Phenomenological emergent dark energy versus the ΛCDM: ellipticity of cosmic voids

We disclose the influences of the phenomenological emergent dark energy (PEDE) and its generalization (GEDE) on the distribution of tidal ellipticity of the cosmic voids. We also compare our results with that of the standard Lambda CDM cosmology. The underlying models consist with recent observations (specially in favour of H0 tension) and may impact the cosmic voids geometry. We employ the analytic approach based on statistics of the tidal tensor eigenvalues. We confirm a significant sensitivity of the ellipticity distribution function for PEDE and GEDE cosmology. We observe the largest deviation from the standard cosmology for GEDE in the range ($z\gt 0, R_{\mathrm{L}}\ge 4\, h<^>{-1}\, \mathrm{Mpc}$). Working on these distribution functions we reveal that the mean ellipticity (<epsilon & rang;) profile of GEDE versus redshift lies below than that of PEDE and Lambda CDM indicating that GEDE leads to a less elongated society of voids with respect to other models. We also identify a tight correlation between sigma 8 and the mean ellipticity evolution. Finally, we explore the mean ellipticity versus RL and estimate that in this case GEDE leads to a different ellipticity curve (up to 11 ${{\ \rm per\ cent}}$ smaller than that of Lambda CDM).