Play with CAMB/CosmoMC
Gong-Bo Zhao
ICG, Portsmouth
May, 2010
Why CAMB/CosmoMC?
 Very efficient
 Well-structured (modulised) -- easy to tweak and hack
 Well-supported – cosmocoffee.info
 Popular – mainstream numeric tool in cosmology
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This 4.5-hr course is to …
 Show you how to run CAMB/CosmoMC
 Link CAMB equations to Ma&Bertschinger ‘96
 Show several useful examples of hacking CAMB
-- dynamical dark energy, modified gravity
 Guide you how to modify CAMB/CosmoMC
for your own research purpose
 Show you useful numerical tricks extensively
used in CAMB
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This course is not on …
 Theory (see Kazuya, Rob and Cyril’s lectures)
 Fortran programming (See Numerical Recipe)
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Warming-ups
 Download, compile and run CAMB
camb.info
make clean; make all
./camb params.ini
 Change model parameters in params.ini and make CMB, P(k) plots
change cosmo. params
add neutrinos
do CMB lensing
do vector and tensor modes
compare with Wayne Hu’s plots at
http://background.uchicago.edu/~whu/metaanim.html
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Look into the code…
Analyze the code using
“understand for fortran”
http://www.scitools.com/download/
(choose the free 15-day trial version)
Structure of CAMB
Messy?
Not really!!
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Structure of CAMB
preparation
core
output results
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Structure of CAMB_GetResults
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Structure of CMBmain
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Structure of CMBmain
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CAMB language A,B,C
a' da /d
=
, tau = conformal time
a
a
dgrho = 8Ga2   ii , dgq = 8Ga2  (  i  pi )v i
Background : grho = 8Ga 2 , adotoa =
T  :
i
i
clxc = c , clxb = b , clxq = DE
G
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
:
h'6'
etak = k, z = h' /(2k), sigma =
2k
ICG PhD lectures
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CAMB vs. M+B ’96
astro-ph/9506072
' k 2 = 4 Ga2 ( P )
' k = dgq/2
Differential equations to evolve in CAMB
1
clxcdot =  kz
 'c =  h'
2
1 a'
2
h' = 4Ga2T00
k 
z = (0.5dgrho/ k + k)/adotoa
2a
Constraint equations (algebraic)
h'6'
2
=
sigma = z +1.5dgq/k
2k

Hacking 1: Dynamical DE
Task:
Default CAMB only works for constant w. Modify it to
implement the CPL parametrisa-tion, i.e. w(a)=w0+wa(1-a)
and calculate the luminosity distance, CMB and P(k) for a model
of {-1.5, +(-)0.4}. Compare your spectra with that of the
LCDM model.
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Start the game!
Spot the dark energy stuff in CAMB
We need w(a), dw/da, Int {[1+w(a)]dlna}
Files to hack: equations.f90, inidriver.F90
Subroutine/functions to hack: dtauda, fderivs, output
Change the background and the DE perturbation
equations!!
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Background evolution
X   exp{3 1 [1 w(a')]dln a'}
0
X
a
For constant w (default CAMB)
grhoa2=grhoa2+grhov*a2**2
 For functional w (hacked)
grhoa2=grhoa2+grhov*Funcofw(a,..)*a2
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function Funcofw(a,deriv)
implicit none
real(dl) a, Funcofw, a0
real(dl) w0, wa
integer deriv
if (a .lt. 1.d-8) then
a0 = 1.d-8
else
a0 = a
end if
if (deriv==0) then
Funcofw = w0+wa*(1.d0-a0)
else if (deriv ==1) then
Funcofw = -wa*a0
else if (deriv ==2) then
Funcofw = a0**(2.d0 - 3.d0*(1.d0+w0+wa))*exp(3.d0*wa*(a0-1.d0))
end if
end function Funcofw
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Output m
In inidriver.F90
open(unit=50,file=‘dL_SN.dat’)
do i=1, 1000
zz(i)=1.7d0+dble(i-1)/dble(1000-1)
write(50,'(100e15.6)') zz(i), 5*log10((1+zz(i)) &
**2*AngularDiameterDistance(zz(i)))+25
end do
close(50)
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DE perturbation equations
ayprime(EV%w_ix)= -3*adotoa*(cs2_lam-Funcofw(a,0))*(clxq+3*adotoa*&
(1+Funcofw(a,0))*vq/k) -(1+Funcofw(a,0))*k*vq -&
(1+Funcofw(a,0))*k*z -3*adotoa*adotoa*Funcofw(a,1)*vq/k
ayprime(EV%w_ix+1) = -adotoa*(1-3*cs2_lam)*vq +
k*cs2_lam*clxq/(1+Funcofw(a,0))
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Output Dark Energy perturbation dDE(h), vDE(h) at k=10-3
Mpc-1
 Note that in CAMB language
dDE = y(EV%w_ix)
vDE = y(EV%w_ix+1)
 Uncomment the stuff in cmbmain.f90,
EV%q=1.d-3; EV%q2=EV%q**2
tol1=tol/exp(AccuracyBoost-1)
do j=1,6000
tauend = taustart * exp(j/6000._dl*log(CP%tau0/taustart))
call GaugeInterface_EvolveScal(EV,tau,y,tauend,tol1,ind,c,w)
write (*,’(4E15.5)') tauend,1/y(1)-1, y(EV%w_ix) ,y(EV%w_ix+1)
end do
stop
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Weller and Lewis, 2003
Singularity?!
 Output CMB Cl’s for the model w0=-1.5, wa=+1.0 to see
what happens.
 This singularity stems from the fact that w crosses -1.
Technically, it’s due to the term of dw/dz/(1+w).
 No-Go Theorem: The w for single fluid (scalar field) cannot
cross -1 in GR! For proof, see Appendix of astroph/0703202.
 Solution: astro-ph/0507482 (quintom scenario),
or arXiv:0808.3125 (PPF implementation)
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One further step?
Generalize our hacked code to make it
work for an arbitrary w(z).
Leave it to you guys to play with it for fun!!
Hacking 2: TO BE OR NOT TO BE
??
-- MODIFY CAMB TO WORK IN MODIFIED
GRAVITY
Task
Default CAMB only works in GR. Modify it to implement MG.
Reproduce the plots on my website.
http://userweb.port.ac.uk/~zhaog/MGCAMB.html
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Universe is Accelerating
Atoms
Dark Matter
 ?!
Scalar-tensor gravity
(e.g. Chameleon, f(R)…)
DGP, Degravitation
…
Indistinguishable at the background level
Need to study the structure growth to break the degeneracy
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Linear perturbation in FRW universe
Modified
Gravity
General Relativity
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What to do technically?
 Given m(a,k) and
g(a,k), we need to solve
k2F
= -m(a,k) 4pG a2rD
F/Y =
g(a,k)
in the synchronous gauge, which is used in CAMB.
Note that
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 So we have
 Finally, we have (for details, see Appendix of 0809.3791),
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 Note that in default CAMB, d (overdensity for different
species) and h (metric perturbation in synchronous
gauge) are actually evolved, and other Einstein equations are used
as constraint equations (see this slide).
 In MG, we need to evolve d and a, and get h from
constraint equations.
 To add one more variable to evolve in CAMB, we need to define it,
set initial condition for it, and change fderivs and output properly.
 See how to modify the code in the lecture.
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1 1k a
1 1k a
(a,k) 
,  (a,k) 
2 s
2 s
1  2 k a
1  2 k a
2
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s
2
s
May, 2010
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Fit your own parameters using CosmoMC
CosmoMC fits your model parameters to data by
exploring the parameter space in a smart way
(Metropolis-Hastings algorithm). It calls CAMB to
calculate the theoretical spectra of a model, and
compare to data.
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How to add your own parameter to CosmoMC?
 Tell CosmoMC your parameters’ names in CMB_Cls_simple.f90
 Define them in cmbtype.f90
 Map them in params_CMB.f90
 Change the # of parameters in settings.f90
 Done!!
 See the example in the lecture!!
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Astro-ph/0511625
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Useful references
 Camb.info; cosmologist.info/cosmomc/
 Cosmocoffee.info
 M+B: astro-ph/9506072
 Jussi’s ICG lectures: www.icg.port.ac.uk/~valiviij/
 Numerical Recipe: www.nr.com
 Plotting software: OriginPro, Matlab, IDL, gnuplot
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Have fun!!
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