1. Play with CAMB/CosmoMC
April 11, 2017
Play with CAMB/CosmoMC
Gong-Bo Zhao
ICG, Portsmouth
May, 2010
ICG PhD lectures

2. Why CAMB/CosmoMC? Very efficient
April 11, 2017
Why CAMB/CosmoMC?
Very efficient
Well-structured (modulised) -- easy to tweak and hack
Well-supported – cosmocoffee.info
Popular – mainstream numeric tool in cosmology
ICG PhD lectures
May, 2010
ICG PhD lectures

3. This 4.5-hr course is to … Show you how to run CAMB/CosmoMC
April 11, 2017
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
ICG PhD lectures
May, 2010
ICG PhD lectures

4. Theory (see Kazuya, Rob and Cyril’s lectures)
April 11, 2017
This course is not on …
Theory (see Kazuya, Rob and Cyril’s lectures)
Fortran programming (See Numerical Recipe)
ICG PhD lectures
May, 2010
ICG PhD lectures

5. April 11, 2017
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
ICG PhD lectures
May, 2010
ICG PhD lectures

6. Look into the code… Analyze the code using “understand for fortran”
(choose the free 15-day trial version)

7. Structure of CAMB
Messy?
Not really!!
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8. Structure of CAMB preparation core output results ICG PhD lectures
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9. Structure of CAMB_GetResults
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10. Structure of CMBmain
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11. Structure of CMBmain
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12. CAMB language A,B,C
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13. CAMB vs. M+B ’96 astro-ph/9506072 Constraint equations (algebraic)
Differential equations to evolve in CAMB
Constraint equations (algebraic) 

14. 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.
ICG PhD lectures
May, 2010

15. 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!!
ICG PhD lectures
May, 2010

16. Background evolution
For constant w (default CAMB) grhoa2=grhoa2+grhov*a2**2 For functional w (hacked) grhoa2=grhoa2+grhov*Funcofw(a,..)*a2
ICG PhD lectures
May, 2010

17. 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 function Funcofw
ICG PhD lectures
May, 2010

18. Output m open(unit=50,file=‘dL_SN.dat’) do i=1, 1000
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)
ICG PhD lectures
May, 2010

20. 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))
ICG PhD lectures
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21. ICG PhD lectures
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23. 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
ICG PhD lectures
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24. Weller and Lewis, 2003

26. 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 astro- ph/
Solution: astro-ph/ (quintom scenario),
or arXiv: (PPF implementation)
ICG PhD lectures
May, 2010

27. ICG PhD lectures
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29. ICG PhD lectures
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30. Generalize our hacked code to make it work for an arbitrary w(z).
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!!

31. Hacking 2: TO BE OR NOT TO BE
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.
ICG PhD lectures
May, 2010

32. Universe is Accelerating
Dark Matter
Atoms
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
UK COSMOS, 11/18/2009

33. Modified Gravity Linear perturbation in FRW universe
General Relativity
UK COSMOS, 11/18/2009

34. 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
ICG PhD lectures
May, 2010

35. Finally, we have (for details, see Appendix of 0809.3791),
So we have
Finally, we have (for details, see Appendix of ),
ICG PhD lectures
May, 2010

36. In MG, we need to evolve d and a, and get h from constraint equations.
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.
ICG PhD lectures
May, 2010

37. ICG PhD lectures
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38. ICG PhD lectures
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39. 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.
ICG PhD lectures
May, 2010

40. 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!!
ICG PhD lectures
May, 2010

41. Astro-ph/
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42. Useful references Camb.info; cosmologist.info/cosmomc/
Cosmocoffee.info
M+B: astro-ph/
Jussi’s ICG lectures:
Numerical Recipe:
Plotting software: OriginPro, Matlab, IDL, gnuplot
ICG PhD lectures
May, 2010

43. Have fun!!
ICG PhD lectures
May, 2010