Non-singular exponential gravity: a simple theory for early- and late-time accelerated expansion

Abstract: A theory of exponential modified gravity which explains both early-time inflation and late-time acceleration, in a unified way, is proposed. The theory successfully passes the local tests and fulfills the cosmological bounds and, remarkably, the corresponding inflationary era is proven to be unstable. Numerical investigation of its late-time evolution leads to the conclusion that the corresponding dark energy epoch is not distinguishable from the one for the $\Lambda$CDM model. Several versions of this exponential gravity, sharing similar properties, are formulated. It is also shown that this theory is non-singular, being protected against the formation of finite-time future singularities. As a result, the corresponding future universe evolution asymptotically tends, in a smooth way, to de Sitter space, which turns out to be the final attractor of the system.