This paper simplifies the induced four-dimensional gravitational equations originating from a five-dimensional bulk within the framework of Nash's embeddings, incorporating them into a well-known μ−Σ modified gravity (MG) parametrization. By leveraging data from Planck Public Release 4 (PR4), BICEP/Keck Array 2018, Planck cosmic microwave background lensing, and baryon acoustic oscillation observations, we establish a stringent lower limit for the tensor-to-scalar ratio parameter: r<0.0303 at a confidence level (CL) of 95\%. This finding suggests the presence of extrinsic dynamics influencing standard four-dimensional cosmology. Notably, this limit surpasses those typically obtained through Bayesian analysis using Markov Chain Monte Carlo (MCMC) techniques, which yield r<0.038, or through the frequentist profile likelihood method, which yields r<0.037 at 95\% CL.
@article{arxiv.2403.13860,
title = {Lower tensor-to-scalar ratio as possible signature of modified gravity},
author = {Abraão J. S. Capistrano and Rafael C. Nunes and Luís A. Cabral},
journal= {arXiv preprint arXiv:2403.13860},
year = {2024}
}