Observations across multiple cosmological probes indicate that the Universe possesses a non-zero cosmological constant, typically associated with vacuum energy density. However, the large discrepancy between observationally inferred and theoretically predicted vacuum energy densities, together with recent analyses in which combined SnIa, H(z), BAO, LSS, BBN, and CMB datasets mildly prefer models with a time-dependent cosmological parameter [1], shows the need to re-examine the assumption that Λ represents the constant vacuum energy density.

In this study, interaction field equations derived from an action incorporating bulk influence, which reduce to the Einstein field equations in the flat-background limit [2], are utilized. A comparison of this set of equations reveals that the effective cosmological parameter is associated with the normalized bulk conformal curvature term, giving rise to an evolving effective Λ influenced by the vacuum energy structure rather than by a fixed density. This framework provides a new perspective on the interpretation of the cosmological parameter and offers a natural reframing of the cosmological constant problem, in which the small observed value of Λ can be understood as reflecting the weak curvature of the bulk while remaining consistent with current observational trends.

References

[1] Solà Peracaula, J., Gómez-Valent, A., de Cruz Pérez, J., & Moreno-Pulido, C. (2023). Running vacuum in the Universe: Phenomenological status in light of the latest observations, and its impact on the σ8 and H0 tensions. Universe, 9(6), 262. https://doi.org/10.3390/universe9060262

[2] Al-Fadhli, M. B. (2023). Gravitational, Electromagnetic and Quantum Interaction: From String to Cloud Theory. Presented at the 2nd Electronic Conference on Universe, 16 February–2 March 2023. Phys. Sci. Forum, 7(1), 55. https://doi.org/10.3390/ECU2023-14063