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

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

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

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

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 http://background.uchicago.edu/~whu/metaanim.html ICG PhD lectures May, 2010 ICG PhD lectures

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!! ICG PhD lectures May, 2010

Structure of CAMB preparation core output results ICG PhD lectures May, 2010

Structure of CAMB_GetResults ICG PhD lectures May, 2010

Structure of CMBmain ICG PhD lectures May, 2010

Structure of CMBmain ICG PhD lectures May, 2010

CAMB language A,B,C ICG PhD lectures May, 2010

CAMB vs. M+B ’96 astro-ph/9506072 Constraint equations (algebraic) Differential equations to evolve in CAMB Constraint equations (algebraic) 

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

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

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

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

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

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 May, 2010

ICG PhD lectures May, 2010

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 May, 2010

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 astro- ph/0703202. Solution: astro-ph/0507482 (quintom scenario), or arXiv:0808.3125 (PPF implementation) ICG PhD lectures May, 2010

ICG PhD lectures May, 2010

ICG PhD lectures May, 2010

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!!

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. http://userweb.port.ac.uk/~zhaog/MGCAMB.html ICG PhD lectures May, 2010

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

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

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

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

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

ICG PhD lectures May, 2010

ICG PhD lectures May, 2010

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

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

Astro-ph/0511625 ICG PhD lectures May, 2010

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 ICG PhD lectures May, 2010

Have fun!! ICG PhD lectures May, 2010