# LISA for Cosmologists: Calculating the Signal-to-Noise Ratio for Stochastic and Deterministic Sources

## TL;DR

This paper provides a comprehensive method for forecasting LISA's sensitivity to gravitational wave sources, including stochastic backgrounds and deterministic signals, with tools and benchmarks for practical calculations.

## Contribution

It introduces a systematic approach and tools for estimating LISA's signal-to-noise ratio and sensitivity curves for various gravitational wave sources, including benchmark comparisons.

## Key findings

- LISA can detect stochastic backgrounds with specific threshold levels.
- LISA's SNR for GW150914-like binaries can be accurately estimated.
- Benchmark sensitivity values facilitate method validation.

## Abstract

We present the steps to forecast the sensitivity of the Laser Interferometer Space Antenna (LISA) to both a stochastic gravitational wave background and deterministic wave sources. We show how to use these expressions to estimate the precision with which LISA can determine parameters associated with these sources. Tools are included to enable easy calculation of the signal-to-noise ratio and draw sensitivity curves. Benchmark values are given for easy comparison and checking of methods in the case of two worked examples. The first benchmark is the threshold stochastic gravitational wave background $\Omega_{GW} h^2$ that LISA can observe. The second is the signal-to-noise ratio that LISA would observe for a binary black hole system identical to GW150914, radiating 4 years before merger.