Probing dynamical embeddings in a five-dimensional spacetime in light of DESI BAO

Capistrano A.J.S. Silva E. Nunes R.C. Luongo O.
13 January 2026 American Physical Society

Physical Review D
2026 #113 Issue 2 1 - 13 pp.

We investigate the observational viability of Nash gravity as an alternative to the standard ΛCDM cosmology. Based on Nash’s embedding theorem, the model introduces orthogonal perturbations via variations in the extrinsic curvature, generating scalar-type metric perturbations directly from geometry, without the need to introduce additional fields. We confront the model with current observational data, including cosmic microwave background measurements from Planck, baryon acoustic oscillations from DESI-DR2, and recent type Ia supernova compilations. Our analysis shows that Nash gravity provides a good fit to the data, yielding a slightly higher value for the Hubble constant, H0 = 69.320.72km=s=Mpc, compared with the ΛCDM model, thus offering a potential alleviation of the H₀ tension. Furthermore, the model naturally predicts a suppressed growth of structure, with S₈ ≈ 0.76 across various joint analyses, potentially alleviating the so-called S₈ tension, assuming that this discrepancy is not solely due to systematic effects in other independent measurements. In some cases, Nash gravity achieves a better fit to the data than the ΛCDM paradigm at the 2σ level.

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Universidade Federal do Paraná, Departmento de Engenharia e Exatas, Brasil and Federal University of Latin American Integration (UNILA), Applied physics graduation program, Avenida Tarquínio Joslin dos Santos, 1000-Polo Universitário, Foz do Iguaçu, Rua Pioneiro, 2153, 85950-000, Paraná/PR, Palotina, 85867-670, Brazil
Instituto de Física, Universidade Federal do Rio Grande do Sul, RS, Porto Alegre, 91501-970, Brazil
Divisão de Astrofísica, Instituto Nacional de Pesquisas Espaciais, Avenida dos Astronautas, São Jos´e dos Campos, São Paulo, 12227-010, Brazil
Department of Nanoscale Science and Engineering, University at Albany-SUNY, Albany, 12222, NY, United States
Universit`a di Camerino, Divisione di Fisica, Via Madonna delle carceri 9, Camerino, 62032, Italy
INFN, Sezione di Perugia, Perugia, 06123, Italy
INAF - Osservatorio Astronomico di Brera, Milano, Italy
Al-Farabi Kazakh National University, Al-Farabi Avenue 71, Almaty, 050040, Kazakhstan

Universidade Federal do Paraná
Instituto de Física
Divisão de Astrofísica
Department of Nanoscale Science and Engineering
Universit`a di Camerino
INFN
INAF - Osservatorio Astronomico di Brera
Al-Farabi Kazakh National University

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