Fifth force potentials, compared to Yukawa modification of Gravity for massive Gravitons, to link Gravitation, and NLED modified GR

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1 1 Fifth foce potentials, compaed to Yukawa modification of Gavity fo massive Gavitons, to link Gavitation, and NED modified GR A. B. Beckwith Physics Depatment, Chongqing Univesity, Chongqing 40014, PRC We use a linkage between gavitation and electodynamics the autho shaed with Unnishkan. Fist step will be to wite up a Yukawa potential modification of Gavity fo the usual 1/ potential, and compaing it to fifth foce potentials.. Details as to NED and Unnishkhan s theoies ae added fo an electomagnetic flavo to fifth foce consideations. eading to a fist pinciple evaluation of the pimodial gaviton mass as linked to NED. Keywods: heavy gavity, fifth foces 1. Intoduction; defining the poblem in tems of ij We stat off with a desciption of both the Fifth foce hypothesis of Fishbach and Talmadge[1] as well as what Unnishkan bought up in Rencontes De Moiond[,3] with one of the pedictions dove tailing closely with use of Gavitons as poduced by ealy univese phase tansition behaviou, leading to how QM elates to a semi classical appoximation fo E and M and othe physical pocesses. Fo the Fifth foce used, we use Fishbach[1], namely V 5th foce G mi m j 1ij exp( / ) (1) Hee, then if mi i m, and if H f G m H, then Q Q () ij i j i j Eq. (1) and Eq.() should be compaed with the gavitational potential of a Yukawa type which looks like Wok patially suppoted by National Natue Science Foundation of China gant No

2 V heavygavity G mi m j exp( mgaviton ) (3) If we take the spatial deivatives of Eq. (1) and Eq. (3) with espect to, and equate the esults fo foce, we obtain that the ange of the fifth foce is ij mgaviton ( small ) ij ij (# 0) 1 mgaviton (4) We will now detemine something of the foces connected with Eq.(1) and Eq.(3) to see if the fifth foce is, indeed, almost infinite in duation. And this will entail looking at the influence of what the fifth foce chages as we can detemine them due to the suggestion made by D. Unnishkan in Rencontes Du Moiond [,3]. Obtaining moe pecise infomation fo the fifth foce chages, as to ask how applicable Eq.(4) is, when we conside Heavy Gavity. This is Q Q / G m m i j i j 1 3 (5) The fist pat of ou document will compae the foce so ceated by Eq.(1) with the situation ceated by a moe typical Yukawa potential fo gavity when thee is a massive Gaviton, with a value initially calculated as in the conclusion. We have that Unnishkan shaed in Rencontes Du Moiond [,3] which is an extension of what he did in [3], i.e. looking at, if i & i 1 ae cuents in electicity and magnetism, and i1 g & i g m1v 1 & mv, ae what we do with a linkage between Gavity and electomagnetism with mv 1 1and mv the mass times the velocity of paticle 1 and paticle, so that the following, up to a point holds i1g ig i i q v ( q v ) G G m v ( m v ) k ~ c c E& M Gavity da N dvi c (6) (7)

3 The above elationship with its focus upon inteexchange elations between gavity and magnetism is in a wod focused upon looking at, if A, the nominal vecto potential used to define the magnetic field as in the Maxwell equation, the elationship we will be using at the beginning of the expansion of the univese, is a vaiation of the quantized Hall effect, i.e. fom Baett [4], the cuent I about a loop with egads to electonic enegy U, of a loop with the A vecto potential going though the loop is given by, if is a unit spatial length, and we appoximate the beginning of the univese as having some of the same chaacteistics as a quantized Hall effect, then, if n is a paticle count, then [4] U I( cuent) ( c / ) A n c e A (8) We will be taking the ight hand side of the A field, in the above, and appoximate Eq.(4) as given by 3 da dn c e (9) Then, we have an appoximation fo witing [4] da dn N dvi dn 3 dvi c e N c e / c (10) Eq. (10) needs to be intepolated, up to a point. I.e. in this case, we will conflate the n, hee as a gaviton count, initially, i.e. the numbe of ealy univese gavitons, then assume that dvi / is a net acceleation tem linked to the beginning of inflation, i.e. that we look then at Ng s infinite quantum statistics [5], with entopy given as, initially a count of gavitons,. Then, we efe to the n of Eq. (5) to Eq. (7) being the numbe of paticles, and entopy is by Ng, [5] S ~ n gavitons.this shows up in the end of ou document.. Entopy, its spatial configuation nea a singulaity and how we use this definition, with NED inputs The usual teatment of entopy, if thee is the equivalent of a event hoizon is, that ( Padmanabhan) [6] with citial to be set at the end of the aticle. And in Eq. (7) is of the ode of magnitude popotional to P. i.e. also to be set at the end of this aticle, i.e. we will suggest a fomal elationship between and P. Hee

4 4 1 c S( classical entopy) 4 Enegy G 4 citial 4P citial (11) If so, then we have that fom fist pinciples dn d (1) 1 citical ~ P citical Then Eq. (7) is e witten in tems of [4] adopted fomulation as given by dn dv d dv N 3 i citical citical i 3 c e / c e P (13) The following paametes will be identified, i.e. what is dvi /, what is, and what is citical. These values will be set towad the end of the manuscipt, with the consequences of the choices made discussed in this document as suggested new aeas of inquiy. Howeve, Eq.(13) will then imply 1 da d citical citical ~ c P e (14) If the value of the time deivative of citical is AMOST time independent, Eq.(14) will then lead to a pimodial value of the A vecto field, fo which we can set the E field 1 dcitical dcitical E ~ c c e citical t P (15) To econstuct we have that we will use 1 A c by [4]. Then if t d t c e P citical ~ (16) The density, then is ead as by [4] d 1 1 citical ~ c 4 c t P e (17)

5 5 The cuent we will wok with, is by ode of magnitude [4] simila to Eq.(18) 1 A dcitical J ~ c e 4c t P (18) Then we get a magnetic field, based upon the NED appoximation [7,8] 16 1 d 3 4 citical c1 B ~ c e P 3 d citical Binitial ~ c e 3 P c1 1/4 (19) Then we can also talk about an effective chage of the fom, given by applying Gauss s law to Eq.(0) of the fom 3 d citical citical Q 0 E nda dv ~ 3 c e S V P (0) This chage, Q, so pesented, will be pat of the effective 5 th foce [1], as to linking E and M and gavity, of Eq. (1). Futhemoe, d c Enegy ~ c B ~ c e ~ citial citical citial citial citial 3 P G (1) Then dcitical / ~ c, and by Padmabhan [9], G 3 Pc 37, so n ~ 10 and initial 4 4 P c c P ninitial citial ~ ninitial Einitial citial ~ () G G 3. Conclusion. We obtain a lowe bound fo the Magnetic field implying a gaviton fequency, and we set the gaviton fequency accoding to the magnetic field being initially less than 1 To with the E and B fields of the same magnitude, using [8] 1 B (3) 10 0

6 6 37 and the initial E field is given by Eq. (), then if n initial ~ 10 ~ N fo a gaviton count in a univese smalle than 1 mete in diamete, is then ij sufficiently small so Eq. (4) in its limits hold, as well. In addition by having 3 1 initial ~ 10 Hz and [9]and [10] using c 1 N N H ~1mete gaviton, with H G m gaviton () (4) c 3 if we ae using n n( paticles ) n( gavitons ) N. Note that the numeical values then link a setting of gaviton mass diectly to the value of the E field. We should compae this N with the todays entopy, with S ~ N given in [11]. Refeences 1.E. Fishbach,C.Talmadge, The Seach fo Non Newtonian Gavity, Spinge-Velag, NewYok, New Yok, USA, C.S. Unnikishnan, fom Rencontes De Moiond, 015, Gavitation, Mach, 015, 3. C. S. Unnikishnan, Int. Jounal. Mod. Phys. (014) WAG T.W. Baet, Topological Foundations of Electomagnetism, Wold Pess Scientific, Wold Scientific Seies in Contempoay Chemical Physics, Volume 6, Singapoe, Republic of Singapoe, Y. Jack Ng, Hologaphic foam, dak enegy and infinite statistics, Phys. ett. B, 657, (007), pp T. Padmanabhan, Gavitation, Foundations and Fonties, Cambidge Univesity Pess, New Yok, New Yok, USA, C. Coda, H. Cuesta Removing Black Hole singulaities with Non inea Electodynamics, Moden Physics A, Volume 5, No. 8 (010), PP C.S. Camaa, M.R. de Gacia Maia, J.C. Cavalho, and J.A.S. ima, Nonsingula FRW cosmology and Non inea dynamics, 9. Padmanabhan, COSMOOGICA CONSTANT THE WEIGHT OF THE VACUUM axiv:hep-th/0190v 6 Feb A. F. Ali, S. Das Cosmology fom Quantum Potential, Physics ettes B 741, (015),pp I. Haanas and I. Gkigkitzis, The Mass of Gaviton and Its Relation to the Numbe of Infomation accoding to the Hologaphic Pinciple, Intenational Scholaly Reseach Notices,Volume014(014),8 pages, 11. C. Egan and C. H. ineweave, A ARGER ESTIMATE OF THE ENTROPY OF THE UNIVERSE, The Astophysical Jounal, 710: , 010 Febuay 0