cosmology.hh

/*
 
 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.*(1.+cosm->w_0+cosm->w_a)) * exp(-3.*(1.0-a)*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/(a*H) * ( -1.5 * cosm->Omega_m / (a2*a) - cosm->Omega_k / a2
      - 1.5 * cosm->Omega_DE * pow( a, -3.*(1.+cosm->w_0+cosm->w_a) ) * exp( -3.*(1.0-a)*cosm->w_a )
      * ( 1. + cosm->w_0 + (1.-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^2 * H(a) * dlogD+ / d log a = a^2 * H'(a) + 5/2 * [ a * 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 * Hp + 2.5 / ( a * Dp * H ) ) * 100.0;
    }
		
	
    //! 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