Title: From infinite to infinitesimal: Using the Universe as a dataset to probe Casimir corrections to the vacuum energy from fields inhabiting the dark dimension

Abstract: Promptly after high-resolution experiments harbinger the field of precision cosmology low- and high-redshift observations abruptly gave rise to a tension in the measurement of the present-day expansion rate of the Universe ($H_0$) and the clustering of matter ($S_8$). The statistically significant discrepancies between the locally measured values of $H_0$ and $S_8$ and the ones inferred from observations of the cosmic microwave background assuming the canonical $\Lambda$ cold dark matter (CDM) cosmological model have become a new cornerstone of theoretical physics. $\Lambda_s$CDM is one of the many beyond Standard Model setups that have been proposed to simultaneously resolve the cosmological tensions. This setup relies on an empirical conjecture, which postulates that $\Lambda$ switched sign (from negative to positive) at a critical redshift $z_c \sim 2$. We reexamine a stringy model that can describe the transition in the vacuum energy hypothesized in $\Lambda_s$CDM. The model makes use of the Casimir forces driven by fields inhabiting the incredible bulk of the dark dimension scenario. Unlike the $\Lambda_s$CDM setup the model deviates from $\Lambda$CDM in the early universe due to the existence of relativistic neutrino-like species. Using the Boltzmann solver CLASS in combination with MontePython we confront predictions of the stringy model to experimental data (from the Planck mission, Pantheon+ supernova type Ia, BAO, and KiDS-1000). We show that the string-inspired model provides a satisfactory fit to the data and can resolve the cosmological tensions.