SA_PS Calculator#

This module provides an efficient framework for performing parameter inference in Warm Inflation (WI) models using a semi-analytical power spectrum.

It relies on the correction function \(G(Q)\) and avoids solving the full stochastic perturbation equations, making it significantly faster than the numerical module.

Directory Structure#

SA_PS_Calculator/
├── Bg.cpp
├── model_calc.cpp
├── llihood.py
├── An_CAMB.py
├── Input_asns.yaml
└── Input.yaml

Overview#

This module computes the WI power spectrum using:

  • Numerical background evolution

  • Semi-analytical expressions for the scalar power spectrum

  • Precomputed or analytical forms of \(G(Q)\)

It is designed primarily for parameter inference using Cobaya.

Defining Your WI Model#

The WI model is defined in:

model_calc.cpp

The structure is identical to the \(G(Q)\) module, with the following simplifications:

  • No need to define \(V''(\phi)\)

  • No need to define derivatives of \(\Upsilon(\phi,T)\)

Only the following functions are required:

  • \(V(\phi)\)

  • \(V'(\phi)\)

  • \(\Upsilon(\phi, T)\) (only if not of the form \(T^p \phi^c\))

If the dissipation coefficient is of the form \(\Upsilon \propto T^p \phi^c\), it is already implemented internally and the user only needs to specify the parameters p and c in the Python scripts. For more general forms of \(\Upsilon(\phi, T)\), the user must explicitly define it in model_calc.cpp.

Important

Any modification to model_calc.cpp requires recompilation.

Role of Core Files#

Bg.cpp#

  • Solves background evolution

  • Determines pivot scale exit (if enabled)

  • Computes the semi-analytical power spectrum

llihood.py#

  • Implements likelihood for:

    • \(A_s\), \(n_s\)

    • optionally \(\alpha_s\) (running of the spectral index)

  • The tensor-to-scalar ratio \(r\) is constrained internally (upper bound) in Bg.cpp.

This script is used with Input_asns.yaml.

An_CAMB.py#

  • Injects the WI primordial power spectrum into CAMB

  • Used for computing the CMB angular power spectra using CAMB

  • Performs full CMB likelihood analysis with Cobaya

\(G(Q)\) Handling#

The semi-analytical power spectrum requires \(G(Q)\), which can be supplied in multiple ways.

Option 2: Internal Analytical Fits#

Set:

read_GQ_from_file = 0

The code uses analytical fitting functions defined in model_calc.cpp:

auto GQ = [p](double Q) -> double {
    if (GQ_from_file == 1) {
        return exp10(logGasQ(log10(Q)));
    }
    else {
        // internal fits depending on p
    }
};

  • Several commonly used fits are already implemented

  • These are available only for specific cases (e.g. \(p = 3, 1, -1\))

Additional fitting functions can be:

  • computed using WarmSPy

  • implemented by modifying the auto GQ function

Warning

Ensure that the \(G(Q)\) used corresponds to the same WI model being analyzed.

C++ – Python Interface#

As in the \(G(Q)\) module, the function signature must match between C++ and Python.

Example:

void model(double phi_ini,double gst,double Q_ini,double V0,double Np,int c,int p,int therm);

This must be consistent in:

  • model_calc.cpp

  • llihood.py (modify the function logp)

  • An_CAMB.py (modify the function feature_power_spectrum)

Important

Any mismatch in function signature will lead to runtime errors or incorrect results.

Full CMB Parameter Interface (An_CAMB.py)#

When using full CMB constraints, the WI model parameters must also be defined in the FeaturePrimordialPk class inside An_CAMB.py.

This step is required for Cobaya to correctly recognize and pass the model parameters.

What Needs to Be Modified#

Update the following section to include your WI model parameters:

class FeaturePrimordialPk(Theory):
    # define parameter names here
    params = {"phi0":None,"gst":None,"Q0":None,"V0":None,"Np":None,"c":None,"p":None,"therm":None}

    def calculate(self, state, want_derived=True, **params_values_dict):
        # extract parameters here
        phi0,gst,Q0,V0,Np,c,p,therm = \
        [params_values_dict[itr] for itr in ["phi0","gst","Q0","V0","Np","c","p","therm"]] 

        ks, Pks = feature_power_spectrum(phi0,gst,Q0,V0,Np,c,p,therm,kp=self.kp) #match function signature

Key Points#

  • The params dictionary must include all WI model parameters

  • The order of parameters extracted in calculate() must match:

    • the params dictionary

    • the C++ function signature

  • The call to feature_power_spectrum(...) must also follow the same ordering

Important

If you add or remove model parameters, you must update:

  • feature_power_spectrum arguments list

  • the params dictionary

  • the parameter extraction list

  • the function call to feature_power_spectrum(...)

Input Parameters#

All runtime parameters are configured in the Python scripts.

llihood.py — \(A_s\), \(n_s\) Inference#

Pivot Scale Handling#

  • Np_autocalc (int, default = 1)
    Controls how the pivot scale exit is determined.

    • 1 → Automatically compute the e-fold \(N_*\) at which the pivot scale exits the horizon

    • 0 → Use user-specified value of Np

    Note

    The integration starts from \(N = 0\), so Np must be specified consistently in this convention when Np_autocalc = 0.

    Automatic computation is recommended unless precise control over the pivot scale is required.

  • kp (float, default = 0.05)
    Pivot scale in \(\mathrm{Mpc}^{-1}\).

\(G(Q)\) Handling#

  • read_GQ_from_file (int, default = 1)

    • 1 → Use precomputed \(G(Q)\) from file

    • 0 → Use internal analytical fits

Spectrum Control#

  • want_full_spectrum (int, do not modify default = 0)

    • 0 → Compute only \(A_s\), \(n_s\)

    • 1 → Compute full power spectrum (not used in this mode)

Numerical Parameters#

  • verbosity (int, default = 0)
    Controls logging output.

Auxiliary Parameters#

(Required by the interface but not used in this mode)

  • kmin (float, default = 1e-6)

  • kmax (float, default = 100.0)

An_CAMB.py — Full CMB Inference#

Pivot Scale Handling#

  • Np_autocalc (int, default = 1)
    Same meaning as in llihood.py.

\(G(Q)\) Handling#

  • read_GQ_from_file (int, default = 1)
    Same meaning as in llihood.py.

Spectrum Control#

  • want_full_spectrum (int, do not modify default = 1)

    • 1 → Required for full CMB computation

    • 0 → Not suitable for this mode

Numerical Parameters#

  • verbosity (int, default = 0)
    Controls logging output.

Running Parameter Inference#

Mode 1: \(A_s\), \(n_s\) (fast)#

cobaya-run Input_asns.yaml

  • Uses llihood.py

  • No full CMB computation

  • Fast and efficient

Mode 2: Full CMB Constraints#

cobaya-run Input.yaml

  • Uses An_CAMB.py

  • Requires:

    • CAMB

    • likelihoods (Planck, ACT, SPT, DESI)

Refer to the Cobaya documentation for installation.

Important

Make sure to set the packages_path: in Input.yaml to the location of your Cobaya installation. Otherwise, Cobaya will not be able to locate external codes (e.g. CAMB) and likelihoods.

Workflow#

  1. Define WI model in model_calc.cpp

  2. Ensure function signatures match in Python files

  3. Provide or compute \(G(Q)\)

  4. Configure input YAML files (priors, parameters)

  5. Run Cobaya

  6. Analyze chains using getdist

Common Pitfalls#

  • Using incorrect or inconsistent \(G(Q)\)

  • Not smoothing \(G(Q)\) computed by SWIM (can introduce noise in inference)

  • Insufficient \(Q\) range in \(G(Q)\) data

  • Function signature mismatch between C++ and Python

  • CAMB overusing threads in multi-chain runs

Important

When running multiple chains (mpirun), limit CAMB threads using:

export OMP_NUM_THREADS=$(( $(nproc --all) / <number-of-chains> ))

Summary#

  • Fast parameter inference using semi-analytical power spectrum

  • Requires \(G(Q)\) as input

  • Supports both simple (\(A_s\), \(n_s\)) and full CMB analyses

  • Designed for efficiency and flexibility