# Cosmological Number Counts in Einstein and Jordan frames

## TL;DR

This paper clarifies that while the matter power spectrum varies between Einstein and Jordan frames, the observable cosmological number counts remain frame independent, resolving previous confusion about frame dependence.

## Contribution

It demonstrates that observable number counts are frame independent despite the frame dependence of the matter power spectrum, and analyzes how this dependence varies with scale.

## Key findings

- Number counts are frame independent.
- Matter power spectrum is frame dependent.
- Frame dependence varies with scale.

## Abstract

Even though we know that physical observations are frame independent, the frame dependence of cosmological perturbations is relatively subtle and has led to confusion in the past. In this paper we show that while the (unobservable) matter power spectrum is frame dependent, the observable number counts are not. We shall also determine how the frame dependence of the power spectrum depends on scale.