Cosmological wormholes in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>theories of gravity

Motivated by recent proposals of possible wormhole existence in galactic halos, we analyze the cosmological evolution of wormhole solutions in modified $f(R)$ gravity. We construct a dynamical wormhole that asymptotically approaches a Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) universe, with supporting material going to the perfect isotropic fluid described by the equation of state for a 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 the reconstruction procedure and use $f(R)$ functions which lead to the experimentally confirmed $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ 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 epochs.

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