# Constraining the Break of Spatial Diffeomorphism Invariance with Planck Data

## TL;DR

This paper uses recent CMB data to constrain models with broken spatial diffeomorphism invariance, exploring their ability to produce a blue tensor spectrum and comparing their viability to standard inflation and String Gas Cosmology.

## Contribution

It provides the first observational constraints on the SDB model using Planck data and compares its predictions with other early universe scenarios.

## Key findings

- Weak evidence for SDB model when the inflation consistency relation is relaxed.
- Strong evidence for the standard inflation model when the relation is imposed.
- SDB model can generate a blue tensor spectrum compatible with observations.

## Abstract

The current most accepted paradigm for the early universe cosmology, the inflationary scenario, shows a good agreement with the recent Cosmic Microwave Background (CMB) and polarization data. However, when the inflation consistency relation is relaxed, these observational data exclude a larger range of red tensor tilt values, prevailing the blue ones which are not predicted by the minimal inflationary models. Recently, it has been shown that the assumption of spatial diffeomorphism invariance breaking (SDB) in the context of an effective field theory of inflation leads to interesting observational consequences. Among them, the possibility of generating a blue tensor spectrum, which can recover the specific consistency relation of the String Gas Cosmology, for a certain choice of parameters. We use the most recent CMB data to constrain the SDB model and test its observational viability through a Bayesian analysis assuming as reference an extended LCDM+tensor perturbation model, which considers a power-law tensor spectrum parametrized in terms of the tensor-to-scalar ratio, r, and the tensor spectral index, n_t. If the inflation consistency relation is imposed, r = -8n_t, we obtain a strong evidence in favor of the reference model whereas if such relation is relaxed, a weak evidence in favor of the model with diffeomorphism breaking is found. We also use the same CMB data set to make an observational comparison between the SDB model, standard inflation and String Gas Cosmology.