Swampland Conjectures

To assess the swampland conjectures, we computed a few additional quantities and made those available through the Python wrapper classy. The swampland conjectures are explained in the thesis and in more detail in the Hitchhiker's Guide to the Swampland. Here, we focus on the technical implementation.

We added various new variables:

• $\phi_i$

Which we implemented in background.c

pba->phi_ini_scf_computed = pvecback_integration[pba->index_bi_phi_scf];
    pba->phi_prime_scf_computed = pvecback_integration[pba->index_bi_phi_prime_scf];
    if (pba->background_verbose > 2)
    {
      printf("[background] attractor_regime_scf=%d, phi_ini_scf_computed=%e, phi_prime_scf_computed=%e\n",
             pba->attractor_regime_scf,
             pba->phi_ini_scf_computed,
             pba->phi_prime_scf_computed);
    }
  }
  else
  {
    pba->phi_ini_scf_computed = 0.0;
    pba->phi_prime_scf_computed = 0.0;
    pba->attractor_regime_scf = 0;
    if (pba->background_verbose > 0)
    {
      printf("No scalar field present. No initial field values set.\n");
    }

background.h

    short attractor_ic_scf;                         /**< whether the scalar field has attractor initial conditions */
    double phi_ini_scf_computed;                    /**< computed initial \f$ \phi \f$ actually used after attractor/NaN checks */
    double phi_prime_scf_computed;                  /**< computed initial \f$ d\phi/d\tau \f$ actually used after attractor/NaN checks */
    double phi_scf_min;                             /**< minimum \f$ \phi \f$ encountered over the background table */
    double phi_scf_max;                             /**< maximum \f$ \phi \f$ encountered over the background table */
    double phi_scf_range;                           /**< \f$ \phi_{max}-\phi_{min} \f$ over the background table */
    double dV_V_scf_min;                            /**< minimum \f$ |dV/d\phi|/V \f$ encountered over the background table (de Sitter Conjecture) */
    double ddV_V_scf_max;                           /**< maximum \f$ d^2V/d\phi^2/V \f$ encountered over the background table (second de Sitter Conjecture) */
    double ddV_V_at_dV_V_min;                       /**< \f$ d^2V/d\phi^2/V \f$ evaluated when \f$ |dV/d\phi|/V \f$ reaches its minimum */
    double dV_V_at_ddV_V_max;                       /**< \f$ |dV/d\phi|/V \f$ evaluated when \f$ d^2V/d\phi^2/V \f$ reaches its maximum */
    double swgc_expr_min;                           /**< minimum of \f$ 2(d^3V/d\phi^3)^2 - (d^2V/d\phi^2)(d^4V/d\phi^4) - (d^2V/d\phi^2)^2 \f$ (scalar weak gravity conjecture) */
    double sswgc_min;                               /**< minimum of the strong scalar weak gravity conjecture expression \f$ M_P^2 m^2 \partial_\phi^2(1/m^2) \f$ */
    double AdSDC2_max;                              /**< maximum of AdSDC2 boundary expression during evolution */
    double AdSDC4_max;                              /**< maximum of AdSDC4 boundary expression during evolution */
    double combined_dSC_min;                        /**< minimum of \f$ (3(dV_p)^2/V^2 - 2 d^2V/d\phi^2/V)/4 \f$ during evolution, a strong form of a combined de Sitter conjecture, stemming from the FLB and the SSWGC. */
    int attractor_regime_scf;                       /**< attractor regime used: 0=no attractor, 1=large-field, 2=approximate, 3=small-field, 4=approximate small-field */

cclassy.pxd

        double phi_ini_scf_computed
        double phi_prime_scf_computed

classy.pyx

            elif name == 'phi_ini_scf_ic':
                value = self.ba.phi_ini_scf_computed
            elif name == 'phi_prime_scf_ic':
                value = self.ba.phi_prime_scf_computed