**Authors:** Andrew Beckwith

The case for a four dimensional graviton mass (non zero) influencing reacceleration of the universe in five dimensions is stated; with emphasis upon if five dimensional geometries as given below give us new physical insight as to cosmological evolution. A calculated inflaton φ(t) may partly reemerge after fading out in the aftermath of inflation. The inflaton may be the source of re acceleration of the universe, especially if the effects of a re emergent inflaton are in tandem with the appearance of macro effects of a small graviton mass, leading to a speed up of the rate of expansion of the universe at red shit value of Z ~ .423. A final statement as to how and why the radius of the universe question may be affected by these deliberations is presented , in terms of if the graviton is either purely a field theoretic , or semi classical object, as via t'Hoofts deterministic QM is presented in the end, as an open question.

**Comments:** 16 pages, four figures. Re statement of prior submission, with specific
commentary as given in Appendix B, and also the radius of the Universe question , as
can be ascertained via modeling included. This material added, to make presentation
conform more closely to the Xian, PRC PIERS presentation given in 2010, March 22, at
11 a.m. which did emphasize, at the end the importance of material in Appendix B, as
well as the given conclusion, and the radius of the Universe question, as of Eq. (38),
as very important to applications of GW/ graviton based astronomy/ astro physics.
Appendix B in particular delves into how massless graviton Field equations, and their
small mass graviton versions do not connect, in the limit of mass of a graviton
approaching zero.

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[v1] 16 Mar 2010

[v2] 28 Mar 2010

[v3] 29 Mar 2010

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