---
abstract: |
    The aim of this paper is to answer the following two questions: (1) Given cosmological observations of the expansion history and linear perturbations in a range of redshifts and scales as precise as is required, which of the properties of dark energy could actually be reconstructed without imposing any parameterization? (2) Are these observables sufficient to rule out not just a particular dark energy model, but the entire general class of viable models comprising a single scalar field?

    This paper bears both good and bad news. On one hand, we find that the goal of reconstructing dark energy models is fundamentally limited by the unobservability of the present values of the matter density $\Omega_{\text{m}0}$, the perturbation normalization $\sigma_{8}$ as well as the present matter power spectrum. On the other, we find that, under certain conditions, cosmological observations can nonetheless rule out the entire class of the most general single scalar-field models, i.e. those based on the Horndeski Lagrangian.
author:
- Luca Amendola
- Martin Kunz
- Mariele Motta
- 'Ippocratis D. Saltas'
- Ignacy Sawicki
bibliography:
- 'observables.bib'
title: Observables and unobservables in dark energy cosmologies
---

Introduction
============

Research in dark energy (DE) cosmology is generally 