# Testing scale-invariant inflation against cosmological data

**Authors:** Chiara Cecchini, Mariaveronica De Angelis, William Giarè, Massimiliano Rinaldi, Sunny Vagnozzi  
**arXiv:** [2403.04316](https://arxiv.org/abs/2403.04316)  
**Date:** 2024-03-07  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2403.04316v1/

## Key points

- Scale-invariance as a fundamental symmetry of Nature
- Focus on a classically scale-invariant inflationary model quadratic in curvature with scalar field non-minimally coupled to gravity
- Exploration of full two-field dynamics to validate earlier findings and establish constraints on model's parameters using latest CMB data
- Demonstration of how scale-invariance dictates trajectory of two fields, leading to single field-like dynamics with vanishing entropy perturbations
- Derivation of stringent upper limits on non-minimal coupling strength, ruling out conformal coupling at high significance levels
- Insensitivity to initial conditions within the model through explicit parameter sampling
- Prediction of minimum level of primordial tensor modes greater than or equal to 0.003, aligning with upcoming CMB experiments
- Importance of future CMB observations as crucial test for scale-invariant inflation and potential differentiation from other inflationary models like Starobinsky and $\alpha$-attractor inflation

## Summary

In their paper titled "Testing scale-invariant inflation against cosmological data," authors Chiara Cecchini, Mariaveronica De Angelis, William Giarè, Massimiliano Rinaldi, and Sunny Vagnozzi delve into the concept of scale-invariance as a fundamental symmetry of Nature. They focus on a recently proposed classically scale-invariant inflationary model that is quadratic in curvature and involves a scalar field non-minimally coupled to gravity. The researchers explore the full two-field dynamics of the system to validate earlier findings and establish robust constraints on the model's parameters using the latest Cosmic Microwave Background (CMB) data from Planck and BICEP/Keck. Through their analysis, they demonstrate how scale-invariance dictates the trajectory of the two fields, leading to effective dynamics resembling that of a single field. This phenomenon results in vanishing entropy perturbations and safeguards the model from destabilization effects. Moreover, they derive stringent upper limits on the non-minimal coupling strength and effectively rule out conformal coupling at high significance levels. By conducting explicit sampling over these parameters, they showcase an overall insensitivity to initial conditions within the model. Importantly, this particular inflationary model predicts a minimum level of primordial tensor modes with a value greater than or equal to 0.003—a prediction well within reach of upcoming CMB experiments. The researchers highlight that future CMB observations will serve as a crucial test for scale-invariant inflation and potentially distinguish it from other inflationary models like Starobinsky and $\alpha$-attractor inflation. Overall, they assert that scale-invariant inflation remains robust and possesses unique features that make it an intriguing benchmark for assessing inflation through forthcoming CMB data analyses.