; /* +1 to match usual definition of n_t (equivalent to n_s-1) */
one_running = ppm->alpha_t;
}
}
class_test(one_amplitude <= 0.,
ppm->error_message,
"inconsistent input for primordial amplitude: %g for index_md=%d, index_ic=%d\n",
one_amplitude,index_md,index_ic1);
index_ic1_ic2 = index_symmetric_matrix(index_ic1,index_ic1,ppm->ic_size[index_md]);
ppm->is_non_zero[index_md][index_ic1_ic2] = _TRUE_;
ppm->amplitude[index_md][index_ic1_ic2] = one_amplitude;
ppm->tilt[index_md][index_ic1_ic2] = one_tilt;
ppm->running[index_md][index_ic1_ic2] = one_running;
}
/* non-diagonal coefficients */
for (index_ic1 = 0; index_ic1 < ppm->ic_size[index_md]; index_ic1++) {
for (index_ic2 = index_ic1+1; index_ic2 < ppm->ic_size[index_md]; index_ic2++) {
if (_scalars_) {
if ((ppt->has_ad == _TRUE_) && (ppt->has_bi == _TRUE_) &&
(((index_ic1 == ppt->index_ic_ad) && (index_ic2 == ppt->index_ic_bi)) ||
((index_ic1 == ppt->index_ic_ad) && (index_ic1 == ppt->index_ic_bi)))) {
one_correlation = ppm->c_ad_bi;
one_tilt = ppm->n_ad_bi;
one_running = ppm->alpha_ad_bi;
}
if ((ppt->has_ad == _TRUE_) && (ppt->has_cdi == _TRUE_) &&
(((index_ic1 == ppt->index_ic_ad) && (index_ic2 == ppt->index_ic_cdi)) ||
((index_ic2 == ppt->index_ic_ad) && (index_ic1 == ppt->index_ic_cdi)))) {
one_correlation = ppm->c_ad_cdi;
one_tilt = ppm->n_ad_cdi;
one_running = ppm->alpha_ad_cdi;
}
if ((ppt->has_ad == _TRUE_) && (ppt->has_nid == _TRUE_) &&
(((index_ic1 == ppt->index_ic_ad) && (index_ic2 == ppt->index_ic_nid)) ||
((index_ic2 == ppt->index_ic_ad) && (index_ic1 == ppt->index_ic_nid)))) {
one_correlation = ppm->c_ad_nid;
one_tilt = ppm->n_ad_nid;
one_running = ppm->alpha_ad_nid;
}
if ((ppt->has_ad == _TRUE_) && (ppt->has_niv == _TRUE_) &&
(((index_ic1 == ppt->index_ic_ad) && (index_ic2 == ppt->index_ic_niv)) ||
((index_ic2 == ppt->index_ic_ad) && (index_ic1 == ppt->index_ic_niv)))) {
one_correlation = ppm->c_ad_niv;
one_tilt = ppm->n_ad_niv;
one_running = ppm->alpha_ad_niv;
}
if ((ppt->has_bi == _TRUE_) && (ppt->has_cdi == _TRUE_) &&
(((index_ic1 == ppt->index_ic_bi) && (index_ic2 == ppt->index_ic_cdi)) ||
((index_ic2 == ppt->index_ic_bi) && (index_ic1 == ppt->index_ic_cdi)))) {
one_correlation = ppm->c_bi_cdi;
one_tilt = ppm->n_bi_cdi;
one_running = ppm->alpha_bi_cdi;
}
if ((ppt->has_bi == _TRUE_) && (ppt->has_nid == _TRUE_) &&
(((index_ic1 == ppt->index_ic_bi) && (index_ic2 == ppt->index_ic_nid)) ||
((index_ic2 == ppt->index_ic_bi) && (index_ic1 == ppt->index_ic_nid)))) {
one_correlation = ppm->c_bi_nid;
one_tilt = ppm->n_bi_nid;
one_running = ppm->alpha_bi_nid;
}
if ((ppt->has_bi == _TRUE_) && (ppt->has_niv == _TRUE_) &&
(((index_ic1 == ppt->index_ic_bi) && (index_ic2 == ppt->index_ic_niv)) ||
((index_ic2 == ppt->index_ic_bi) && (index_ic1 == ppt->index_ic_niv)))) {
one_correlation = ppm->c_bi_niv;
one_tilt = ppm->n_bi_niv;
one_running = ppm->alpha_bi_niv;
}
if ((ppt->has_cdi == _TRUE_) && (ppt->has_nid == _TRUE_) &&
(((index_ic1 == ppt->index_ic_cdi) && (index_ic2 == ppt->index_ic_nid)) ||
((index_ic2 == ppt->index_ic_cdi) && (index_ic1 == ppt->index_ic_nid)))) {
one_correlation = ppm->c_cdi_nid;
one_tilt = ppm->n_cdi_nid;
one_running = ppm->alpha_cdi_nid;
}
if ((ppt->has_cdi == _TRUE_) && (ppt->has_niv == _TRUE_) &&
(((index_ic1 == ppt->index_ic_cdi) && (index_ic2 == ppt->index_ic_niv)) ||
((index_ic2 == ppt->index_ic_cdi) && (index_ic1 == ppt->index_ic_niv)))) {
one_correlation = ppm->c_cdi_niv;
one_tilt = ppm->n_cdi_niv;
one_running = ppm->alpha_cdi_niv;
}
if ((ppt->has_nid == _TRUE_) && (ppt->has_niv == _TRUE_) &&
(((index_ic1 == ppt->index_ic_nid) && (index_ic2 == ppt->index_ic_niv)) ||
((index_ic2 == ppt->index_ic_nid) && (index_ic1 == ppt->index_ic_niv)))) {
one_correlation = ppm->c_nid_niv;
one_tilt = ppm->n_nid_niv;
one_running = ppm->alpha_nid_niv;
}
}
class_test((one_correlation < -1) || (one_correlation > 1),
ppm->error_message,
"inconsistent input for isocurvature cross-correlation\n");
index_ic1_ic2 = index_symmetric_matrix(index_ic1,index_ic2,ppm->ic_size[index_md]);
index_ic1_ic1 = index_symmetric_matrix(index_ic1,index_ic1,ppm->ic_size[index_md]);
index_ic2_ic2 = index_symmetric_matrix(index_ic2,index_ic2,ppm->ic_size[index_md]);
if (one_correlation == 0.) {
ppm->is_non_zero[index_md][index_ic1_ic2] = _FALSE_;
ppm->amplitude[index_md][index_ic1_ic2] = 0.;
ppm->tilt[index_md][index_ic1_ic2] = 0.;
ppm->running[index_md][index_ic1_ic2] = 0.;
}
else {
ppm->is_non_zero[index_md][index_ic1_ic2] = _TRUE_;
ppm->amplitude[index_md][index_ic1_ic2] =
sqrt(ppm->amplitude[index_md][index_ic1_ic1]*
ppm->amplitude[index_md][index_ic2_ic2])*
one_correlation;
ppm->tilt[index_md][index_ic1_ic2] =
0.5*(ppm->tilt[index_md][index_ic1_ic1]
+ppm->tilt[index_md][index_ic2_ic2])
+ one_tilt;
ppm->running[index_md][index_ic1_ic2] =
0.5*(ppm->running[index_md][index_ic1_ic1]
+ppm->running[index_md][index_ic2_ic2])
+ one_running;
}
}
}
}
return _SUCCESS_;
}
/**
* This routine returns the primordial spectrum in the simple analytic case with
* amplitudes, tilts, runnings, for each mode (scalar/tensor...),
* pair of initial conditions, and wavenumber.
*
* @param ppm Input/output: pointer to primordial structure
* @param index_md Input: index of mode (scalar, tensor, ...)
* @param index_ic1_ic2 Input: pair of initial conditions (ic1, ic2)
* @param k Input: wavenumber in same units as pivot scale, i.e. in 1/Mpc
* @param pk Output: primordial power spectrum A (k/k_pivot)^(n+...)
* @return the error status
*/
int primordial_analytic_spectrum(
struct primordial * ppm,
int index_md,
int index_ic1_ic2,
double k,
double * pk
) {
if (ppm->is_non_zero[index_md][index_ic1_ic2] == _TRUE_) {
*pk = ppm->amplitude[index_md][index_ic1_ic2]
*exp((ppm->tilt[index_md][index_ic1_ic2]-1.)*log(k/ppm->k_pivot)
+ 0.5 * ppm->running[index_md][index_ic1_ic2] * pow(log(k/ppm->k_pivot), 2.));
}
else {
*pk = 0.;
}
return _SUCCESS_;
}
/**
* This routine encodes the inflaton scalar potential
*
* @param ppm Input: pointer to primordial structure
* @param phi Input: background inflaton field value in units of Mp
* @param V Output: inflaton potential in units of \f$ Mp^4\f$
* @param dV Output: first derivative of inflaton potential wrt the field
* @param ddV Output: second derivative of inflaton potential wrt the field
* @return the error status
*/
int primordial_inflation_potential(
struct primordial * ppm,
double phi,
double * V,
double * dV,
double * ddV
) {
double e,de,dde,mu,dmu,ddmu,l,dl,ddl,p,dp,ddp;
switch (ppm->potential) {
/* V(phi)=polynomial in phi */
case polynomial:
*V = ppm->V0+phi*ppm->V1+pow(phi,2)/2.*ppm->V2+pow(phi,3)/6.*ppm->V3+pow(phi,4)/24.*ppm->V4;
*dV = ppm->V1+phi*ppm->V2+pow(phi,2)/2.*ppm->V3+pow(phi,3)/6.*ppm->V4;
*ddV = ppm->V2+phi*ppm->V3+pow(phi,2)/2.*ppm->V4;
break;
/* V(phi) = Lambda^4(1+cos(phi/f)) = V0 (1+cos(phi/V1)) */
case natural:
*V = ppm->V0*(1.+cos(phi/ppm->V1));
*dV = -ppm->V0/ppm->V1*sin(phi/ppm->V1);
*ddV = -ppm->V0/ppm->V1/ppm->V1*cos(phi/ppm->V1);
break;
/* Higgs inflation from arXiv:1403.6078 */
case higgs_inflation:
// correspondence with 1403.6078:
// V0 = b
// V1 = ksi
// V2 = kappa
// V3 = delta_lambda
// mu = bar(mu)/M_P
// phi = -chi/M_P