We study unified theory with gauge group SU(11). The subgroup SU(6) has been interpreted as a new type of energy source other than SU(5). We consider a (4 + D)-dimensional Friedmann-Robertson-Walker type Universe having complex scale factor R+iR_I, where R is the scale factor corresponding to the usual 4-dimensional Universe while R_I is that of D-dimensional space. It is then compared with (4+D)-dimensional Kaluza-Klein Cosmology having two scale factors R and a(= iR_I). It is shown that the rate of compactification of higher dimension depends on extra dimension 'D'. The Wheeler-DeWitt equation and general solution is obtained. It is founded that for D = 6 (i.e. in 10 dimension), the Wheeler-DeWitt equation is symmetric under the exchange R_I ? R.
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