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equations_ppf.f90
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equations_ppf.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 2012, updated PPF version but now only simple case for w, w_a (no anisotropic stresses etc)
! Feb 2013: fixed various issues with accuracy at larger neutrino masses
! Oct 2013: fix PPF, consistent with updated equations_cross
! Mar 2014: fixes for tensors with massive neutrinos
module LambdaGeneral
use precision
use ModelParams
implicit none
real(dl) :: w_lam = -1_dl !p/rho for the dark energy (assumed constant)
! w_lam is now w0
!comoving sound speed. Always exactly 1 for quintessence
!(otherwise assumed constant, though this is almost certainly unrealistic)
real(dl) :: cs2_lam = 1_dl
!cs2_lam now is ce^2
logical :: use_tabulated_w = .false.
real(dl) :: wa_ppf = 0._dl
real(dl) :: c_Gamma_ppf = 0.4_dl
integer, parameter :: nwmax = 5000, nde = 2000
integer :: nw_ppf
real(dl) w_ppf(nwmax), a_ppf(nwmax), ddw_ppf(nwmax)
real(dl) rde(nde),ade(nde),ddrde(nde)
real(dl), parameter :: amin = 1.d-9
logical :: is_cosmological_constant
private nde,ddw_ppf,rde,ade,ddrde,amin
contains
subroutine DarkEnergy_ReadParams(Ini)
use IniFile
Type(TIniFile) :: Ini
character(LEN=Ini_max_string_len) wafile
integer i
if (Ini_HasKey_File(Ini,'usew0wa')) then
stop 'input variables changed from usew0wa: now use_tabulated_w or w, wa'
end if
use_tabulated_w = Ini_Read_Logical_File(Ini,'use_tabulated_w',.false.)
if(.not. use_tabulated_w)then
w_lam = Ini_Read_Double_File(Ini,'w', -1.d0)
wa_ppf = Ini_Read_Double_File(Ini,'wa', 0.d0)
if (Feedback >0) write(*,'("(w0, wa) = (", f8.5,", ", f8.5, ")")') w_lam,wa_ppf
else
wafile = Ini_Read_String_File(Ini,'wafile')
open(unit=10,file=wafile,status='old')
nw_ppf=0
do i=1,nwmax+1
read(10,*,end=100)a_ppf(i),w_ppf(i)
a_ppf(i)=dlog(a_ppf(i))
nw_ppf=nw_ppf+1
enddo
write(*,'("Note: ", a, " has more than ", I8, " data points")') trim(wafile), nwmax
write(*,*)'Increase nwmax in LambdaGeneral'
stop
100 close(10)
write(*,'("read in ", I8, " (a, w) data points from ", a)') nw_ppf, trim(wafile)
call setddwa
call interpolrde
endif
cs2_lam = Ini_Read_Double_File(Ini,'cs2_lam',1.d0)
call setcgammappf
end subroutine DarkEnergy_ReadParams
subroutine setddwa
real(dl), parameter :: wlo=1.d30, whi=1.d30
call spline(a_ppf,w_ppf,nw_ppf,wlo,whi,ddw_ppf) !a_ppf is lna here
end subroutine setddwa
function w_de(a)
real(dl) :: w_de, al
real(dl), intent(IN) :: a
if(.not. use_tabulated_w) then
w_de=w_lam+wa_ppf*(1._dl-a)
else
al=dlog(a)
if(al.lt.a_ppf(1)) then
w_de=w_ppf(1) !if a < minimum a from wa.dat
elseif(al.gt.a_ppf(nw_ppf)) then
w_de=w_ppf(nw_ppf) !if a > maximus a from wa.dat
else
call cubicsplint(a_ppf,w_ppf,ddw_ppf,nw_ppf,al,w_de)
endif
endif
end function w_de ! equation of state of the PPF DE
function drdlna_de(al)
real(dl) :: drdlna_de, a
real(dl), intent(IN) :: al
a=dexp(al)
drdlna_de=3._dl*(1._dl+w_de(a))
end function drdlna_de
subroutine interpolrde
real(dl), parameter :: rlo=1.d30, rhi=1.d30
real(dl) :: atol, almin, al, rombint, fint
integer :: i
external rombint
atol=1.d-5
almin=dlog(amin)
do i=1,nde
al=almin-almin/(nde-1)*(i-1) !interpolate between amin and today
fint=rombint(drdlna_de, al, 0._dl, atol)+4._dl*al
ade(i)=al
rde(i)=dexp(fint) !rho_de*a^4 normalize to its value at today
enddo
call spline(ade,rde,nde,rlo,rhi,ddrde)
end subroutine interpolrde
function grho_de(a) !8 pi G a^4 rho_de
real(dl) :: grho_de, al, fint
real(dl), intent(IN) :: a
if(.not. use_tabulated_w) then
grho_de=grhov*a**(1._dl-3.*w_lam-3.*wa_ppf)*exp(-3.*wa_ppf*(1._dl-a))
else
if(a.eq.0.d0)then
grho_de=0.d0 !assume rho_de*a^4-->0, when a-->0, OK if w_de always <0.
else
al=dlog(a)
if(al.lt.ade(1))then
fint=rde(1)*(a/amin)**(1.-3.*w_de(amin)) !if a<amin, assume here w=w_de(amin)
else !if amin is small enough, this extrapolation will be unnecessary.
call cubicsplint(ade,rde,ddrde,nde,al,fint)
endif
grho_de=grhov*fint
endif
endif
end function grho_de
!-------------------------------------------------------------------
SUBROUTINE cubicsplint(xa,ya,y2a,n,x,y)
INTEGER n
real(dl)x,y,xa(n),y2a(n),ya(n)
INTEGER k,khi,klo
real(dl)a,b,h
klo=1
khi=n
1 if (khi-klo.gt.1) then
k=(khi+klo)/2
if(xa(k).gt.x)then
khi=k
else
klo=k
endif
goto 1
endif
h=xa(khi)-xa(klo)
if (h.eq.0.) stop 'bad xa input in splint'
a=(xa(khi)-x)/h
b=(x-xa(klo))/h
y=a*ya(klo)+b*ya(khi)+&
((a**3-a)*y2a(klo)+(b**3-b)*y2a(khi))*(h**2)/6.d0
END SUBROUTINE cubicsplint
!--------------------------------------------------------------------
subroutine setcgammappf
c_Gamma_ppf=0.4d0*sqrt(cs2_lam)
end subroutine setcgammappf
end module LambdaGeneral
!cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
!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
use LambdaGeneral
!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
is_cosmological_constant = .not. use_tabulated_w .and. w_lam==-1_dl .and. wa_ppf==0._dl
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 (is_cosmological_constant) then
grhoa2=grhoa2+grhov*a2**2
else
grhoa2=grhoa2+ grho_de(a)
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 = 'equations_ppf-Jan15'
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
!PPF parameters
real(dl) dgrho_e_ppf, dgq_e_ppf
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 (.not. is_cosmological_constant) then
EV%w_ix = neq+1
neq=neq+1 !ppf
maxeq=maxeq+1
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
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)*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 (.not. is_cosmological_constant) then
yout(EVout%w_ix)=y(EV%w_ix)
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) stop '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