# Do joint CMB and HST data support a scale invariant spectrum?

## TL;DR

This paper assesses whether combining CMB, HST, and BBN data supports a scale-invariant spectrum, finding that certain extensions with additional parameters are favored by Bayesian analysis.

## Contribution

It provides a Bayesian analysis of the scale invariant Harrison-Zeldovich-Peebles spectrum and its extensions using combined cosmological data sets.

## Key findings

- HZP + $N_{eff}$ model is favored over standard cosmology.
- Preferred $N_{eff}$ value is around 3.70 ± 0.13.
- Extensions with $Y_P$ and $N_{eff}$ improve data fit.

## Abstract

We combine current measurements of the local expansion rate, $H_0$, and Big Bang Nucleosynthesis (BBN) estimates of helium abundance with the latest cosmic microwave background (CMB) data from the Planck Collaboration to discuss the observational viability of the scale invariant Harrison-Zeldovch-Peebles (HZP) spectrum. We also analyze some of its extensions, namely, HZP + $Y_P$ and HZP + $N_{eff}$, where $Y_P$ is the primordial helium mass fraction and $N_{eff}$ is the effective number of relativistic degrees of freedom. We perform a Bayesian analysis and show that the latter model is favored with respect to the standard cosmology for values of $N_{eff}$ lying in the interval $3.70 \pm 0.13$ ($1\sigma$), which is currently allowed by some independent analyses.