Abstract
A class of cosmological solutions is found to the vacuum field equations of an effective field theory derived from string theory in a -dimensional spacetime. This effective field theory concerns only the massless sector of the parent string theory. In order to make it operationally accessible, it has been proposed that the notion of the dimension of spacetime be based on measure-theoretic concepts, thus admitting the possibility of non-integer dimensions. As a consequence of the dimension of actual spacetime less than four , a relativistic quantum field theory becomes finite. Also, the radiative corrections of perturbation theory are sensitive to the actual value of the dimension . Present experimental results and standard theoretical predictions for the electromagnetic moment of the electron seem to suggest a non-vanishing value for . We take . In this paper, it has been proved that the coupling coefficients of high-order terms of the equations of the effective field theory depend on the value of . The results have been compared with the ones in the literature.
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