Cosmological wormholes in $f(R)$ theories of gravity

TL;DR

This paper investigates the evolution of cosmological wormholes within $f(R)$ gravity, showing that certain solutions can exist without exotic matter and align with the universe's expansion history.

Contribution

It constructs dynamical wormhole solutions in $f(R)$ gravity that match FLRW cosmology and do not require exotic matter, unlike in standard General Relativity.

Findings

Wormholes can asymptotically approach FLRW universe.

No exotic matter needed near the wormhole throat in $f(R)$ models.

Solutions are consistent with $ ext{Λ}$CDM expansion history.

Abstract

Motivated by recent proposals of possible wormhole existence in galactic halos, we analyse the cosmological evolution of wormhole solutions in modified $f(R)$ gravity. We construct a dynamical wormhole that asymptotically approaches FLRW universe, with supporting material going to the perfect isotropic fluid described by the equation of state for radiation and matter dominated universe respectively. Our analysis is based on an approximation of a small wormhole - a wormhole that can be treated as matched with the FLRW metric at some radial coordinate much smaller than the Hubble radius, so that cosmological boundary conditions are satisfied. With a special interest in viable wormhole solutions, we refer to the results of reconstruction procedure and use $f(R)$ functions which lead to the experimentally confirmed $\Lambda$CDM expansion history of the Universe. Solutions we find imply no need for exotic matter near the throat of considered wormholes, while in the limit of $f(R)=R$ this need is always present during radiation and matter dominated epoch.