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equations.f90
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equations.f90
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! Equations module for dark energy with constant equation of state parameter w
! allowing for perturbations based on a quintessence model
! by Antony Lewis (http://cosmologist.info/)
! Dec 2003, fixed (fatal) bug in tensor neutrino setup
! Changes to tight coupling approximation
! June 2004, fixed problem with large scale polarized tensors; support for vector modes
! Generate vector modes on their own. The power spectrum is taken from the scalar parameters.
! August 2004, fixed reionization term in lensing potential
! Nov 2004, change massive neutrino l_max to be consistent with massless if light
! Apr 2005, added DoLateRadTruncation option
! June 2006, added support for arbitary neutrino mass splittings
! Nov 2006, tweak to high_precision transfer function accuracy at lowish k
! June 2011, improved radiation approximations from arXiv: 1104.2933; Some 2nd order tight coupling terms
! merged fderivs and derivs so flat and non-flat use same equations; more precomputed arrays
! optimized neutrino sampling, and reorganised neutrino integration functions
! Feb 2013: fixed various issues with accuracy at larger neutrino masses
! Mar 2014: fixes for tensors with massive neutrinos
module LambdaGeneral
use precision
implicit none
real(dl) :: w_lam = -1_dl !p/rho for the dark energy (assumed constant)
real(dl) :: cs2_lam = 1_dl
!comoving sound speed. Always exactly 1 for quintessence
!(otherwise assumed constant, though this is almost certainly unrealistic)
real(dl), parameter :: wa_ppf = 0._dl !Not used here, just for compatibility with e.g. halofit
logical :: w_perturb = .true.
!If you are tempted to set this = .false. read
! http://cosmocoffee.info/viewtopic.php?t=811
! http://cosmocoffee.info/viewtopic.php?t=512
contains
subroutine DarkEnergy_ReadParams(Ini)
use IniFile
Type(TIniFile) :: Ini
w_lam = Ini_Read_Double_File(Ini,'w', -1.d0)
cs2_lam = Ini_Read_Double_File(Ini,'cs2_lam',1.d0)
end subroutine DarkEnergy_ReadParams
end module LambdaGeneral
!Return OmegaK - modify this if you add extra fluid components
function GetOmegak()
use precision
use ModelParams
real(dl) GetOmegak
GetOmegak = 1 - (CP%omegab+CP%omegac+CP%omegav+CP%omegan)
end function GetOmegak
subroutine init_background
!This is only called once per model, and is a good point to do any extra initialization.
!It is called before first call to dtauda, but after
!massive neutrinos are initialized and after GetOmegak
end subroutine init_background
!Background evolution
function dtauda(a)
!get d tau / d a
use precision
use ModelParams
use MassiveNu
use LambdaGeneral
implicit none
real(dl) dtauda
real(dl), intent(IN) :: a
real(dl) rhonu,grhoa2, a2
integer nu_i
a2=a**2
! 8*pi*G*rho*a**4.
grhoa2=grhok*a2+(grhoc+grhob)*a+grhog+grhornomass
if (w_lam == -1._dl) then
grhoa2=grhoa2+grhov*a2**2
else
grhoa2=grhoa2+grhov*a**(1-3*w_lam)
end if
if (CP%Num_Nu_massive /= 0) then
!Get massive neutrino density relative to massless
do nu_i = 1, CP%nu_mass_eigenstates
call Nu_rho(a*nu_masses(nu_i),rhonu)
grhoa2=grhoa2+rhonu*grhormass(nu_i)
end do
end if
dtauda=sqrt(3/grhoa2)
end function dtauda
!cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
!Gauge-dependent perturbation equations
module GaugeInterface
use precision
use ModelParams
use MassiveNu
use LambdaGeneral
use Errors
use Transfer
implicit none
public
!Description of this file. Change if you make modifications.
character(LEN=*), parameter :: Eqns_name = 'gauge_inv'
integer, parameter :: basic_num_eqns = 5
logical :: DoTensorNeutrinos = .true.
logical :: DoLateRadTruncation = .true.
!if true, use smooth approx to radition perturbations after decoupling on
!small scales, saving evolution of irrelevant osciallatory multipole equations
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
integer w_ix !Index of two quintessence equations
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 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 !For tight coupling
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 polarization indices
real(dl) denlkt(4,max_l_evolve),Kft(max_l_evolve)
real, pointer :: OutputTransfer(:) => null()
end type EvolutionVars
!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) nu_tau_notmassless(nqmax0+1,max_nu), nu_tau_nonrelativistic(max_nu),nu_tau_massive(max_nu)
contains
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 next_nu_nq(nq) result (next_nq)
integer, intent(in) :: nq
integer q, next_nq
if (nq==0) then
next_nq=1
else
q = nu_q(nq)
if (q>=10) then
next_nq = 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 ThermoData
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
noSwitch= CP%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
!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) /= 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 (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*AccuracyBoost,min(taurend,matter_verydom_tau))
if (.not. EV%no_phot_multpoles .and. (.not.CP%WantCls .or. EV%k_buf>0.03*AccuracyBoost)) &
tau_switch_no_phot_multpoles =max(15/EV%k_buf,taurend)*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)
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 thermo(tau,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.
EV%nq(1:CP%Nu_mass_eigenstates) = 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) /= nqmax .and. &
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
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
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,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 ) = 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
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)
use ThermoData
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
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 thermo(tau,cs2,opacity)
y(EV%g_ix+2)= 32._dl/45._dl*EV%k_buf/opacity*y(3)
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 = DeltaTime(a1,1.01_dl, tol)
else
t= 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/CP%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
do nu_i=1, CP%Nu_Mass_eigenstates
nu_mass = max(0.1_dl,nu_masses(nu_i))
a_mass = 1.e-1_dl/nu_mass/lAccuracyBoost
!if (HighAccuracyDefault) a_mass=a_mass/4
time=DeltaTime(0._dl,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*AccuracyBoost !!!Feb13tweak
nu_tau_nonrelativistic(nu_i) =DeltaTimeMaxed(0._dl,a_nonrel)
a_massive = 17.d0/nu_mass*AccuracyBoost
nu_tau_massive(nu_i) =nu_tau_nonrelativistic(nu_i) + DeltaTimeMaxed(a_nonrel,a_massive)
end do
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 (w_lam /= -1 .and. w_Perturb) then
EV%w_ix = neq+1
neq=neq+2
maxeq=maxeq+2
else
EV%w_ix=0
end if
!Massive neutrinos
if (CP%Num_Nu_massive /= 0) then
EV%has_nu_relativistic = any(EV%nq(1:CP%Nu_Mass_eigenstates)/=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) = lmaxnu_high_ktau *lAccuracyBoost
else
EV%lmaxnu_tau(nu_i) =max(min(nint(0.8_dl*EV%q*nu_tau_nonrelativistic(nu_i)*lAccuracyBoost),EV%lmaxnu),3)
!!!Feb13tweak
if (EV%nu_nonrelativistic(nu_i)) EV%lmaxnu_tau(nu_i)=min(EV%lmaxnu_tau(nu_i),nint(4*lAccuracyBoost))
end if
if (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 + 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)
if (w_lam /= -1 .and. w_Perturb) then
yout(EVout%w_ix)=y(EV%w_ix)
yout(EVout%w_ix+1)=y(EV%w_ix+1)
end if
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=nu_q(i)
pert_scale=(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
end subroutine CopyScalarVariableArray
subroutine SetupTensorArrayIndices(EV, maxeq)
type(EvolutionVars) EV
integer nu_i, neq
integer, optional, intent(out) :: maxeq
neq=3
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 =3 + (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*tau_maxvis*AccuracyBoost
if (EV%EvolveTensorMassiveNu(nu_i)) then
EV%nu_ix(nu_i)=neq-1
neq = neq+ nqmax*(EV%lmaxnut-1)
if (present(maxeq)) maxeq = maxeq + 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(1:3) = y(1:3)
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,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(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, nqmax
!two different q's here EV%q ~k
if (nu_q(j) > nu_masses(nu_i)*adotrad/EV%q) exit
q_rel = q_rel + 1
end do
if (q_rel>= nqmax-2 .or. CP%WantTensors) then
EV%nq(nu_i)=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*lAccuracyBoost)
else
EV%lmaxnu=max(3,nint(10*lAccuracyBoost))
if (max_nu_mass>700) EV%lmaxnu=max(3,nint(15*lAccuracyBoost)) !Feb13 tweak
endif
end if
if (CP%closed) then
EV%FirstZerolForBeta = nint(EV%q*CP%r)
else
EV%FirstZerolForBeta=l0max !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.
if (HighAccuracyDefault .and. CP%AccuratePolarization) then
EV%lmaxg = max(nint(11*lAccuracyBoost),3)
else
EV%lmaxg = max(nint(8*lAccuracyBoost),3)
end if
EV%lmaxnr = max(nint(14*lAccuracyBoost),3)
if (max_nu_mass>700 .and. HighAccuracyDefault) EV%lmaxnr = max(nint(32*lAccuracyBoost),3) !Feb13 tweak
EV%lmaxgpol = EV%lmaxg
if (.not.CP%AccuratePolarization) EV%lmaxgpol=max(nint(4*lAccuracyBoost),3)
if (EV%q < 0.05) then
!Large scales need fewer equations
scal = 1
if (CP%AccuratePolarization) scal = 4 !But need more to get polarization right
EV%lmaxgpol=max(3,nint(min(8,nint(scal* 150* EV%q))*lAccuracyBoost))
EV%lmaxnr=max(3,nint(min(7,nint(sqrt(scal)* 150 * EV%q))*lAccuracyBoost))
EV%lmaxg=max(3,nint(min(8,nint(sqrt(scal) *300 * EV%q))*lAccuracyBoost))
if (CP%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*lAccuracyBoost))
EV%lmaxg = min(EV%lmaxg,nint(6*lAccuracyBoost))
end if
if (CP%Transfer%high_precision) then
if (HighAccuracyDefault) then
EV%lmaxnr=max(nint(45*lAccuracyBoost),3)
else
EV%lmaxnr=max(nint(30*lAccuracyBoost),3)
endif
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%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 (CP%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*lAccuracyBoost))
EV%lmaxpolt = max(3,nint(4*lAccuracyBoost))
! if (EV%q < 1e-3) EV%lmaxpolt=EV%lmaxpolt+1
if (DoTensorNeutrinos) then
EV%lmaxnrt=nint(6*lAccuracyBoost)
EV%lmaxnut=EV%lmaxnrt
else
EV%lmaxnut=0
EV%lmaxnrt=0
end if
if (CP%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*lAccuracyBoost))
EV%lmaxpolv = max(5,nint(5*lAccuracyBoost))
EV%nvarv=(EV%lmaxv)+(EV%lmaxpolv-1)*2+3
EV%lmaxnrv=nint(30*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
!cccccccccccccccccccccccccccccccccc
subroutine SwitchToMassiveNuApprox(EV,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)
a=y(1)
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 Nu_background(a*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
call Nu_Intvsq(EV,y, a, nu_i, EVout%G11(nu_i),EVout%G30(nu_i))
!Analytic solution for higher moments, proportional to a^{-3}
EVout%G11(nu_i)=EVout%G11(nu_i)*a2*a/rhonu
EVout%G30(nu_i)=EVout%G30(nu_i)*a2*a/rhonu
EV=EVout
y=yout
end subroutine SwitchToMassiveNuApprox
subroutine MassiveNuVarsOut(EV,y,yprime,a,grho,gpres,dgrho,dgq,dgpi, gdpi_diff,pidot_sum,clxnu_all)
implicit none
type(EvolutionVars) EV
real(dl) :: y(EV%nvar), yprime(EV%nvar),a
real(dl), optional :: grho,gpres,dgrho,dgq,dgpi, gdpi_diff,pidot_sum,clxnu_all
!grho = a^2 kappa rho
!gpres = a^2 kappa p
!dgrho = a^2 kappa \delta\rho
!dgp = a^2 kappa \delta p
!dgq = a^2 kappa q (heat flux)
!dgpi = a^2 kappa pi (anisotropic stress)
!dgpi_diff = a^2 kappa (3*p -rho)*pi
integer nu_i
real(dl) pinudot,grhormass_t, rhonu, pnu, rhonudot
real(dl) adotoa, grhonu_t,gpnu_t
real(dl) clxnu, qnu, pinu, dpnu, grhonu, dgrhonu
real(dl) dtauda
grhonu=0
dgrhonu=0
do nu_i = 1, CP%Nu_mass_eigenstates
grhormass_t=grhormass(nu_i)/a**2
!Get density and pressure as ratio to massless by interpolation from table
call Nu_background(a*nu_masses(nu_i),rhonu,pnu)
if (EV%MassiveNuApprox(nu_i)) then
clxnu=y(EV%nu_ix(nu_i))
!dpnu = y(EV%iq0+1+off_ix)
qnu=y(EV%nu_ix(nu_i)+2)
pinu=y(EV%nu_ix(nu_i)+3)
pinudot=yprime(EV%nu_ix(nu_i)+3)
else
!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
adotoa = 1/(a*dtauda(a))
rhonudot = Nu_drho(a*nu_masses(nu_i),adotoa,rhonu)
call Nu_pinudot(EV,y, yprime, a,adotoa, nu_i,pinudot)
pinudot=pinudot/rhonu - rhonudot/rhonu*pinu
endif
grhonu_t=grhormass_t*rhonu
gpnu_t=grhormass_t*pnu
grhonu = grhonu + grhonu_t
if (present(gpres)) gpres= gpres + gpnu_t
dgrhonu= dgrhonu + grhonu_t*clxnu
if (present(dgq)) dgq = dgq + grhonu_t*qnu
if (present(dgpi)) dgpi = dgpi + grhonu_t*pinu
if (present(gdpi_diff)) gdpi_diff = gdpi_diff + pinu*(3*gpnu_t-grhonu_t)
if (present(pidot_sum)) pidot_sum = pidot_sum + grhonu_t*pinudot
end do
if (present(grho)) grho = grho + grhonu
if (present(dgrho)) dgrho= dgrho + dgrhonu
if (present(clxnu_all)) clxnu_all = dgrhonu/grhonu
end subroutine MassiveNuVarsOut
subroutine Nu_Integrate_L012(EV,y,a,nu_i,drhonu,fnu,dpnu,pinu)
type(EvolutionVars) EV
! Compute the perturbations of density and energy flux
! of one eigenstate of massive neutrinos, in units of the mean
! density of one eigenstate of massless neutrinos, by integrating over
! momentum.
integer, intent(in) :: nu_i
real(dl), intent(in) :: a, y(EV%nvar)
real(dl), intent(OUT) :: drhonu,fnu
real(dl), optional, intent(OUT) :: dpnu,pinu
real(dl) tmp, am, aq,v, pert_scale
integer iq, ind
! q is the comoving momentum in units of k_B*T_nu0/c.
drhonu=0
fnu=0
if (present(dpnu)) then