# Quasi-cosmological Traversable Wormholes in $f(R)$ Gravity

## TL;DR

This paper explores traversable wormholes within $f(R)$ gravity, finding exact solutions that can satisfy energy conditions unlike in Einstein gravity, and matching various FRW metrics.

## Contribution

It provides new exact wormhole solutions in $f(R)$ gravity that respect energy conditions, expanding possibilities beyond Einstein gravity.

## Key findings

- Wormhole solutions can satisfy NEC at the throat in $f(R)$ gravity.
- Some models respect WEC throughout the space.
- Solutions match spherical, flat, and hyperbolic FRW metrics.

## Abstract

In this paper we study traversable wormholes in the context of $f(R)$ gravity. Exact solutions of traversable wormholes are found by imposing the nonconstant Ricci scalar. These solutions asymptotically match spherical, flat and hyperbolic FRW metric. By choosing some static $f(R)$ gravity models, we verify the standard energy conditions for the asymptotically spherical, flat and hyperbolic wormhole solutions. Unlike the Einstein gravity, we find that in the context of $f(R)$ modified gravity, the asymptotically spherical, flat and hyperbolic wormhole solutions can respect the null energy condition (NEC) at the wormhole throat and near that. We find that in some static $f(R)$ models, asymptotically flat and hyperbolic wormholes respect the weak energy condition (WEC) through the whole space.