In this paper, we would like to examine whether a novel
Starobinsky-Bel-Robinson gravity model admits stable exponential inflationary
solutions with or without spatial anisotropies. As a result, we are able to
derive an exact de Sitter inflationary to this Starobinsky-Bel-Robinson model.
Furthermore, we observe that an exact Bianchi type I inflationary solution does
not exist in the Starobinsky-Bel-Robinson model. However, we find that a
modified Starobinsky-Bel-Robinson model, in which the sign of coefficient of
R2 term is flipped from positive to negative, can admit the corresponding
Bianchi type I inflationary solution. Unfortunately, stability analysis using
the dynamical system approach indicates that both of these inflationary
solutions turn out to be unstable. Interestingly, we show that a stable de
Sitter inflationary solution can be obtained in the modified
Starobinsky-Bel-Robinson gravity.Comment: 26 pages, 2 figures. V2 with the abstract revised to improve its
clarity, some relevant references added, and some typos fixed. All main
calculations and conclusions remain unchanged. Comments are welcom