# Forecastfiso planck

## Overview

We can improve constraints on isocurvature perturbations from Planck with observations from S4.

Here we consider the curvaton model: there is one isocurvature mode: the CDM isocurvature, and the spectral index of the CDM mode is the same as that of the adiabatic scalar perturbations, n_s. In this scenario, the CDM mode is either totally correlated or anti-correlated with the adiabatic perturbations.

The parameter we are constraining is f_iso, the primordial fraction of CDM isocurvature amplitude to the scalar perturbation amplitude. Specifically, the final spectra is

Cl^{tot} = Cl^{ad} + f_iso^2 Cl^{cdm iso} + 2* f_iso * Cl^{correlated}

where Cl^{cdm iso} is generated such that it has the same primordial power A_s as the scalar perturbations, and similarly for Cl^{correlated}.

## Planck test

To check that we are getting reasonable results, we run the Fisher matrix with LCDM+Mnu+f_iso with Planck noise levels, beams, and fsky as specified in previous forecast checks.

We tested for fiducial cosmology f_iso=0 with 100% correlated CDM isocurvature modes; The following constraints use TT/EE/TE lensed spectra.

The following are the constraints we get:

LCDM+Mnu+f_iso=0 | |

och2 | 0.001523 |

obh2 | 0.000163 |

onuh2 | 0.005396 |

10^9 As | 0.2589 |

ns | 0.00486 |

tau | 0.0597 |

hubble | 4.84 |

f_iso | 0.00391 |

We are doing a literature search to find previous forecasts that uses a similar parameterization (as opposed to the alpha or beta parameterization) to compare our results.