Cosmic Shear Calculator

Cosmic Shear Calculator is a powerful, free online tool that computes weak gravitational lensing statistics using rigorously validated cosmological formulas from peer-reviewed literature (e.g., LSST, Euclid, DES, KiDS surveys). It calculates the cosmic shear angular power spectrum C^ℓ(E/B), convergence power spectrum, shear correlation functions ξ₊(θ) and ξ_-(θ), and tomographic signal-to-noise forecasts — all based on the Limber approximation, nonlinear Halofit matter power spectrum (Takahashi et al. 2012), and IAC intrinsic alignment model.

About the Cosmic Shear Calculator

The Cosmic Shear Calculator is a scientifically accurate, open-access tool designed for cosmologists, astrophysicists, students, and researchers studying weak gravitational lensing and large-scale structure. Cosmic shear — the subtle distortion of distant galaxy shapes by foreground mass — is one of the most powerful probes of dark energy, modified gravity, and neutrino mass available today.

What is Cosmic Shear?

Cosmic shear refers to the weak gravitational lensing effect caused by the large-scale structure of the Universe on light from distant galaxies. As light travels from background galaxies to us, it gets deflected by intervening matter (both dark and baryonic), causing small, coherent shape distortions (shear γ) and size changes (convergence κ). These distortions are typically at the 1–3% level but are statistically measurable over millions of galaxies.

The leading surveys using cosmic shear include the Dark Energy Survey (DES), Kilo-Degree Survey (KiDS), Hyper Suprime-Cam (HSC), the upcoming Rubin Observatory Legacy Survey of Space and Time (LSST), Euclid, and Roman Space Telescope. Learn more at the official LSST page on Cosmic Shear.

Scientific Foundation of This Calculator

This calculator implements the full nonlinear cosmic shear formalism as used in modern analyses:

• Limber approximation (Limber 1953, Kaiser 1992)
• Revised Halofit nonlinear matter power spectrum (Takahashi et al. 2012)
• Takada & Jain (2009) tomographic formalism
• Intrinsic Alignment contamination (IA) using the NLA model (Bridle & King 2007)
• Shape noise from ellipticities σ_ε = 0.26 per component
• Accurate redshift distributions using the standard LSST/Euclid n(z) form

Key Outputs of the Calculator

When you press “Calculate”, the tool returns:

1. Convergence Power Spectrum C^ℓ_κκ(ℓ)
2. E-mode Shear Power Spectrum C^ℓ_EE(ℓ)
3. Shear Correlation Functions ξ₊(θ) and ξ₋(θ) via Hankel transform
4. Signal-to-Noise Forecast for a given survey area and galaxy density
5. Figure-of-Merit for dark energy (w₀–wₐ) constraints

Why Use the Cosmic Shear Calculator?

This tool is invaluable when:

• Preparing observing proposals for LSST, Euclid, or Roman
• Teaching graduate courses on cosmological probes
• Quickly checking how changing Ω_m, σ₈, or w affects lensing signal
• Comparing intrinsic alignment mitigation strategies
• Understanding the σ₈–Ω_m degeneracy

User Guidelines

For realistic LSST-like forecasts, use: Ω_m=0.315, σ₈=0.811, survey area=18,000 deg², n_gal=27 arcmin⁻², median z≈1.0–1.2. For Euclid, use ~15,000 deg² and n_gal≈30 arcmin⁻².

The calculator runs entirely in your browser — no data is sent to any server.