Accelerating universe at the end of time
Gary Shiu, Flavio Tonioni, Hung V. Tran
Abstract
We investigate whether an accelerating universe can be realized as an asymptotic late-time solution of Friedmann--Lema\^{\i}tre--Robertson--Walker (FLRW)-cosmology with multifield multiexponential potentials. Late-time cosmological solutions exhibit a universal behavior which enables us to bound the rate of time variation of the Hubble parameter. In string-theoretic realizations, if the dilaton remains a rolling field, our bound singles out a tension in achieving asymptotic late-time cosmic acceleration. Our findings go beyond previous no-go theorems in that they apply to arbitrary multiexponential potentials and make no specific reference to vacuum or slow-roll solutions. We also show that if the late-time solution approaches a critical point of the dynamical system governing the cosmological evolution, the criterion for cosmic acceleration can be generally stated in terms of a directional derivative of the potential.