Limits on the time evolution of space dimensions from Newton's constant

摘要

Limits are imposed upon the possible rate of change of extra spatial dimensions in a decrumpling model Universe with time variable spatial dimensions (TVSD) by considering the time variation of (1 + 3)-dimensional Newton's constant. Previous studies on the time variation of (1 + 3)-dimensional Newton's constant in TVSD theory had not include the effects of the volume of the extra dimensions and the effects of the surface area of the unit sphere in D-space dimensions. Our main result is that the absolute value of the present rate of change of spatial dimensions to be less than about 10(-14) yr(-1). Our results would appear to provide a prima facie case for ruling the TVSD model out. We show that based on observational bounds on the present variation of Newton's constant, one would have to conclude that the spatial dimension of the Universe when the Universe was "at the Planck scale" to be less than or equal to 3.09. If the dimension of space when the Universe was "at the Planck scale" is constrained to be fractional and very close to 3, then the whole edifice of TVSD model loses credibility.