Multi-Dimensional Cosmology and DSR-GUP

A multidimensional cosmology with FRW type metric having 4-dimensional space-time and $d$-dimensional Ricci-flat internal space is considered with a higher dimensional cosmological constant. The classical cosmology in commutative and DSR-GUP contexts is studied and the corresponding exact solutions for negative and positive cosmological constants are obtained. In the positive cosmological constant case, it is shown that unlike the commutative as well as GUP cases, in DSR-GUP case both scale factors of internal and external spaces after accelerating phase will inevitably experience decelerating phase leading simultaneously to a big crunch. This demarcation from GUP originates from the difference between the GUP and DSR-GUP algebras. The important result is that unlike GUP which results in eternal acceleration, DSR-GUP at first generates acceleration but prevents the eternal acceleration at late times and turns it into deceleration.