Does negative energy in Casimir effect cause repulsive gravity? In the Casimir effect a negative vacuum energy exists between two plates. Does this cause repulsive gravity?
Can this have consequences for the situation near the big bang, in relation to inflation?
 A: You are talking of this:

In the Casimir effect, two flat plates placed very close together restrict the wavelengths of quanta which can exist between them. This in turn restricts the types and hence number and density of virtual particle pairs which can form in the intervening vacuum and can result in a negative energy density.

you ask:

Can this have consequences for the situation near the big bang, in relation to inflation?

I suppose you mean that "as negative energy can exist", will this have consequences in the inflation era.
If you search there are a number of models  that use the concept of negative energy, example from the abstract

We find a unique way of realizing inflation through cyclic phases in an universe with negative vacuum energy.

Also in the cosmological models, negative energy, if it exists, plays a role.

in a universe in which positive energy dominates will eventually collapse in a "Big Crunch", while an "open" universe in which negative energy dominates will either expand indefinitely or eventually disintegrate in a "big rip"

