/* cosmology.hh - This file is part of MUSIC - a code to generate multi-scale initial conditions for cosmological simulations Copyright (C) 2010 Oliver Hahn */ #ifndef _COSMOLOGY_HH #define _COSMOLOGY_HH #include "transfer_function.hh" #include "mesh.hh" #include "general.hh" /*! * @class CosmoCalc * @brief provides functions to compute cosmological quantities * * This class provides member functions to compute cosmological quantities * related to the Friedmann equations and linear perturbation theory */ class CosmoCalc { public: //! data structure to store cosmological parameters Cosmology m_Cosmology; //! pointer to an instance of a transfer function plugin transfer_function_plugin *m_pTransferFunction; //! constructor for a cosmology calculator object /*! * @param acosmo a cosmological parameters structure * @param pTransferFunction pointer to an instance of a transfer function object */ CosmoCalc( const Cosmology acosmo, transfer_function_plugin *pTransferFunction ) { m_Cosmology = acosmo; m_pTransferFunction = pTransferFunction; } //! returns the amplitude of amplitude of the power spectrum /*! * @param k the wave number in h/Mpc * @param a the expansion factor of the universe * @returns power spectrum amplitude for wave number k at time a */ inline real_t Power( real_t k, real_t a ){ real_t m_Dplus = CalcGrowthFactor( a ); real_t m_DplusOne = CalcGrowthFactor( 1.0 ); real_t m_pNorm = ComputePNorm( 1e4 ); m_Dplus /= m_DplusOne; m_DplusOne = 1.0; real_t scale = m_Dplus/m_DplusOne; return m_pNorm*scale*scale*TransferSq(k)*pow((double)k,(double)m_Cosmology.nspect); } inline static double H_of_a( double a, void *Params ) { Cosmology *cosm = (Cosmology*)Params; double a2 = a*a; double Ha = sqrt(cosm->Omega_m/(a2*a) + cosm->Omega_k/a2 + cosm->Omega_DE * pow(a,3.+3.*cosm->w_0) * exp(-3.*(a-1.0)*cosm->w_a) ); return Ha; } inline static double Hprime_of_a( double a, void *Params ) { Cosmology *cosm = (Cosmology*)Params; double a2 = a*a; double H = H_of_a( a, Params ); double Hprime = -1.5 * cosm->Omega_m / (a2*a2*H) - cosm->Omega_k / (a2*a*H) + 0.5 * cosm->Omega_DE * pow( a, 3.+3.*cosm->w_0 ) * exp( -3.*(a-1.)*cosm->w_a ) * 1.5 / a * ( 1. + cosm->w_0 - a * cosm->w_a ); return Hprime; } //! Integrand used by function CalcGrowthFactor to determine the linear growth factor D+ inline static double GrowthIntegrand( double a, void *Params ) { double Ha = a * H_of_a( a, Params ); return 2.5/( Ha * Ha * Ha ); } //! Computes the linear theory growth factor D+ /*! Function integrates over member function GrowthIntegrand and computes * /a * D+(a) = 5/2 H(a) * | [a'^3 * H(a')^3]^(-1) da' * /0 */ real_t CalcGrowthFactor( real_t a ) { real_t integral = integrate( &GrowthIntegrand, 0.0, a, (void*)&m_Cosmology ); return H_of_a( a, (void*)&m_Cosmology ) * integral; } //! Compute the factor relating particle displacement and velocity /*! Function computes * * vfac = a * H(a) * dlogD+ / d log a = a^3 * H'(a) + 5/2 * [ a^2 * D+(a) * H(a) ]^(-1) * */ real_t CalcVFact( real_t a ) { real_t Dp = CalcGrowthFactor( a ); real_t H = H_of_a( a, (void*)&m_Cosmology ); real_t Hp = Hprime_of_a( a, (void*)&m_Cosmology ); real_t a2 = a*a; return a2*a * Hp + 2.5 / ( a2 * Dp * H ); } #if 0 //! Integrand used by function CalcGrowthFactor to determine the linear growth factor D+ inline static double GrowthIntegrand( double a, void *Params ) { Cosmology *cosm = (Cosmology*)Params; double eta = sqrt((double)(cosm->Omega_r/a/a+cosm->Omega_m/a+cosm->Omega_DE*a*a +1.0-cosm->Omega_m-cosm->Omega_DE)); return 2.5/(eta*eta*eta); } //! Computes the linear theory growth factor D+ /*! Function integrates over member function GrowthIntegrand */ inline real_t CalcGrowthFactor( real_t a ) { real_t eta = sqrt((double)(m_Cosmology.Omega_r/a/a+m_Cosmology.Omega_m/a+m_Cosmology.Omega_DE*a*a +1.0-m_Cosmology.Omega_m-m_Cosmology.Omega_DE)); real_t integral = integrate( &GrowthIntegrand, 0.0, a, (void*)&m_Cosmology ); return eta/a*integral; } //! Compute the factor relating particle displacement and velocity real_t ComputeVFact( real_t a ){ real_t fomega, dlogadt, eta; real_t Omega_k = 1.0 - m_Cosmology.Omega_m - m_Cosmology.Omega_DE; real_t Dplus = CalcGrowthFactor( a ); eta = sqrt( (double)(m_Cosmology.Omega_r/a/a+m_Cosmology.Omega_m/a+ m_Cosmology.Omega_DE*a*a + Omega_k )); fomega = (2.5/Dplus-1.5*m_Cosmology.Omega_m/a-Omega_k)/eta/eta; dlogadt = a*eta; //... /100.0 since we would have to multiply by H0 to convert //... the displacement to velocity units. But displacement is //... in Mpc/h, and H0 in units of h is 100. return fomega * dlogadt/a *100.0; } #endif //! Integrand for the sigma_8 normalization of the power spectrum /*! Returns the value of the primordial power spectrum multiplied with the transfer function and the window function of 8 Mpc/h at wave number k */ static double dSigma8( double k, void *Params ) { if( k<=0.0 ) return 0.0f; transfer_function *ptf = (transfer_function *)Params; double x = k*8.0; double w = 3.0*(sin(x)-x*cos(x))/(x*x*x); static double nspect = (double)ptf->cosmo_.nspect; double tf = ptf->compute(k, total); //... no growth factor since we compute at z=0 and normalize so that D+(z=0)=1 return k*k * w*w * pow((double)k,(double)nspect) * tf*tf; } //! Integrand for the sigma_8 normalization of the power spectrum /*! Returns the value of the primordial power spectrum multiplied with the transfer function and the window function of 8 Mpc/h at wave number k */ static double dSigma8_0( double k, void *Params ) { if( k<=0.0 ) return 0.0f; transfer_function *ptf = (transfer_function *)Params; double x = k*8.0; double w = 3.0*(sin(x)-x*cos(x))/(x*x*x); static double nspect = (double)ptf->cosmo_.nspect; double tf = ptf->compute(k, total0); //... no growth factor since we compute at z=0 and normalize so that D+(z=0)=1 return k*k * w*w * pow((double)k,(double)nspect) * tf*tf; } //! Computes the square of the transfer function /*! Function evaluates the supplied transfer function m_pTransferFunction * and returns the square of its value at wave number k * @param k wave number at which to evaluate the transfer function */ inline real_t TransferSq( real_t k ){ //.. parameter supplied transfer function real_t tf1 = m_pTransferFunction->compute(k, total); return tf1*tf1; } //! Computes the normalization for the power spectrum /*! * integrates the power spectrum to fix the normalization to that given * by the sigma_8 parameter */ real_t ComputePNorm( real_t kmax ) { real_t sigma0, kmin; kmax = m_pTransferFunction->get_kmax();//m_Cosmology.H0/8.0; kmin = m_pTransferFunction->get_kmin();//0.0; if( !m_pTransferFunction->tf_has_total0() ) sigma0 = 4.0 * M_PI * integrate( &dSigma8, (double)kmin, (double)kmax, (void*)m_pTransferFunction ); else sigma0 = 4.0 * M_PI * integrate( &dSigma8_0, (double)kmin, (double)kmax, (void*)m_pTransferFunction ); return m_Cosmology.sigma8*m_Cosmology.sigma8/sigma0; } }; //! compute the jeans sound speed /*! given a density in g/cm^-3 and a mass in g it gives back the sound * speed in cm/s for which the input mass is equal to the jeans mass * @param rho density * @param mass mass scale * @returns jeans sound speed */ inline double jeans_sound_speed( double rho, double mass ) { const double G = 6.67e-8; return pow( 6.0*mass/M_PI*sqrt(rho)*pow(G,1.5), 1.0/3.0 ); } //! computes the density from the potential using the Laplacian void compute_Lu_density( const grid_hierarchy& u, grid_hierarchy& fnew, unsigned order=4 ); //! computes the 2nd order density perturbations using also off-diagonal terms in the potential Hessian void compute_LLA_density( const grid_hierarchy& u, grid_hierarchy& fnew, unsigned order=4 ); //! computes the source term for the 2nd order perturbations in the displacements void compute_2LPT_source( const grid_hierarchy& u, grid_hierarchy& fnew, unsigned order=4 ); void compute_2LPT_source_FFT( config_file& cf_, const grid_hierarchy& u, grid_hierarchy& fnew ); #endif // _COSMOLOGY_HH