# On the Expanding Phase of a Singular Bounce and Intermediate Inflation: The Modified Gravity Description

## TL;DR

This paper explores the connection between singular bounce cosmology and intermediate inflation within modified gravity theories, analyzing their implications on the power spectrum and observational viability.

## Contribution

It demonstrates that a Type III singular bounce can replicate intermediate inflation and evaluates the power spectrum in various modified gravity models.

## Key findings

- Intermediate inflation is a Type III singular cosmology.
- A Type III singular bounce can mimic intermediate inflation.
- Power spectrum calculations show viability within certain modified gravity models.

## Abstract

We demonstrate that the intermediate inflation scenario, is a singular inflation cosmology, with the singularity at the origin $t=0$ being a pressure and energy density singularity and particularly a Type III singularity. Also, we show that the expanding phase of a singular bounce, can be identical to the intermediate inflation scenario, if the singular bounce has a Type III singularity at the origin. For the intermediate inflation scenario we examine the cosmological implications on the power spectrum in the context of various forms of modified gravity. Particularly we calculate the power spectrum in the context of $F(R)$, $F(G)$ Gauss-Bonnet gravity and also for $F(T)$ gravity and we discuss the viability of each scenario by comparing the resulting spectral index with the latest observational data.