Derive Lovelock Gravity from String Theory in Cosmological Background

It was proved more than three decades ago, that the first order ${\alpha }^{\mathrm{\prime }}$ correction of string effective theory could be written as the Gauss-Bonnet term, which is the quadratic term of Lovelock gravity. In cosmological background, with an appropriate field redefinition, we reorganize the infinite ${\alpha }^{\mathrm{\prime }}$ corrections of string effective action into a finite term expression for any specific dimension. This finite term expression matches Lovelock gravity exactly and thus fix the couplings of Lovelock gravity by the coefficients of string effective action. This result thus provides a strong support to string theory.