The de Sitter spacetime as an attractor solution in fourth-order gravity

Abstract

Continues the investigation by Starobinsky and Schmidt (1987) on a general vacuum solution of fourth-order gravity. Now the author includes the Bach tensor. For L2=1/3( mu R2)+1/2( alpha C2) the expanding de Sitter spacetime is an attractor in the set of axially symmetric Bianchi type-I models if and only if alpha mu <or=0 or alpha >4 mu holds. (The absence of tachyons in LE=R/2x+L2 implies alpha mu <or=0!) It will be argued that this result holds true for a large class of inhomogeneous models. A new closed-form cosmological solution is obtained. Finally, the author proves a general conformal equivalence theorem between Lg=L(R)+1/2( alpha C2) and L0=(R/2x)-1/2( phi ;i phi ;i)+V( phi )+1/2( alpha C2). Therefore, de Sitter spacetime is also an attractor for the Bach-Einstein gravity with a minimally coupled scalar field phi . Specialised to Einstein gravity (i.e. alpha =0 above) this conformal equivalence remains a non-trivial one.