Sub-Planckian scale and limits for $f(R)$ models

TL;DR

This paper investigates the evolution of the universe from sub-Planckian scales within $f(R)$ gravity models, identifying parameter restrictions necessary for exponential expansion consistent with observations.

Contribution

It provides new constraints on $f(R)$ models by analyzing universe evolution from sub-Planckian scales to the present, considering initial conditions and expansion requirements.

Findings

Restrictions on $f(R)$ parameters for exponential expansion

Initial universe modeled as maximally symmetric with positive curvature

Conditions for $f(R)$ models to match observed universe evolution

Abstract

We study the Universe evolution starting from the sub-Planckian scale to present times. The requirement for an exponential expansion of the space with the observed metric as a final stage leads to significant restrictions on the parameter values of a $f(R)$-function. An initial metric of the Universe is supposed to be maximally symmetric with the positive curvature.