Structure Formation in Non-local Bouncing Models

In this study, we investigate the growth of structures within the Deser-Woodard nonlocal theory and extend it to various bouncing cosmology scenarios. Our findings show that the observable structure growth rate, $f\sigma_8$, in a vacuum-dominated universe is finite within the redshift range of $0<z<2$, contrary to previous literature. Although $f\sigma_8$ exhibits no divergences, we observe a slight difference between the evolution of the $\Lambda$CDM and the non-local DW II models. Regarding structure formation in bouncing cosmologies, we evaluate the evolution of $f\sigma_8$ near the bouncing point. Among the different bouncing cases we explore, the oscillatory bounce and pre-inflationary asymmetrical bounce demonstrate a physical profile where the growth rate begins as a small perturbation in the early epoch and increases with inflation, which can be regarded as the seeds of large-scale structures. These findings are significant because they shed light on the growth of seed fluctuations into cosmic structures resulting from non-local effects.