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equations.f90
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! Equations module for background and ! To avoid circular module issues, some things are not part of module
! Background evolution, return d tau/ d a, where tau is the conformal time
function dtauda(this,a)
use results
use DarkEnergyInterface
implicit none
class(CAMBdata) :: this
real(dl), intent(in) :: a
real(dl) :: dtauda, grhoa2, grhov_t
call this%CP%DarkEnergy%BackgroundDensityAndPressure(this%grhov, a, grhov_t)
! 8*pi*G*rho*a**4.
grhoa2 = this%grho_no_de(a) + grhov_t * a**2
if (grhoa2 <= 0) then
call GlobalError('Universe stops expanding before today (recollapse not supported)', error_unsupported_params)
dtauda = 0
else
dtauda = sqrt(3 / grhoa2)
end if
end function dtauda
!cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
!Gauge-dependent perturbation equations
module GaugeInterface
use precision
use results
use MassiveNu
use DarkEnergyInterface
use Transfer
implicit none
public
! Equations and relation to synchronous gauge variables documented in the notes:
! https://cosmologist.info/notes/CAMB.pdf
!Description of this file. Change if you make modifications.
character(LEN=*), parameter :: Eqns_name = 'cdm_gauge'
logical, parameter :: plot_evolve = .false. !for outputing time evolution
integer, parameter :: basic_num_eqns = 4
integer, parameter :: ix_etak=1, ix_clxc=2, ix_clxb=3, ix_vb=4 !Scalar array indices for each quantity
integer, parameter :: ixt_H = 1, ixt_shear = 2 !tensor indices
logical :: DoTensorNeutrinos = .true.
logical, parameter :: second_order_tightcoupling = .true.
real(dl) :: Magnetic = 0._dl
!Vector mode anisotropic stress in units of rho_gamma
real(dl) :: vec_sig0 = 1._dl
!Vector mode shear
integer, parameter :: max_l_evolve = 256 !Maximum l we are ever likely to propagate
!Note higher values increase size of Evolution vars, hence memory
!Supported scalar initial condition flags
integer, parameter :: initial_adiabatic=1, initial_iso_CDM=2, &
initial_iso_baryon=3, initial_iso_neutrino=4, initial_iso_neutrino_vel=5, initial_vector = 0
integer, parameter :: initial_nummodes = initial_iso_neutrino_vel
type EvolutionVars
real(dl) q, q2
real(dl) k_buf,k2_buf ! set in initial
logical :: is_cosmological_constant
integer w_ix !Index of two quintessence equations
integer Tg_ix !index of matter temerature perturbation
integer reion_line_ix !index of matter temerature perturbation
integer xe_ix !index of x_e perturbation
integer Ts_ix !index of Delta_{T_s}
integer r_ix !Index of the massless neutrino hierarchy
integer g_ix !Index of the photon neutrino hierarchy
integer q_ix !index into q_evolve array that gives the value q
logical TransferOnly
! nvar - number of scalar (tensor) equations for this k
integer nvar,nvart, nvarv
!Max_l for the various hierarchies
integer lmaxg,lmaxnr,lmaxnu,lmaxgpol,MaxlNeeded
integer lmaxnrt, lmaxnut, lmaxt, lmaxpolt, MaxlNeededt
logical EvolveTensorMassiveNu(max_nu)
integer lmaxnrv, lmaxv, lmaxpolv
integer lmaxline !21cm multipoles for getting reionization effect
integer polind !index into scalar array of polarization hierarchy
!array indices for massive neutrino equations
integer nu_ix(max_nu), nu_pert_ix
integer nq(max_nu), lmaxnu_pert
logical has_nu_relativistic
!Initial values for massive neutrino v*3 variables calculated when switching
!to non-relativistic approx
real(dl) G11(max_nu),G30(max_nu)
!True when using non-relativistic approximation
logical MassiveNuApprox(max_nu)
real(dl) MassiveNuApproxTime(max_nu)
!True when truncating at l=2,3 when k*tau>>1 (see arXiv:1104.2933)
logical high_ktau_neutrino_approx
!Massive neutrino scheme being used at the moment
integer NuMethod
!True when using tight-coupling approximation (required for stability at early times)
logical TightCoupling, TensTightCoupling
real(dl) TightSwitchoffTime
!Numer of scalar equations we are propagating
integer ScalEqsToPropagate
integer TensEqsToPropagate
!beta > l for closed models
integer FirstZerolForBeta
!Tensor vars
real(dl) aux_buf
real(dl) pig, pigdot
real(dl) poltruncfac
logical no_nu_multpoles, no_phot_multpoles
integer lmaxnu_tau(max_nu) !lmax for massive neutinos at time being integrated
logical nu_nonrelativistic(max_nu)
real(dl) denlk(max_l_evolve),denlk2(max_l_evolve), polfack(max_l_evolve)
real(dl) Kf(max_l_evolve)
integer E_ix, B_ix !tensor polarizatisdon indices
real(dl) denlkt(4,max_l_evolve),Kft(max_l_evolve)
logical :: saha !still high x_e
logical :: evolve_TM !\delta T_g evolved separately
logical :: evolve_baryon_cs !evolving sound speed rather than using background approx
!Workaround for ifort, gives class pointer to avoid creating temps and huge slow down
class(TThermoData), pointer :: ThermoData => null()
real, pointer :: OutputTransfer(:) => null()
real(dl), pointer :: OutputSources(:) => null()
real(dl), pointer :: CustomSources(:) => null()
integer :: OutputStep = 0
end type EvolutionVars
ABSTRACT INTERFACE
SUBROUTINE TSource_func(sources, tau, a, adotoa, grho, gpres,w_lam, cs2_lam, &
grhob_t,grhor_t,grhoc_t,grhog_t,grhov_t,grhonu_t, &
k,etak, etakdot, phi, phidot, sigma, sigmadot, &
dgrho, clxg,clxb,clxc,clxr, clxnu, clxde, delta_p_b, &
dgq, qg, qr, qde, vb, qgdot, qrdot, vbdot, &
dgpi, pig, pir, pigdot, pirdot, diff_rhopi, &
polter, polterdot, polterddot, octg, octgdot, E, Edot, &
opacity, dopacity, ddopacity, visibility, dvisibility, ddvisibility, exptau, &
tau0, tau_maxvis, Kf, f_K)
use precision
real(dl), intent(out) :: sources(:)
real(dl), intent(in) :: tau, a, adotoa, grho, gpres,w_lam, cs2_lam, &
grhob_t,grhor_t,grhoc_t,grhog_t,grhov_t,grhonu_t, &
k,etak, etakdot, phi, phidot, sigma, sigmadot, &
dgrho, clxg,clxb,clxc, clxr, clxnu, clxde, delta_p_b, &
dgq, qg, qr, qde, vb, qgdot, qrdot, vbdot, &
dgpi, pig, pir, pigdot, pirdot, diff_rhopi, &
polter, polterdot, polterddot, octg, octgdot, E(2:3), Edot(2:3), &
opacity, dopacity, ddopacity, visibility, dvisibility, ddvisibility, exptau, &
tau0, tau_maxvis
REAL(dl), intent(in) :: Kf(*)
real(dl), external :: f_K
END SUBROUTINE TSource_func
END INTERFACE
class(CAMBdata), pointer :: State !Current state.
!(Due to ifort bug State needs to be class pointer to avoid making temp class pointers when calling functions)
type(CAMBParams), pointer :: CP !Current parameters (part of state)
!precalculated arrays
real(dl) polfac(max_l_evolve),denl(max_l_evolve),vecfac(max_l_evolve),vecfacpol(max_l_evolve)
real(dl), parameter :: ep0=1.0d-2
integer, parameter :: lmaxnu_high_ktau=4 !Jan2015, increased from 3 to fix mpk for mnu~6eV
real(dl) epsw
real(dl), allocatable :: nu_tau_notmassless(:,:)
real(dl) nu_tau_nonrelativistic(max_nu), nu_tau_massive(max_nu)
procedure(state_function), private :: dtauda
contains
subroutine SetActiveState(P)
class(CAMBdata), target :: P
State => P
CP => P%CP
end subroutine SetActiveState
subroutine GaugeInterface_ScalEv(EV,y,tau,tauend,tol1,ind,c,w)
type(EvolutionVars) EV
real(dl) c(24),w(EV%nvar,9), y(EV%nvar), tol1, tau, tauend
integer ind
call dverk(EV,EV%ScalEqsToPropagate,derivs,tau,y,tauend,tol1,ind,c,EV%nvar,w)
if (ind==-3) then
call GlobalError('Dverk error -3: the subroutine was unable to satisfy the error ' &
//'requirement with a particular step-size that is less than or * ' &
//'equal to hmin, which may mean that tol is too small' &
//'--- but most likely you''ve messed up the y array indexing; ' &
//'compiling with bounds checking may (or may not) help find the problem.',error_evolution)
end if
end subroutine GaugeInterface_ScalEv
function f_K(x)
real(dl) :: f_K
real(dl), intent(in) :: x
f_K = State%curvature_radius*State%rofChi(x/State%curvature_radius)
end function f_K
function next_nu_nq(nq) result (next_nq)
integer, intent(in) :: nq
integer q, next_nq
if (nq==0) then
next_nq=1
else
q = int(State%NuPerturbations%nu_q(nq))
if (q>=10) then
next_nq = State%NuPerturbations%nqmax
else
next_nq = nq+1
end if
end if
end function next_nu_nq
recursive subroutine GaugeInterface_EvolveScal(EV,tau,y,tauend,tol1,ind,c,w)
use Recombination, only : CB1
type(EvolutionVars) EV, EVout
real(dl) c(24),w(EV%nvar,9), y(EV%nvar), yout(EV%nvar), tol1, tau, tauend
integer ind, nu_i
real(dl) cs2, opacity, dopacity
real(dl) tau_switch_ktau, tau_switch_nu_massless, tau_switch_nu_massive, next_switch
real(dl) tau_switch_no_nu_multpoles, tau_switch_no_phot_multpoles,tau_switch_nu_nonrel
real(dl) noSwitch, smallTime
!Sources
real(dl) tau_switch_saha, Delta_TM, xe,a,tau_switch_evolve_TM
noSwitch= State%tau0+1
smallTime = min(tau, 1/EV%k_buf)/100
tau_switch_ktau = noSwitch
tau_switch_no_nu_multpoles= noSwitch
tau_switch_no_phot_multpoles= noSwitch
!Massive neutrino switches
tau_switch_nu_massless = noSwitch
tau_switch_nu_nonrel = noSwitch
tau_switch_nu_massive= noSwitch
!Sources
tau_switch_saha=noSwitch
if (CP%Evolve_delta_xe .and. EV%saha) tau_switch_saha = EV%ThermoData%recombination_saha_tau
tau_switch_evolve_TM=noSwitch
if (EV%Evolve_baryon_cs .and. .not. EV%Evolve_tm) tau_switch_evolve_TM = EV%ThermoData%recombination_Tgas_tau
!Evolve equations from tau to tauend, performing switches in equations if necessary.
if (.not. EV%high_ktau_neutrino_approx .and. .not. EV%no_nu_multpoles ) then
tau_switch_ktau= max(20, EV%lmaxnr-4)/EV%k_buf
end if
if (CP%Num_Nu_massive /= 0) then
do nu_i = 1, CP%Nu_mass_eigenstates
if (EV%nq(nu_i) /= State%NuPerturbations%nqmax) then
tau_switch_nu_massless = min(tau_switch_nu_massless,nu_tau_notmassless(next_nu_nq(EV%nq(nu_i)),nu_i))
else if (.not. EV%nu_nonrelativistic(nu_i)) then
tau_switch_nu_nonrel = min(nu_tau_nonrelativistic(nu_i),tau_switch_nu_nonrel)
else if (EV%NuMethod==Nu_trunc .and..not. EV%MassiveNuApprox(nu_i)) then
tau_switch_nu_massive = min(tau_switch_nu_massive,EV%MassiveNuApproxTime(nu_i))
end if
end do
end if
if (CP%DoLateRadTruncation) then
if (.not. EV%no_nu_multpoles) & !!.and. .not. EV%has_nu_relativistic .and. tau_switch_nu_massless ==noSwitch) &
tau_switch_no_nu_multpoles= &
max(15/EV%k_buf*CP%Accuracy%AccuracyBoost,min(State%taurend,EV%ThermoData%matter_verydom_tau))
if (.not. EV%no_phot_multpoles .and. (.not.CP%WantCls .or. EV%k_buf>0.03*CP%Accuracy%AccuracyBoost)) &
tau_switch_no_phot_multpoles =max(15/EV%k_buf,State%taurend)*CP%Accuracy%AccuracyBoost
end if
next_switch = min(tau_switch_ktau, tau_switch_nu_massless,EV%TightSwitchoffTime, tau_switch_nu_massive, &
tau_switch_no_nu_multpoles, tau_switch_no_phot_multpoles, tau_switch_nu_nonrel, noSwitch, &
tau_switch_saha, tau_switch_evolve_TM)
if (next_switch < tauend) then
if (next_switch > tau+smallTime) then
call GaugeInterface_ScalEv(EV, y, tau,next_switch,tol1,ind,c,w)
if (global_error_flag/=0) return
end if
EVout=EV
if (next_switch == EV%TightSwitchoffTime) then
!TightCoupling
EVout%TightCoupling=.false.
EVout%TightSwitchoffTime = noSwitch
call SetupScalarArrayIndices(EVout)
call CopyScalarVariableArray(y,yout, EV, EVout)
EV=EVout
y=yout
ind=1
!Set up variables with their tight coupling values
y(EV%g_ix+2) = EV%pig
call EV%ThermoData%Values(tau,a, cs2,opacity,dopacity)
if (second_order_tightcoupling) then
! Francis-Yan Cyr-Racine November 2010
y(EV%g_ix+3) = (3._dl/7._dl)*y(EV%g_ix+2)*(EV%k_buf/opacity)*(1._dl+dopacity/opacity**2) + &
(3._dl/7._dl)*EV%pigdot*(EV%k_buf/opacity**2)*(-1._dl)
y(EV%polind+2) = EV%pig/4 + EV%pigdot*(1._dl/opacity)*(-5._dl/8._dl- &
(25._dl/16._dl)*dopacity/opacity**2) + &
EV%pig*(EV%k_buf/opacity)**2*(-5._dl/56._dl)
y(EV%polind+3) = (3._dl/7._dl)*(EV%k_buf/opacity)*y(EV%polind+2)*(1._dl + &
dopacity/opacity**2) + (3._dl/7._dl)*(EV%k_buf/opacity**2)*((EV%pigdot/4._dl)* &
(1._dl+(5._dl/2._dl)*dopacity/opacity**2))*(-1._dl)
else
y(EV%g_ix+3) = 3./7*y(EV%g_ix+2)*EV%k_buf/opacity
y(EV%polind+2) = EV%pig/4
y(EV%polind+3) =y(EV%g_ix+3)/4
end if
else if (next_switch==tau_switch_ktau) then
!k tau >> 1, evolve massless neutrino effective fluid up to l=2
EVout%high_ktau_neutrino_approx=.true.
EVout%nq(1:CP%Nu_mass_eigenstates) = State%NuPerturbations%nqmax
call SetupScalarArrayIndices(EVout)
call CopyScalarVariableArray(y,yout, EV, EVout)
y=yout
EV=EVout
else if (next_switch == tau_switch_nu_massless) then
!Mass starts to become important, start evolving next momentum mode
do nu_i = 1, CP%Nu_mass_eigenstates
if (EV%nq(nu_i) /= State%NuPerturbations%nqmax) then
if (next_switch == nu_tau_notmassless(next_nu_nq(EV%nq(nu_i)),nu_i)) then
EVOut%nq(nu_i) = next_nu_nq(EV%nq(nu_i))
call SetupScalarArrayIndices(EVout)
call CopyScalarVariableArray(y,yout, EV, EVout)
EV=EVout
y=yout
exit
endif
end if
end do
else if (next_switch == tau_switch_nu_nonrel) then
!Neutrino becomes non-relativistic, don't need high L
do nu_i = 1, CP%Nu_mass_eigenstates
if (.not. EV%nu_nonrelativistic(nu_i) .and. next_switch==nu_tau_nonrelativistic(nu_i) ) then
EVout%nu_nonrelativistic(nu_i)=.true.
call SetupScalarArrayIndices(EVout)
call CopyScalarVariableArray(y,yout, EV, EVout)
EV=EVout
y=yout
exit
end if
end do
else if (next_switch == tau_switch_nu_massive) then
!Very non-relativistic neutrinos, switch to truncated velocity-weight hierarchy
call EV%ThermoData%Values(tau,a, cs2,opacity)
do nu_i = 1, CP%Nu_mass_eigenstates
if (.not. EV%MassiveNuApprox(nu_i) .and. next_switch== EV%MassiveNuApproxTime(nu_i) ) then
call SwitchToMassiveNuApprox(EV, a, y, nu_i)
exit
end if
end do
else if (next_switch==tau_switch_no_nu_multpoles) then
!Turn off neutrino hierarchies at late time where slow and not needed.
ind=1
EVout%no_nu_multpoles=.true.
EVOut%nq(1:CP%Nu_mass_eigenstates ) = State%NuPerturbations%nqmax
call SetupScalarArrayIndices(EVout)
call CopyScalarVariableArray(y,yout, EV, EVout)
y=yout
EV=EVout
else if (next_switch==tau_switch_no_phot_multpoles) then
!Turn off photon hierarchies at late time where slow and not needed.
ind=1
EVout%no_phot_multpoles=.true.
call SetupScalarArrayIndices(EVout)
call CopyScalarVariableArray(y,yout, EV, EVout)
y=yout
EV=EVout
else if (next_switch==tau_switch_saha) then
!Sources
ind=1
EVout%saha = .false.
call SetupScalarArrayIndices(EVout)
call CopyScalarVariableArray(y,yout, EV, EVout)
call EV%ThermoData%Values(tau,a, cs2,opacity)
y=yout
EV=EVout
Delta_Tm = y(EV%g_ix)/4 ! assume delta_TM = delta_T_gamma
xe= CP%Recomb%x_e(a)
y(EV%xe_ix) = (1-xe)/(2-xe)*(-y(ix_clxb) + (3./2+ CB1/(CP%TCMB/a))*Delta_TM)
else if (next_switch==tau_switch_evolve_TM) then
!Sources
ind=1
EVout%evolve_TM = .true.
call SetupScalarArrayIndices(EVout)
call CopyScalarVariableArray(y,yout, EV, EVout)
y=yout
EV=EVout
y(EV%Tg_ix) =y(EV%g_ix)/4 ! assume delta_TM = delta_T_gamma
end if
call GaugeInterface_EvolveScal(EV,tau,y,tauend,tol1,ind,c,w)
return
end if
call GaugeInterface_ScalEv(EV,y,tau,tauend,tol1,ind,c,w)
end subroutine GaugeInterface_EvolveScal
subroutine GaugeInterface_EvolveTens(EV,tau,y,tauend,tol1,ind,c,w)
type(EvolutionVars) EV, EVOut
real(dl) c(24),w(EV%nvart,9), y(EV%nvart),yout(EV%nvart), tol1, tau, tauend
integer ind
real(dl) opacity, cs2, a
if (EV%TensTightCoupling .and. tauend > EV%TightSwitchoffTime) then
if (EV%TightSwitchoffTime > tau) then
call dverk(EV,EV%TensEqsToPropagate, derivst,tau,y,EV%TightSwitchoffTime,tol1,ind,c,EV%nvart,w)
end if
EVOut=EV
EVOut%TensTightCoupling = .false.
call SetupTensorArrayIndices(EVout)
call CopyTensorVariableArray(y,yout,Ev, Evout)
Ev = EvOut
y=yout
call EV%ThermoData%Values(tau,a,cs2,opacity)
y(EV%g_ix+2)= 32._dl/45._dl*EV%k_buf/opacity*y(ixt_shear)
y(EV%E_ix+2) = y(EV%g_ix+2)/4
end if
call dverk(EV,EV%TensEqsToPropagate, derivst,tau,y,tauend,tol1,ind,c,EV%nvart,w)
end subroutine GaugeInterface_EvolveTens
function DeltaTimeMaxed(a1,a2, tol) result(t)
real(dl) a1,a2,t
real(dl), optional :: tol
if (a1>1._dl) then
t=0
elseif (a2 > 1._dl) then
t = State%DeltaTime(a1,1.01_dl, tol)
else
t = State%DeltaTime(a1,a2, tol)
end if
end function DeltaTimeMaxed
subroutine GaugeInterface_Init
!Precompute various arrays and other things independent of wavenumber
integer j, nu_i
real(dl) a_nonrel, a_mass,a_massive, time, nu_mass
epsw = 100/State%tau0
if (CP%WantScalars) then
do j=2,max_l_evolve
polfac(j)=real((j+3)*(j-1),dl)/(j+1)
end do
end if
if (CP%WantVectors) then
do j=2,max_l_evolve
vecfac(j)=real((j+2),dl)/(j+1)
vecfacpol(j)=real((j+3)*j,dl)*(j-1)*vecfac(j)/(j+1)**2
end do
end if
do j=1,max_l_evolve
denl(j)=1._dl/(2*j+1)
end do
if (CP%Nu_Mass_eigenstates>0) then
associate(nqmax => State%NuPerturbations%nqmax, nu_q => State%NuPerturbations%nu_q)
if (allocated(nu_tau_notmassless)) deallocate(nu_tau_notmassless)
allocate(nu_tau_notmassless(nqmax,max_nu))
do nu_i=1, CP%Nu_Mass_eigenstates
nu_mass = max(0.1_dl,State%nu_masses(nu_i))
a_mass = 1.e-1_dl/nu_mass/CP%Accuracy%lAccuracyBoost
time=State%DeltaTime(0._dl,State%NuPerturbations%nu_q(1)*a_mass)
nu_tau_notmassless(1, nu_i) = time
do j=2,nqmax
!times when each momentum mode becomes signficantly nonrelativistic
time= time + DeltaTimeMaxed(nu_q(j-1)*a_mass,nu_q(j)*a_mass, 0.01_dl)
nu_tau_notmassless(j, nu_i) = time
end do
a_nonrel = 2.5d0/nu_mass*CP%Accuracy%AccuracyBoost
nu_tau_nonrelativistic(nu_i) =DeltaTimeMaxed(0._dl,a_nonrel)
a_massive = 17.d0/nu_mass*CP%Accuracy%AccuracyBoost
nu_tau_massive(nu_i) =nu_tau_nonrelativistic(nu_i) + DeltaTimeMaxed(a_nonrel,a_massive)
end do
end associate
end if
end subroutine GaugeInterface_Init
subroutine SetupScalarArrayIndices(EV, max_num_eqns)
!Set up array indices after the lmax have been decided
use MassiveNu
!Set the numer of equations in each hierarchy, and get total number of equations for this k
type(EvolutionVars) EV
integer, intent(out), optional :: max_num_eqns
integer neq, maxeq, nu_i
neq=basic_num_eqns
maxeq=neq
if (.not. EV%no_phot_multpoles) then
!Photon multipoles
EV%g_ix=basic_num_eqns+1
if (EV%TightCoupling) then
neq=neq+2
else
neq = neq+ (EV%lmaxg+1)
!Polarization multipoles
EV%polind = neq -1 !polind+2 is L=2, for polarizationthe first calculated
neq=neq + EV%lmaxgpol-1
end if
end if
if (.not. EV%no_nu_multpoles) then
!Massless neutrino multipoles
EV%r_ix= neq+1
if (EV%high_ktau_neutrino_approx) then
neq=neq + 3
else
neq=neq + (EV%lmaxnr+1)
end if
end if
maxeq = maxeq + (EV%lmaxg+1)+(EV%lmaxnr+1)+EV%lmaxgpol-1
!Dark energy
if (.not. CP%DarkEnergy%is_cosmological_constant) then
EV%w_ix = neq + 1
neq = neq + CP%DarkEnergy%num_perturb_equations
maxeq = maxeq + CP%DarkEnergy%num_perturb_equations
else
EV%w_ix = 0
end if
!Sources
if (CP%Evolve_delta_xe) then
if (.not. EV%saha) then
EV%xe_ix = neq+1
neq=neq+1
end if
maxeq=maxeq+1
end if
if (EV%Evolve_baryon_cs) then
if (EV%Evolve_TM) then
EV%Tg_ix = neq+1
neq=neq+1
end if
maxeq=maxeq+1
if (CP%Do21cm .and. CP%SourceTerms%line_reionization) then
EV%reion_line_ix = neq+1
neq=neq+ EV%lmaxline+1 + EV%lmaxline-1
maxeq=maxeq+EV%lmaxline+1 + EV%lmaxline-1
end if
end if
if (CP%Evolve_delta_Ts) then
EV%Ts_ix = neq+1
neq=neq+1
maxeq=maxeq+1
end if
!Massive neutrinos
if (CP%Num_Nu_massive /= 0) then
EV%has_nu_relativistic = any(EV%nq(1:CP%Nu_Mass_eigenstates)/=State%NuPerturbations%nqmax)
if (EV%has_nu_relativistic) then
EV%lmaxnu_pert=EV%lmaxnu
EV%nu_pert_ix=neq+1
neq = neq+ EV%lmaxnu_pert+1
maxeq=maxeq+ EV%lmaxnu_pert+1
else
EV%lmaxnu_pert=0
end if
do nu_i=1, CP%Nu_Mass_eigenstates
if (EV%high_ktau_neutrino_approx) then
EV%lmaxnu_tau(nu_i) = int(lmaxnu_high_ktau *CP%Accuracy%lAccuracyBoost)
if (CP%Transfer%accurate_massive_neutrinos) EV%lmaxnu_tau(nu_i) = EV%lmaxnu_tau(nu_i) *3
else
EV%lmaxnu_tau(nu_i) =max(min(nint(0.8_dl*EV%q*nu_tau_nonrelativistic(nu_i) &
*CP%Accuracy%lAccuracyBoost),EV%lmaxnu),3)
!!!Feb13tweak
if (EV%nu_nonrelativistic(nu_i)) EV%lmaxnu_tau(nu_i)= &
min(EV%lmaxnu_tau(nu_i),nint(4*CP%Accuracy%lAccuracyBoost))
end if
if (State%nu_masses(nu_i) > 5000 .and. CP%Transfer%high_precision) &
EV%lmaxnu_tau(nu_i) = EV%lmaxnu_tau(nu_i)*2 !megadamping
EV%lmaxnu_tau(nu_i)=min(EV%lmaxnu,EV%lmaxnu_tau(nu_i))
EV%nu_ix(nu_i)=neq+1
if (EV%MassiveNuApprox(nu_i)) then
neq = neq+4
else
neq = neq+ EV%nq(nu_i)*(EV%lmaxnu_tau(nu_i)+1)
endif
maxeq = maxeq + State%NuPerturbations%nqmax*(EV%lmaxnu+1)
end do
else
EV%has_nu_relativistic = .false.
end if
EV%ScalEqsToPropagate = neq
if (present(max_num_eqns)) then
max_num_eqns=maxeq
end if
end subroutine SetupScalarArrayIndices
subroutine CopyScalarVariableArray(y,yout, EV, EVout)
type(EvolutionVars) EV, EVOut
real(dl), intent(in) :: y(EV%nvar)
real(dl), intent(out) :: yout(EVout%nvar)
integer lmax,i, nq
integer nnueq,nu_i, ix_off, ix_off2, ind, ind2
real(dl) q, pert_scale
yout=0
yout(1:basic_num_eqns) = y(1:basic_num_eqns)
! DarkEnergy
if (CP%DarkEnergy%num_perturb_equations > 0) &
yout(EVOut%w_ix:EVOut%w_ix + CP%DarkEnergy%num_perturb_equations - 1) = &
y(EV%w_ix:EV%w_ix + CP%DarkEnergy%num_perturb_equations - 1)
if (.not. EV%no_phot_multpoles .and. .not. EVout%no_phot_multpoles) then
if (EV%TightCoupling .or. EVOut%TightCoupling) then
lmax=1
else
lmax = min(EV%lmaxg,EVout%lmaxg)
end if
yout(EVout%g_ix:EVout%g_ix+lmax)=y(EV%g_ix:EV%g_ix+lmax)
if (.not. EV%TightCoupling .and. .not. EVOut%TightCoupling) then
lmax = min(EV%lmaxgpol,EVout%lmaxgpol)
yout(EVout%polind+2:EVout%polind+lmax)=y(EV%polind+2:EV%polind+lmax)
end if
end if
if (.not. EV%no_nu_multpoles .and. .not. EVout%no_nu_multpoles) then
if (EV%high_ktau_neutrino_approx .or. EVout%high_ktau_neutrino_approx) then
lmax=2
else
lmax = min(EV%lmaxnr,EVout%lmaxnr)
end if
yout(EVout%r_ix:EVout%r_ix+lmax)=y(EV%r_ix:EV%r_ix+lmax)
end if
if (CP%Num_Nu_massive /= 0) then
do nu_i=1,CP%Nu_mass_eigenstates
ix_off=EV%nu_ix(nu_i)
ix_off2=EVOut%nu_ix(nu_i)
if (EV%MassiveNuApprox(nu_i) .and. EVout%MassiveNuApprox(nu_i)) then
nnueq=4
yout(ix_off2:ix_off2+nnueq-1)=y(ix_off:ix_off+nnueq-1)
else if (.not. EV%MassiveNuApprox(nu_i) .and. .not. EVout%MassiveNuApprox(nu_i)) then
lmax=min(EV%lmaxnu_tau(nu_i),EVOut%lmaxnu_tau(nu_i))
nq = min(EV%nq(nu_i), EVOut%nq(nu_i))
do i=1,nq
ind= ix_off + (i-1)*(EV%lmaxnu_tau(nu_i)+1)
ind2=ix_off2+ (i-1)*(EVOut%lmaxnu_tau(nu_i)+1)
yout(ind2:ind2+lmax) = y(ind:ind+lmax)
end do
do i=nq+1, EVOut%nq(nu_i)
lmax = min(EVOut%lmaxnu_tau(nu_i), EV%lmaxnr)
ind2=ix_off2+ (i-1)*(EVOut%lmaxnu_tau(nu_i)+1)
yout(ind2:ind2+lmax) = y(EV%r_ix:EV%r_ix+lmax)
!Add leading correction for the mass
q=State%NuPerturbations%nu_q(i)
pert_scale=(State%nu_masses(nu_i)/q)**2/2
lmax = min(lmax,EV%lmaxnu_pert)
yout(ind2:ind2+lmax) = yout(ind2:ind2+lmax) &
+ y(EV%nu_pert_ix:EV%nu_pert_ix+lmax)*pert_scale
end do
end if
end do
if (EVOut%has_nu_relativistic .and. EV%has_nu_relativistic) then
lmax = min(EVOut%lmaxnu_pert, EV%lmaxnu_pert)
yout(EVout%nu_pert_ix:EVout%nu_pert_ix+lmax)= y(EV%nu_pert_ix:EV%nu_pert_ix+lmax)
end if
end if
!Sources
if (.not. EV%saha .and. .not. EVOut%saha) then
yout(EVOut%xe_ix) =y(EV%xe_ix)
end if
if (EV%Evolve_baryon_cs) then
if (EV%Evolve_TM .and. EVout%Evolve_TM) yout(EVOut%Tg_ix) = y(EV%Tg_ix)
if (CP%Do21cm .and. CP%SourceTerms%line_reionization) then
yout(EVOut%reion_line_ix:EVOut%reion_line_ix+EVout%lmaxline + EVout%lmaxline-1) = &
y(EV%reion_line_ix:EV%reion_line_ix+EV%lmaxline + EV%lmaxline-1)
end if
end if
if (CP%Evolve_delta_Ts) then
yout(EVOut%Ts_ix) = y(EV%Ts_ix)
end if
end subroutine CopyScalarVariableArray
subroutine SetupTensorArrayIndices(EV, maxeq)
type(EvolutionVars) EV
integer nu_i, neq
integer, optional, intent(out) :: maxeq
neq=2
EV%g_ix = neq-1 !EV%g_ix+2 is quadrupole
if (.not. EV%TensTightCoupling) then
EV%E_ix = EV%g_ix + (EV%lmaxt-1)
EV%B_ix = EV%E_ix + (EV%lmaxpolt-1)
neq = neq+ (EV%lmaxt-1)+(EV%lmaxpolt-1)*2
end if
if (present(maxeq)) then
maxeq = 2 + (EV%lmaxt-1)+(EV%lmaxpolt-1)*2
end if
EV%r_ix = neq -1
if (DoTensorNeutrinos) then
neq = neq + EV%lmaxnrt-1
if (present(maxeq)) maxeq = maxeq+EV%lmaxnrt-1
if (CP%Num_Nu_massive /= 0 ) then
do nu_i=1, CP%nu_mass_eigenstates
EV%EvolveTensorMassiveNu(nu_i) = &
nu_tau_nonrelativistic(nu_i) < 0.8*State%tau_maxvis*CP%Accuracy%AccuracyBoost
if (EV%EvolveTensorMassiveNu(nu_i)) then
EV%nu_ix(nu_i)=neq-1
neq = neq+ State%NuPerturbations%nqmax*(EV%lmaxnut-1)
if (present(maxeq)) maxeq = maxeq + State%NuPerturbations%nqmax*(EV%lmaxnut-1)
end if
end do
end if
end if
EV%TensEqsToPropagate = neq
end subroutine SetupTensorArrayIndices
subroutine CopyTensorVariableArray(y,yout, EV, EVout)
type(EvolutionVars) EV, EVOut
real(dl), intent(in) :: y(EV%nvart)
real(dl), intent(out) :: yout(EVout%nvart)
integer lmaxpolt, lmaxt, nu_i, ind, ind2, i
yout=0
yout(1:2) = y(1:2)
if (.not. EVOut%TensTightCoupling .and. .not.EV%TensTightCoupling) then
lmaxt = min(EVOut%lmaxt,EV%lmaxt)
yout(EVout%g_ix+2:EVout%g_ix+lmaxt)=y(EV%g_ix+2:EV%g_ix+lmaxt)
lmaxpolt = min(EV%lmaxpolt, EVOut%lmaxpolt)
yout(EVout%E_ix+2:EVout%E_ix+lmaxpolt)=y(EV%E_ix+2:EV%E_ix+lmaxpolt)
yout(EVout%B_ix+2:EVout%B_ix+lmaxpolt)=y(EV%B_ix+2:EV%B_ix+lmaxpolt)
end if
if (DoTensorNeutrinos) then
lmaxt=min(EV%lmaxnrt,EVOut%lmaxnrt)
yout(EVout%r_ix+2:EVout%r_ix+lmaxt)=y(EV%r_ix+2:EV%r_ix+lmaxt)
do nu_i =1, CP%nu_mass_eigenstates
if (EV%EvolveTensorMassiveNu(nu_i)) then
lmaxt=min(EV%lmaxnut,EVOut%lmaxnut)
do i=1,State%NuPerturbations%nqmax
ind= EV%nu_ix(nu_i) + (i-1)*(EV%lmaxnut-1)
ind2=EVOut%nu_ix(nu_i)+ (i-1)*(EVOut%lmaxnut-1)
yout(ind2+2:ind2+lmaxt) = y(ind+2:ind+lmaxt)
end do
end if
end do
end if
end subroutine CopyTensorVariableArray
subroutine GetNumEqns(EV)
use MassiveNu
!Set the numer of equations in each hierarchy, and get total number of equations for this k
type(EvolutionVars) EV
real(dl) scal, max_nu_mass
integer nu_i,q_rel,j
if (CP%Num_Nu_massive == 0) then
EV%lmaxnu=0
max_nu_mass=0
else
max_nu_mass = maxval(State%nu_masses(1:CP%Nu_mass_eigenstates))
do nu_i = 1, CP%Nu_mass_eigenstates
!Start with momentum modes for which t_k ~ time at which mode becomes non-relativistic
q_rel=0
do j=1, State%NuPerturbations%nqmax
!two different q's here EV%q ~k
if (State%NuPerturbations%nu_q(j) > State%nu_masses(nu_i)*State%adotrad/EV%q) exit
q_rel = q_rel + 1
end do
if (q_rel>= State%NuPerturbations%nqmax-2 .or. CP%WantTensors) then
EV%nq(nu_i)=State%NuPerturbations%nqmax
else
EV%nq(nu_i)=q_rel
end if
!q_rel = nint(nu_masses(nu_i)*adotrad/EV%q) !two dffierent q's here EV%q ~k
!EV%nq(nu_i)=max(0,min(nqmax0,q_rel)) !number of momentum modes to evolve intitially
EV%nu_nonrelativistic(nu_i) = .false.
end do
EV%NuMethod = CP%MassiveNuMethod
if (EV%NuMethod == Nu_Best) EV%NuMethod = Nu_Trunc
!l_max for massive neutrinos
if (CP%Transfer%high_precision) then
EV%lmaxnu=nint(25*CP%Accuracy%lAccuracyBoost)
else
EV%lmaxnu=max(3,nint(10*CP%Accuracy%lAccuracyBoost))
if (max_nu_mass>700) EV%lmaxnu=max(3,nint(15*CP%Accuracy%lAccuracyBoost)) !Feb13 tweak
endif
end if
if (State%closed) then
EV%FirstZerolForBeta = nint(EV%q*State%curvature_radius)
else
EV%FirstZerolForBeta= 100000 !a large number
end if
EV%high_ktau_neutrino_approx = .false.
if (CP%WantScalars) then
EV%TightCoupling=.true.
EV%no_phot_multpoles =.false.
EV%no_nu_multpoles =.false.
EV%MassiveNuApprox=.false.
!Sources
EV%saha = .true.
EV%Evolve_TM = .false.
if (CP%Accuracy%AccuratePolarization) then
EV%lmaxg = max(nint(11*CP%Accuracy%lAccuracyBoost),3)
else
EV%lmaxg = max(nint(8*CP%Accuracy%lAccuracyBoost),3)
end if
EV%lmaxnr = max(nint(14*CP%Accuracy%lAccuracyBoost),3)
if (max_nu_mass>700) EV%lmaxnr = max(nint(32*CP%Accuracy%lAccuracyBoost),3) !Feb13 tweak
EV%lmaxgpol = EV%lmaxg
if (.not.CP%Accuracy%AccuratePolarization) EV%lmaxgpol=max(nint(4*CP%Accuracy%lAccuracyBoost),3)
if (EV%q < 0.05) then
!Large scales need fewer equations
scal = 1
if (CP%Accuracy%AccuratePolarization) scal = 4 !But need more to get polarization right
EV%lmaxgpol=max(3,nint(min(8,nint(scal* 150* EV%q))*CP%Accuracy%lAccuracyBoost))
EV%lmaxnr=max(3,nint(min(7,nint(sqrt(scal)* 150 * EV%q))*CP%Accuracy%lAccuracyBoost))
if (EV%lmaxnr < EV%lmaxnu) then
! Nov 2020 change following Pavel Motloch report
EV%lmaxnr = EV%lmaxnu
!EV%lmaxnu = min(EV%lmaxnu, EV%lmaxnr) ! may be better but have not tested and makes small result changes
endif
EV%lmaxg=max(3,nint(min(8,nint(sqrt(scal) *300 * EV%q))*CP%Accuracy%lAccuracyBoost))
!Sources
if (CP%SourceTerms%line_phot_quadrupole) then
EV%lmaxg=EV%lmaxg*8
EV%lmaxgpol=EV%lmaxgpol*4
elseif (CP%Accuracy%AccurateReionization) then
EV%lmaxg=EV%lmaxg*4
EV%lmaxgpol=EV%lmaxgpol*2
end if
end if
if (EV%TransferOnly) then
EV%lmaxgpol = min(EV%lmaxgpol,nint(5*CP%Accuracy%lAccuracyBoost))
EV%lmaxg = min(EV%lmaxg,nint(6*CP%Accuracy%lAccuracyBoost))
end if
if (CP%Transfer%high_precision .or. CP%Do21cm) then
EV%lmaxnr=max(nint(45*CP%Accuracy%lAccuracyBoost),3)
if (EV%q > 0.04 .and. EV%q < 0.5) then !baryon oscillation scales
EV%lmaxg=max(EV%lmaxg,10)
end if
end if
if (CP%Do21cm .and. CP%SourceTerms%line_reionization) then
EV%lmaxg = EV%lmaxg*8
EV%lmaxgpol = EV%lmaxgpol*3
end if
EV%Evolve_baryon_cs = CP%Do21cm .or.CP%Evolve_delta_xe .or. CP%Evolve_delta_Ts
if (CP%Do21cm .and. CP%SourceTerms%line_reionization) then
EV%lmaxline = EV%lmaxg
end if
if (State%closed) then
EV%lmaxnu=min(EV%lmaxnu, EV%FirstZerolForBeta-1)
EV%lmaxnr=min(EV%lmaxnr, EV%FirstZerolForBeta-1)
EV%lmaxg=min(EV%lmaxg, EV%FirstZerolForBeta-1)
EV%lmaxgpol=min(EV%lmaxgpol, EV%FirstZerolForBeta-1)
end if
EV%poltruncfac=real(EV%lmaxgpol,dl)/max(1,(EV%lmaxgpol-2))
EV%MaxlNeeded=max(EV%lmaxg,EV%lmaxnr,EV%lmaxgpol,EV%lmaxnu)
if (EV%MaxlNeeded > max_l_evolve) call MpiStop('Need to increase max_l_evolve')
call SetupScalarArrayIndices(EV,EV%nvar)
if (State%closed) EV%nvar=EV%nvar+1 !so can reference lmax+1 with zero coefficient
EV%lmaxt=0
else
EV%nvar=0
end if
if (CP%WantTensors) then
EV%TensTightCoupling = .true.
EV%lmaxt=max(3,nint(8*CP%Accuracy%lAccuracyBoost))
EV%lmaxpolt = max(3,nint(4*CP%Accuracy%lAccuracyBoost))
! if (EV%q < 1e-3) EV%lmaxpolt=EV%lmaxpolt+1
if (DoTensorNeutrinos) then
EV%lmaxnrt=nint(6*CP%Accuracy%lAccuracyBoost)
EV%lmaxnut=EV%lmaxnrt
else
EV%lmaxnut=0
EV%lmaxnrt=0
end if
if (State%closed) then
EV%lmaxt=min(EV%FirstZerolForBeta-1,EV%lmaxt)
EV%lmaxpolt=min(EV%FirstZerolForBeta-1,EV%lmaxpolt)
EV%lmaxnrt=min(EV%FirstZerolForBeta-1,EV%lmaxnrt)
EV%lmaxnut=min(EV%FirstZerolForBeta-1,EV%lmaxnut)
end if
EV%MaxlNeededt=max(EV%lmaxpolt,EV%lmaxt, EV%lmaxnrt, EV%lmaxnut)
if (EV%MaxlNeededt > max_l_evolve) call MpiStop('Need to increase max_l_evolve')
call SetupTensorArrayIndices(EV, EV%nvart)
else
EV%nvart=0
end if
if (CP%WantVectors) then
EV%lmaxv=max(10,nint(8*CP%Accuracy%lAccuracyBoost))
EV%lmaxpolv = max(5,nint(5*CP%Accuracy%lAccuracyBoost))
EV%nvarv=(EV%lmaxv)+(EV%lmaxpolv-1)*2+3
EV%lmaxnrv=nint(30*CP%Accuracy%lAccuracyBoost)
EV%nvarv=EV%nvarv+EV%lmaxnrv
if (CP%Num_Nu_massive /= 0 ) then
call MpiStop('massive neutrinos not supported for vector modes')
end if
else
EV%nvarv=0
end if
end subroutine GetNumEqns
subroutine SwitchToMassiveNuApprox(EV,a, y, nu_i)
!When the neutrinos are no longer highly relativistic we use a truncated
!energy-integrated hierarchy going up to third order in velocity dispersion
type(EvolutionVars) EV, EVout
integer, intent(in) :: nu_i
real(dl) a,a2,pnu,clxnu,dpnu,pinu,rhonu
real(dl) qnu
real(dl) y(EV%nvar), yout(EV%nvar)
a2=a*a
EVout=EV
EVout%MassiveNuApprox(nu_i)=.true.
call SetupScalarArrayIndices(EVout)
call CopyScalarVariableArray(y,yout, EV, EVout)
!Get density and pressure as ratio to massles by interpolation from table
call ThermalNuBack%rho_P(a*State%nu_masses(nu_i),rhonu,pnu)
!Integrate over q
call Nu_Integrate_L012(EV, y, a, nu_i, clxnu,qnu,dpnu,pinu)
!clxnu_here = rhonu*clxnu, qnu_here = qnu*rhonu
dpnu=dpnu/rhonu
qnu=qnu/rhonu
clxnu = clxnu/rhonu
pinu=pinu/rhonu
yout(EVout%nu_ix(nu_i))=clxnu
yout(EVout%nu_ix(nu_i)+1)=dpnu
yout(EVout%nu_ix(nu_i)+2)=qnu
yout(EVout%nu_ix(nu_i)+3)=pinu