Multiverse.jl

A Julia Framework for Multi-universe Cosmological Inference via the Effort.jl Likelihood Interface

Author: Batuhan Ayrıbaş

Overview

Multiverse.jl is a Julia software package designed to orchestrate and evaluate large ensembles of cosmological model realizations ("universes") against observational constraints through a likelihood-based workflow.

The package centers on a simulation object that couples physical model parameters and observation-derived likelihood terms, with an emphasis on composability and a lightweight user-facing API.

Features

• 🔗 Composable Architecture - Simulation and Likelihood objects are instantiated independently and connected explicitly
• 🎯 Minimal Surface Area - Small number of high-level operations reduces cognitive load
• 🔀 Separation of Concerns - Likelihood evaluation delegated to Effort.jl
• 📊 Planck 2018 Support - Direct integration with Planck observational data

Installation

using Pkg
Pkg.add("Multiverse")

Quick Start

using Multiverse
using Effort

# Create likelihood object with Planck data
lkl = Likelihood(Planck())

# Configure simulation with model parameters
simulation = Simulation(
    "inftypes", # model tag
    (ns = 0.96, r = 0.02, log10_10As = 3.044)
)

# Initialize simulation with likelihood
Multiverse.init!(simulation, lkl)

Usage

Likelihood Evaluation

# Evaluate likelihood for a parameter vector
value = lkl([0.97, 0.1, 3.044])

Best-fit Query

# Get best-fit parameters and objective value
bf = bestfit(simulation, lkl)

Architecture

┌─────────────┐       ┌─────────────────┐       ┌─────────────────┐
│  User Code  │──────▶│  Multiverse.jl  │──────▶│   Effort.jl     │
│   (Julia)   │       │   Simulation    │       │   Likelihood    │
└─────────────┘       │  orchestration  │       │   interface     │
                      └─────────────────┘       └────────┬────────┘
                                                         │
                                                         ▼
                                                ┌─────────────────┐
                                                │ Observational   │
                                                │ Data (Planck)   │
                                                └─────────────────┘

Workflow

1. Define Model - Create named-tuple with cosmological parameters
2. Construct Simulation - Initialize Simulation object with model tag
3. Construct Likelihood - Create Likelihood via Effort.jl
4. Initialize - Bind likelihood to simulation with Multiverse.init!
5. Evaluate - Run likelihood evaluations in outer loop (grid scan, optimizer, or sampler)
6. Query Results - Record values and diagnostics using bestfit

Algorithm

Input: simulation configuration S, likelihood object L, parameter set θ

1: Multiverse.init!(S, L)        # bind L to S; perform required setup
2: for each θ in parameter_sets do
3:     ℓ(θ) ← L(θ)               # evaluate likelihood via Effort.jl
4: end for
5: optionally: (ℓ*, θ*) ← bestfit(S, L)

Output: likelihood evaluations {ℓ(θ)} and/or best-fit summary

Complexity

The dominant computational cost is the likelihood evaluation performed by the Effort.jl backend. For N parameter sets with each likelihood call costing time T:

$$\text{Runtime} = \Theta(NT)$$

Reproducibility

To ensure computational reproducibility:

• Pin Julia environment using Project.toml and Manifest.toml
• Record Julia version and platform
• If randomized steps exist, capture seeds and deterministic execution settings
• For observational likelihoods, include precise data release identifiers and checksum-verified downloads

Related Work

Multiverse.jl interoperates with Effort.jl for likelihood computation and is designed as a lightweight orchestration layer for cosmological inference.

Other relevant tools in the ecosystem:

• CLASS - Cosmic Linear Anisotropy Solving System
• CAMB - Code for Anisotropies in the Microwave Background
• Turing.jl - Probabilistic programming in Julia

References

1. (2025). Effort.jl: A package for cosmological parameter inference using modern programming paradigms. arXiv:2501.04639.

2. Planck Collaboration. (2020). Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics, 641, A6.

3. Bezanson, J., Edelman, A., Karpinski, S., & Shah, V. B. (2017). Julia: A fresh approach to numerical computing. SIAM Review, 59(1), 65-98.

4. Lewis, A., Challinor, A., & Lasenby, A. (2000). Efficient computation of CMB anisotropies in closed FRW models. The Astrophysical Journal, 538(2), 473-476.

5. Blas, D., Lesgourgues, J., & Tram, T. (2011). The Cosmic Linear Anisotropy Solving System (CLASS). Journal of Cosmology and Astroparticle Physics, 2011(07), 034.