Fermionic condensate in de Sitter spacetime

Fermionic condensate is investigated in $(D+1)$-dimensional de Sitter spacetime by using the cutoff function regularization. In order to fix the renormalization ambiguity for massive fields an additional condition is imposed, requiring the condensate to vanish in the infinite mass limit. For large values of the field mass the condensate decays exponentially in odd dimensional spacetimes and follows a power law decay in even dimensional spacetimes. For a massless field the fermionic condensate vanishes for odd values of the spatial dimension $D$ and is nonzero for even $D$. Depending on the spatial dimension the fermionic condensate can be either positive or negative. The change in the sign of the condensate may lead to instabilities in interacting field theories.