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

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