Question about inflation_V_end

[JeremiasBezerra]

Hello everyone, I have a question about the inflationary part of CLASS. In particular, I want to understand what the Vparam are when I use inflation_V_end.

I insert Type P_k_ini = inflation_V_end

In the "default.ini" document, it makes it clear that I need to specify three parameters: 1 - field value at minimum potential after inflation (phi_end) 2 - potential format (full_potential) 3 - potential parameters (Vparam0, Vparam1, Vparam2, Vparam3, Vparam4)

The same document states that "The meaning of each parameter is explained in the primrodial_inflation_potential() function in source/primordial.c", however, I did not find an explanation for these Vparam.

[schoeneberg]

Dear @JeremiasBezerra ,

The explanation is indeed in the given function that is cited. The only difference is that we renamed the parameters in that function from VparamI -> VI (e.g. Vparam0 -> V0) Here is an excerpt of the code:

    /* V(phi)=polynomial in phi */
  case polynomial:

    *V   = ppm->V0+phi*ppm->V1+pow(phi,2)/2.*ppm->V2+pow(phi,3)/6.*ppm->V3+pow(phi,4)/24.*ppm->V4;
    *dV  = ppm->V1+phi*ppm->V2+pow(phi,2)/2.*ppm->V3+pow(phi,3)/6.*ppm->V4;
    *ddV = ppm->V2+phi*ppm->V3+pow(phi,2)/2.*ppm->V4;
    break;

    /* V(phi) = Lambda^4(1+cos(phi/f)) = V0 (1+cos(phi/V1)) */
  case natural:

    *V   = ppm->V0*(1.+cos(phi/ppm->V1));
    *dV  = -ppm->V0/ppm->V1*sin(phi/ppm->V1);
    *ddV = -ppm->V0/ppm->V1/ppm->V1*cos(phi/ppm->V1);
    break;

    /* Higgs inflation from arXiv:1403.6078 */
  case higgs_inflation:

    // correspondence with 1403.6078:
    // V0 = b
    // V1 = ksi
    // V2 = kappa
    // V3 = delta_lambda
    // mu = bar(mu)/M_P
    // phi = -chi/M_P

    e = exp(2./sqrt(6.)*sqrt(8.*_PI_)*phi);
    de = 2./sqrt(6.)*sqrt(8.*_PI_)*e;
    dde = 2./3. * 8.*_PI_ * e;

    mu = pow(1.-e,0.5);
    dmu = -0.5*de*pow(1.-e,-0.5);
    ddmu = -0.5*dde*pow(1.-e,-0.5)-0.25*de*de*pow(1.-e,-1.5);

    l = log(mu/ppm->V2);
    dl = dmu/mu;
    ddl = ddmu/mu - dl*dl;

    p = 1./16. + ppm->V3/ppm->V0 + l*l;
    dp = 2.*dl*l;
    ddp = 2.*ddl*l+2.*dl*dl;

    *V = ppm->V0/4./pow(8.*_PI_,2)/ppm->V1/ppm->V1*p*pow(mu,4);
    *dV = ppm->V0/4./pow(8.*_PI_,2)/ppm->V1/ppm->V1*(dp*pow(mu,4)+4.*p*dmu*pow(mu,3));
    *ddV = ppm->V0/4./pow(8.*_PI_,2)/ppm->V1/ppm->V1*(ddp*pow(mu,4)+8.*dp*dmu*pow(mu,3)+4.*p*ddmu*pow(mu,3)+12.*p*pow(dmu*mu,2));

    //fprintf(stderr,"%e  %e  %e\n",*V,p,mu);

If you need other shapes that are analytical functions, there is still plenty of room left below these well known shapes

[JeremiasBezerra]

Thanks for the clarification