Lower tensor-to-scalar ratio as possible signature of modified gravity

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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 $\mu-\Sigma$ 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.