  In this work we demonstrate that wormholes can in principle be naturally
created during the cosmological bounce without the need for the exotic matter
or any kind of additional modifications of the gravitational sector, apart from
the one enabling the cosmological bounce. This result is general and does not
depend on the details of the modifications of gravitational equations needed to
support the bounce. To study the possible existence of wormholes around the
cosmological bounce we introduce general modifications of Einstein's field
equations need to support the bouncing solutions. In this regime we show that
it is possible to construct a cosmological wormhole solution supported by
matter, radiation and vacuum energy, satisfying the Weak Energy Condition
(WEC), which asymptotically approaches the
Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) metric. However, at a specific
cosmological time, which depends on the parameters of the bouncing cosmological
model, the WEC describing the matter needed to support such wormholes is
spontaneously violated. This means that such wormholes could potentially exist
in large numbers during some period around the bounce, significantly changing
the causal structure of space-time, and then vanish afterwards.
