Light Speed Expansion and Rotation of a Very Dark Machian Universe Having Internal Acceleration

Home , Black hole cosmology, Dwarf galaxy, Dwarf spiral galaxy, Hubble volume

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LIGHT SPEED EXPANSION AND ROTATION OF A VERY DARK MACHIAN UNIVERSE HAVING INTERNAL ACCELERATION

U.V.S. Seshavatharam1 and S. Lakshminarayana2

1Honorary faculty, I-SERVE, Survey no-42, Hitech city, Hyderabad-84,Telangana, India 2 Dept. of Nuclear Physics, Andhra University, Visakhapatnam-03,AP, India Emails: [email protected] (and) [email protected] Orcid numbers : 0000-0002-1695-6037 (and) 0000-0002-8923-772X

Abstract: We present a Machian model of Quantum Cosmology with full dark matter and light speed expansion and rotation. During galaxy formation and evolution, fraction of dark matter transforms to visual matter with a relation of the form, m_vis = constant * (m_dark)^2/3. Using this relation and replacing MOND’s ‘critical acceleration’ with “current cosmic maximum angular acceleration”, galactic flat rotation speed range of (50 to 500) km/sec can be fitted well. Estimated flat rotation speeds of DD168, Milky Way and UGC12591 are 49.96 km/sec, 199.66 km/sec and 521.75 km/sec respectively. Based on these striking coincidences, it is possible to say that, MOND’s approach is implicitly connected with cosmological estimation of 95% invisible matter. Considering galactic total matter and current cosmic maximum angular acceleration, galactic working radii, angular velocity and visual matter density can be estimated. Even though, this model is free from ‘big bang’, ‘inflation’, ‘dark energy’, ‘flatness’ and ‘red shift’

issues, at T0  2.722 K , estimated present Hubble parameter is H0  66.24 km/Mpc/sec, cosmic radius is 146.3 times the Hubble radius, angular velocity is 146.3 times lower than the Hubble parameter and cosmic age is 146.3 times the Hubble age. With future observations and advanced telescopes, it may be possible to see far distant galaxies and very old stars far beyond the current observable cosmic radius.

Keywords: Planck scale; Machian universe; Speed of light; Galactic dark matter; Galactic visible mass; Galactic visible mass density; Cosmic anisotropy; Galactic internal acceleration; Cosmic graviton wavelength;

1. Introduction looked the same in every direction around us, but not around other points in the universe”. We would like to emphasize the fact that, the basic principles of cosmology were developed when the In our earlier and recent published papers subject of cosmology was in its budding stage. [3-20] we tried to highlight the basic drawbacks of Friedmann made two simple assumptions about the big bang, inflation and galactic red shift in various universe [1,2]. They can be stated in the following possible ways. As of now, theoretically and observa- way. tionally, with respect to inflation, isotropy, expansion speed, dark matter, dark energy and rotation, whole 1) When viewed at large enough scales, universe subject of cosmology is being driven into many con- appears the same in every direction. troversies and dividing cosmologists into various 2) When viewed at large enough scales, universe groups with difference of opinions. On the other hand, appears the same from every location. very unfortunate thing is that, quantum cosmology point of view, ‘as a whole’, progress is very poor [21]. In this context, Hawking expressed that [2]: “There is Instead of discussing the controversies, we would no scientific evidence for the Friedmann’s second like to propose a new model which can pave a new assumption. We believe it only on the grounds of way for understanding and correlating astrophysical modesty: it would be most remarkable if the universe and cosmological observations in terms of quantum

[20] Seshavatharam UVS and Lakshminarayana S. (2020) Light speed expansion and rotation of a primordial cosmic black hole universe having internal acceleration. International Astronomy and As- trophysics Research Journal. 2(2): 9-27.

A review on Reference [20]

mechanics and general theory of relativity in a Ma- have developed a very tight quantum gravity relation chian view. It needs further study. for correlating cosmic temperature and Hubble parameter independent of galactic red shifts and galactic With reference to our very recent publica- distances. It can be applied to different time periods tion [20], in this version, of the past.

1) Implemented Mach’s relation in place of 2. Holographic principle and Mach’s relation Schwarzschild radius of black hole. 2) We tried to couple cosmic gravitational self According to G’t Hooft, the combination of energy density and cosmic thermal energy den- quantum mechanics and gravity requires the three sity. dimensional world to be an image of data that can be 3) Tried to define the Gamma parameter with the stored on a two dimensional projection much like a ratio of past and current temperatures [10,11]. It holographic image [35,36]. The ‘holographic prin- helps in estimating the Hubble parameter with a ciple’ is a property of string theory and a supposed direct relation rather than trial-error approach. property of quantum gravity that states that the de- 4) Made an attempt to bring clarity in the estima- scription of a volume of space can be thought of as tion of galactic dark matter. encoded on a lower-dimensional boundary. Based on 5) Tried to define a dark matter reference mass this concept, for the four dimensional spacetime un- unit of 3.523 1038 kg in terms of current cos- iverse, its three dimensional increasing volume can mic mass and Planck mass. 2 be set by Mach’s principle, GMt cR t   1. Clearly 6) Tried to provide a clear procedure for under- speaking, information of the evolving universe, can standing galactic dark matter via Inverse square GM law and cosmic angular acceleration. be extracted from R  t . With this proposal, at t 2 7) Removed some topics pertaining to ‘Cold dark c matter’ and ‘Relativistic dark matter” of galax- any stage of cosmic evolution, a closed and massive ies. universe can be defined with its minimum possible 8) Removed Tables and Figures in view of compil- radius. One can find interesting technical discussion ing updated data on galactic visual masses and on this relation by D.W.Sciama, R.H. Dicke, C. rotational curves extended to increasing galactic Brans and G. J. Whitrow [27-34]. radii. 3. Reasons for choosing light speed With three simplified assumptions, an attempt Based on the following reasons, we consider has been made to develop a practical model of the light speed as a special feature of cosmic expansion universe. As so many galaxies are rotating and all the and rotation. cosmic observations are being carried out with photons, we consider a light speed expanding [22-26] 1) All cosmic observations are being studied with and light speed rotating universe. As galaxies are the photons. key building blocks of the evolving universe and as 2) It is well believed that gravity propagates with all galaxies constitute massive rotating dark holes at light speed. their centers, we consider a growing and rotating Ma- 3) It is well established that electromagnetic inte- chian universe model [27-34]. That is why we call it raction propagates with light speed. a practical model. Interesting point to be noted is that, 4) It is well proved that, light speed is the ultimate our model is absolutely free from ‘cosmic red shift’ speed of material particles. concept. Most important point to be noted is that, we 2

[20] Seshavatharam UVS and Lakshminarayana S. (2020) Light speed expansion and rotation of a primordial cosmic black hole universe having internal acceleration. International Astronomy and Astrophysics Re- search Journal. 2(2): 9-27.

Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 12 July 2020 doi:10.20944/preprints202007.0200.v2

A review on Reference [20]

5) So far, it has not yet been possible physically to rent physical parameters of the observable un- measure the actual galactic receding speeds. iverse. 6) So far, it has not yet been possible to demon- 6) At any stage of cosmic expansion, if the un- strate and distinguish ‘space without matter’ and iverse wishes to maintain a closed boundary to ‘matter without space’. In this ambiguous situa- have its size minimum, it is having an option to follow the “Mach’s relation” at that time. It may tion, without knowing the origins of ‘space’ and be noted that, Machian radius is 2 times less ‘matter’, it is quite illogical to say that, space than the Schwarzschild radius of a black hole. drags massive galaxies at super luminal speeds. At any stage of cosmic evolution, if one is will- 7) So far, either at microscopic level or at macros- ing to consider the ‘Machian radius’ of the copic level, it has not yet been possible to estab- evolving universe as its minimum possible ra- lish a common understanding among quantum dius, corresponding other characteristic cosmic mechanics and gravity. physical parameters can be estimated/predicted easily and can be compared with time to time 4. Reasons for considering universe as a cosmological observations. Machian Sphere 5. List of symbols Based on the following reasons, we consider a Ma- chian universe. At any stage of cosmic evolution,

1) Without a radial in-flow of matter in all direc- 1) Cosmic time = t

tions towards one specific point, one cannot ex- 2) Cosmic Hubble parameter = H t pect a big crunch and without a big crunch, one 3) Cosmic angular velocity =  cannot expect a big bang. Really if there was a t ‘big bang’ in the past, with reference to forma- 4) Ratio of Hubble parameter to angular velocity =

tion of big bang as predicted by GTR and with t reference to the cosmic rate of expansion that 5) Cosmic radius = R might have taken place simultaneously in all di- t rections at a ‘naturally selected rate’ about the 6) Cosmic total dark mass = Mt point of big bang - ‘point’ of big bang can be 7) Cosmic volume =  considered as the characteristic reference point t of cosmic expansion in all directions. Thinking 8) Cosmic temperature = Tt in this way, to some extent, point of big bang 9) Galactic distance from cosmic centre = r  can be considered as a possible centre of cosmic Gdis t evolution. If so, thinking about a centre less un- 10) Galactic receding speed from cosmic centre = iverse is illogical. v  2) Mass and size pertaining to pre and post big Gres t bang [35] are unclear. 11) Increment in expansion distance =  d  exp t 3) Whether Planck scale is associated with big 12) Distance from cosmic centre = r bang or big bang is associated with Planck scale  d t is also unclear. 13) Wavelength of cosmic graviton = gw  4) As there exist no clear reasons for understand- t ing the occurrence of exponential expansion, 14) Frequency of cosmic graviton =   gw t cosmologists are having different opinions on 15) Galactic star rotation speed = V  cosmic inflation [36]. Grot t 16) Galactic angular velocity =  5) So far, it has not yet been possible to establish  Grot t solid connection between Planck scale and cur- 17) Estimated visible mass of galaxy = M  Gvis t

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A review on Reference [20]

18) Estimated visible mass density of galaxy = self energy density and thermal energy density are  equal in magnitude and can be expressed as follows.  Gvis t

19) Estimated total mass of galaxy = M Gtot  t 4 3  Let, Cosmic volume = t  R t  (5) 20) Estimated dark mass of galaxy = M 3  Gdark t   21) Ratio of dark mass of galaxy to visible mass of Based on relations (3) and (5), gravitational self galaxy = Dark mass factor = X  Gdark t energy density can be expressed as, X   Gdark t 22) %Dark mass of galaxy =  100 2 2 2 2 1 X  gsc  c 3GM  4  9 c Gdark t  t t3 t   Rt   (6)  5R   3  20 G t t  Note: Planck scale symbols can be understood with a subscript ‘pl’ and current symbols can be understood 2 2 9 c 4 with a subscript ‘0’. t aT 0 20G t (7) 6. Three simple assumptions 92c 2 t  aT 4 We propose the following three assumptions. 20G t (8)

Assumption-1: By following Mach’s principle, right 7. Expressions for cosmic temperature and age from the beginning of Planck scale, universe is expanding with speed of light and rotating with speed Rewriting relation (8) with respect to the radiation of light from and about the cosmic centre. It can be  2k 4 energy density constant, a  B and considering expressed with, 3 3 15 c relation (3), cosmic temperature can be estimated in GM cR2 (1) t t the following way.

GM c Based on assumption (3) and relation (8), R t  (2) t 2 c t 2 4 4 2 2 c3 kTBt9  t c  M  (3)  (9) t 15 3c 3 20G Gt 

Assumption-2: At any stage of cosmic evolution, By proceeding in the following way, a very simple ratio of Hubble parameter to angular velocity can be expression for cosmic temperature can be obtained. expressed as,

  Ht Tpl   1 ln     (4)  T  t t t  

where Tpl  Planck scale temperature.

Assumption-3: Right from the beginning of Planck scale, at any stage of cosmic expansion, gravitational 4

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1 4 1 4 135  2 3c 5  2 2  2 2  k4 T 4  t  9Hcpl 9 Hc pl B t 3   T     20  G  pl 20Ga  20  Ga  (14) 2 3 5     135  c G c t     31 3   9.67791  10 K 20 G  Gc   2 4 6 1 As per the 2015 Planck data (Planck Collaboration 2015) 135 t  c c       [37], 20 3 G 2 G  2 4 6 2  (10) 135   c c  4 Gc2 6  The current value of the Hubble parameter is reported t     3  2  2 6  to be: 20  GG  4 Gc   Planck TT+low P:  67.31 0.96 km/sec/Mpc  2 2 4 12 3   135  c c  c         Planck TE+low P:  67.73 0.92  km/sec/Mpc  3  4      20  G G 2 Gt    Planck TT,TE,EE+low P:  67.7 0.66  km/sec/Mpc 135  4c 12    3  4 2 2  The current value of CMBR temperature is reported 20  G Mpl M t   to be:  Hence, Planck TT + lowP + BAO:  2.722 0.027 K   1 Planck TT; TE; EE + low P + BAO:  2.718 0.021  K 3 3  135 4 c 0.6831  c Tt    (11) 20 3  kGMM kGMM In this paper, for calculation purpose, we consider B tpl B tpl Hence, T0  2.722 K.

As universe is always expanding with speed of light, Tpl   R ct.Hence, (15) t 0 1 ln    146.3 T0   R 1  t t   t (12) 20GaT 4 ct H t t 20 -1 0  1.4674 10 rad.sec (16) 9c2 8. Current cosmic physical parameters at cur-

rent cosmic temperature H  2.14675  1018 sec -1 0 0 0 (17) Following the assumptions, the Planck scale Hubble  66.24 km/Mpc/sec parameter can be expressed as follows: c c  3 R     c c 0 0 H (18)    H 0 0  pl pl GMpl R pl (13)  2.043  1028 m  1.85492  1043 sec -1 3 2 3 35 c 55 where Rpl GM pl c  Gc 1.6162 10 m M0  2.751  10 kg (19) G is the Planck length and the assumed radius con- 0 nected with the Planck mass. 1  t  0  2159.5 Billion years (20) Planck scale cosmic temperature can be expressed as 0 0H 0

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9. Cosmic rotation According to T. Valery and S. V. Timkov, current universe is rotating with light speed and angular As ‘spin’ is a basic property of quantum mechan- velocity equal to the current Hubble parameter [45]. ics, from the subject point of quantum gravity, un- Very recent and advanced studies of Lior Shamir iverse must have ‘rotation’. If it is assumed that, un- suggest [46] that, the distribution of galaxy spin di- iverse is a Machian sphere, it is quite natural to ex- rections in SDSS and Pan-STARRS shows patterns in pect ‘cosmic rotation’. the asymmetry between galaxies with opposite spin Kurt G¨odel put lot of efforts in developing a directions and can be considered as an evidence for realistic universe model with rotation and expansion. large-scale anisotropy and an indication for a rotating His heuristic results were presented at International universe. Congress of Mathematics held at Cambridge (Massa- chusetts) from 30th August to 5th September 1950 10. Understanding galactic dark matter and its [38]. estimation The first experimental evidence of the Universe rotation was done by Birch in 1982 evidently [39]. As per modern cosmological observations, dark mat- According to Birch, there appears to be strong evi- ter seems to have a major role in understanding ga- dence that the Universe is anisotropic on a large scale, lactic rotational curves, gravitational lensing, galactic producing position angle offsets in the polarization evolution, galactic collisions, motion of galaxies and brightness distributions of radio sources. These within galaxy clusters and cosmic microwave fluc- can probably be explained on the basis of a rotation tuations [47,48]. In this context we propose our views of the Universe with an angular velocity of approx- in the following way. 13 imately 10 rad/year. In our model, current cosmic 1) Right from the beginning of Planck scale, ‘un- angular velocity is 4.631 1013 rad/year. Observa- iverse’ is generating dark mass only. 2) Dark mass plays the complete role in the forma- tional effects of current cosmic rotation can be un- tion and evolution of galaxies. derstood with the works of Obukhov [40], Godlowski 3) During cosmic evolution, for any galaxy, part of [41], Longo [42] and Chechin [43]. dark mass slowly transforms to visual mass. Yuri N. Obukhov says: “Whether our universe is 4) Current galactic visual mass can be understood rotating or not, it is of fundamental interest to under- with the following relation. stand the interrelation between rotation and other

aspects of cosmological models as well as to under- 1 2 stand the observational significance of an overall M  M M 3 (21) Gvis 0 X 0  Gdark  0  rotation”.   According to Michael Longo the universe has a where M = Current visual mass of galaxy. net angular momentum and was born in a spin.  Gvis 0 M = Dark mass of galaxy. Whittaker says [44]: “however, that any of the  Gdark 0 mathematical-physical theories that have been put 1 3 4 forward to explain spin (rotation) in the universe has M0 M pl  M  3.523 1038 kg yet won complete and universal acceptance; but X 0 1  progress has been so rapid in recent years that it is 0  reasonable to hope for a not long-delayed solution of = Current semi empirical mass of reference [20].

this fundamental problem of cosmology”. 5) By estimating the current galactic visual mass, current galactic dark mass can be understood with the following relations. 6

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3 M Observed galactic flat rotation curves can be unders- Gvis 0 MGdark   (22) tood in the following way. At present, for any galaxy, 0 M X 0 let,

3 2 M  M  (23) GMG1  GM G 2  GM G 3  Gdark0 Gvis 0 V  0  0  0 Grot 0 r r r G1 0 G 2  0 G 3  0 6) Current galactic dark mass factor can be unders- (28) tood with the following relation. where, V Current observed flat orbiting velocity of  Grot 0 = MGdark   M Gvis  X 0  0 (24) Gdark 0 galactic star. MGvis   M X  0 0 r,, r r  G10 G 2 0 G 3  0  XGdark  = Current total mass factor of galaxy. 0  Increasing galctic distances from galactic centre.

M X M (25) MG1 ,, M G 2  M G 3   Gdark0 Gdark 0 Gvis  0 0 0 0  Increasing galctic masses at r  , r  , r  . G10 G 2 0 G 3 0 7) Current galactic total mass can be understood with the following relation. MG1  M G 2  M G 3   0 0  0  Constant  r r r  MGtot   M Gdark   M Gvis  G1 0 G 2  0 G 3  0  0 0 0 (26) 1  X  M Point to be noted is that, star’s orbiting velocity Gdark 0  Gvis  0 changes with changing galactic dark mass distribu- where, M = Current total mass of galaxy.  Gtot 0 tion and it needs further study and observational data for a number of galaxies. Let, 8) Current galactic dark mass percentage can be understood with the following relation. G M Gtot 0 VGrot   (29) MGdark  0 %M  0  100 rGeffe  Gdark 0 M  0 Gtot 0 (27) where, X  Gdark 0 V  Observed current flat orbiting speed of   100  Grot 0 1 X   Gdark 0  galactic star. r  Current galctic effective radius. 11. To develop a MOND like relation for galactic  Geffe 0 flat orbiting speed with cosmic angular veloc- G MGtot  ity and galactic total mass Writing r  0 and eliminating Geffe 0 2 VGrot  Even though MOND approach [49,50,51] was aimed 0 for understanding galactic rotation curves without r ,  Geffe 0 dark matter, with reference to the proposed current GM v 4 cosmic angular velocity and relation (10), it is possi- Gtot 0 Grot  0  (30) ble to fit the rotation curves and thereby galactic dark 2 G M r Gtot 0 masses can be inferred. Geffe 0

Now, based on MOND approach, assume that, 7

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flat rotation speed, can be called as galactic 4 ‘visual radius’ and can be expressed as, vGrot  0  c (31) G M 0 Gtot 0 G M M where, Gvis 0 Gvis  0 rGvis    0 1 X  c c Current possible maximum cosmic GMGtot  c0 Gdark 0 0 0  0   angular acceleration. (36) Thus, 4) Based on relations (28), (34) and (35), if dark 4 VGrot GM  Gtot  c0 matter distribution is ‘as expected’, galaxy 0 0 (32) should follow flat rotation speeds in between 4 GX1   Mc Gdark 0  Gvis  0 0 rGvis  and rGeffe  A least, close to the geo- 0 0 . Based on this relation, estimated flat rotation speeds metric mean of r  and r rotation of DD168, Milky Way and UGC12591 are 49.96 Gvis 0  Geffe 0 km/sec, 199.66 km/sec and 521.75 are 52 km/sec, speed should be flat. It can be expressed as, 202.6 km/sec and 500 km/sec respectively. As per the reference photometric data [49] and [52], their cor- G M  responding flat rotation speeds km/sec respectively. Gvis 0 (37) rGgeom   rr Geffe Gvis   Within a range of (50 to 500) km/sec, these striking 0 0 0 c 0 coincidences are strongly supporting our proposed concepts. We are working on collecting data for most 5) Effective, geometric and visual radii can be ex- of the galaxies and updating this draft with detailed pressed with a common relation of the form, Tables and Figures in our next revision.

p G M  In this way, r1  X  Gvis 0 Gx0  Gdark  0  c0 (38) 1) Current galactic angular velocity can be unders- 1 1  where, p  ,0,   tood with the following relations. 2 2 

3 V 6) With reference to the observed ordinary matter Grot 0 Grot   (33) density [37,53], we noticed that, for any galaxy, 0 G M  Gtot 0

  where,  = Current galactic angular ve- VGrot   MGvis  M Gtot    Grot 0   0 0 0 Gvis 0     locity c  4 3    rGeffe   3 0  (39) VGrot  Grot   c 0 (34) 0 0   VGrot   3 M Gvis   X  1 0 0 dark    3  2) Based on relations (28), (31) and (32), effective c    4 rGeffe   radius of galaxy can be expressed as, 0 

It may also be noted that, based on the average GM  GM  r Gtot0  Gtot 0 (35) mass-to-light ratio for any galaxy, present mat- Geffe 0 GM c c0 Gtot 0 0 ter density can be expressed with the following relation [53]. 3) Based on relation (28), as a special case, radius 1.5  1032 h gram/cm 3 of galaxy corresponding to its visual mass and  Gvis 0 0 (40)

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 M M where Rpl is the Planck scale cosmic radius.   and Here,  L galaxyL su n .  Z  exp xx  1 (43) h0  H0 100 Km/sec/Mpc  0.68 0 t 

Note that elliptical galaxies probably comprise about 60% of the galaxies in the universe and Based on these two ad hoc definitions, it is possible spiral galaxies thought to make up about 20% to show that, percent of the galaxies in the universe. Almost 80% of the galaxies are in the form of elliptical and       R0 Rt   spiral galaxies. For spiral galaxies, h1  9  1 Z exp 1  ln   1 ln     1 0 R   R   pl   pl    and for elliptical galaxies,h1  10  2 . For our  0        R0 Rt  1  exp ln   ln      1  44  galaxy inner part, h0  6  2 . Thus the average R   R   pl   pl     h1 is very close to 8 to 9 and its corresponding 0 R   R  0  0  matter density is close to (5.55 to 6.24)  10-32  expln    1 1 Rt   R t  gram/cm3 and can be compared with the above  proposed magnitude of 6.25  10-32 gram/cm3. With respect to the proposed assumptions, it is Note: Important point to be noted is that, in esti- clear that at any stage of cosmic expansion, mating the approximate visual mass of the universe, while multiplying the average galactic vis- 1) Cosmic radius is inversely proportional to ual matter density with total cosmic volume, one cosmic angular velocity. must exclude the intergalactic volume or volume 2) Cosmic angular velocity is directly propor- occupied by the free space. Clearly speaking, one tional to squared cosmic temperature. must find the ratio of total galactic volume and total free space volume. Hence,

7) With reference to MSTG and MOND approach- R TT2 Z 0 1t  1 t  1 t 1 (45) es [49], approximate galactic core radius can be R T 2 T expressed as, t 00 0

where T is the past cosmic temperature r  G M  t Gvis01  Gvis 0 (41) rGcore      0 2 2X 1 c  and T0 is the current cosmic temperature.   dark  0 T  Z  1 t (46) 12. To understand cosmic redshift associated with T0 cosmic current and past temperatures 13. To understand Hubble’s law and to locate the With reference to the light emitted from first hydro- cosmic centre gen atoms, we define the following two ad hoc relations. Based on first assumption and special theory of rela- R  tivity, from and about the cosmic centre, for any ma- Let, x  1  ln t  (42) t   terialistic galaxy, its current receding speed can be Rpl  understood in the following way. 9

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r  c3 c  Gdis 0   v  c Egw    Gres 0   0 2GMM RR (50) R0 0pl 0 pl   (47) 1   0.0003434 eV r  rH Gdis 00  Gdis  0 0 0  15. Understanding cosmic anisotropy

In this way qualitatively Hubble’s [54] law can be As universe is always expanding at speed of light, at

understood. Since 0 is known, by knowing the ac- any stage of expansion, cosmic boundary expands by tual galactic receding speed, its distance from the 3 108 m in one second. In between the cosmic cen- cosmic centre can be estimated. By estimating the tre and cosmic boundary, expansion distance covered cosmic radial distances of galaxies along with their in one second can be expressed as, locations, it seems possible to locate the cosmic cen-

tre. If any galaxy’s actual receding speed is found to rd  d t 3  108 m (51) be faster than speed of light, our model can be falsi- exp t   Rt fied. where, 14. To estimate current cosmic gravitational wave  d = Increment in expansion distance at time t . length  exp t

With reference to current cosmic mass and Planck r = Distance from cosmic centre at time t.  d t mass, wavelength of current gravitational waves [55] can be obtained as follows. Rt = Cosmic radius at time t . Our idea is that, at any stage of cosmic evolution, Clearly speaking, ‘evolving universe’ is an ‘internal accelerating’ ob- ject and wavelength of cosmic graviton is equal to 1) Distance moved near to cosmic boundary is 2 times the geometric mean of radius of universe at more compared to distance moved near to cos- time t and Planck scale radius. It can be expressed as, mic centre. 2) Rate of volume change near to cosmic boundary Based on this idea, at present, is higher than the rate of volume change near to cosmic centre. G M M  0 pl  3) Anisotropy [46,56] gradually increases from gw  2 R0 R pl  2  0 c2  cosmic centre to cosmic boundary.   (48)

2G M0 M pl 16. Understanding (internal) cosmic acceleration   0.00361 m c2 According to Saul Perlmutter, Adam Riess and Brian Corresponding frequency and energy can be ex- Schmidt, observable universe is accelerating [57,58]. pressed as, Clearly speaking, expansion of the universe is such c c that the velocity at which a distant galaxy is receding    gw 0 from the observer is continuously increasing with gw  2 R0 Rpl 0 (49) time. It can be understood in the following way. c3   83.033 GHz 2G M0 M pl 10

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Based on relation (47) and with reference to two logical observation or no ground based experiment could shed light on the physical nature of dark energy. time periods t2 t 1  , ratio of galactic receding speeds can be expressed as, 18. Understanding cosmic age

v r   Grest Gdis  ttR  Observable cosmic radius is just 2.2 times the Hubble 2  2  1  (52)   radius and corresponding cosmic age is 1/H . Our vGres   r Gdis   R t  0  t1 t 1 2  where, model result of cosmic radius is 146.3 times the Hubble radius and corresponding light speed cosmic age is 146.3 times In this way, our model vGres  and vGres  = Galactic receding 1/H0  . t1 t2 result of cosmic age can be justified. We would like speeds corresponding to t, t respectively where 1 2 to emphasize that, vGres   v Gres  . t2 t 1 1) Modern cosmological observations are limited to 2.2 times the Hubble radius and needs further rGdis  and rGdis  = Galactic distances cor- t1 t2 study.

responding to t1, t 2 respectively where 2) Time is a dynamic and emerging cosmic parameter. rGdis   r Gdis  . t2 t 1 3) Cosmic age depends on the model under consideration. R and R = Theoretical cosmic radii corres- t1 t2 4) One should not worry about the absolute value ponding to t, t respectively where R R . of cosmic age. 1 2  t2 t 1  19. Understanding nucleosynthesis Clearly speaking, Based on relations (1) to (20) and by assuming 1) Within the cosmic horizon, second by second, appropriate density range or temperature range that is galactic receding speeds are increasing and re- required for formation of nucleons and atoms, cosmic semble a kind of internal cosmic acceleration. physical parameters pertaining to nucleosynthesis can 2) Acceleration seems to be higher near to cosmic be understood [61]. For example, cosmic age corres- centre and gradually reaches to zero at horizon. ponding to a temperature of 1010 K is 5.05 sec. It 3) Hubble’s law pertaining to two increasing time needs further study. Estimated cosmic age corres- periods seems to be a natural consequence of 6 internal cosmic acceleration. ponding to 3000 K is 1.78 10 years. This estima- 4) Cosmic horizon is always expanding at speed tion is 4.68 times higher than the current estimation of light. of 3.8 105 years. Clearly speaking, starting from the

17. To relinquish dark energy Planck scale, without considering ‘inflation’ like cooling pattern, our model follows a slow thermal If it is assumed that, universe is always expand- cooling pattern throughout the cosmic evolution. ing with speed of light, then, considering ‘dark energy’ like concepts need not be required [59,60]. If one 20. Inferences of growing Machian universe is able to understand the reasons for light speed ex- Based on the proposed assumptions and with pansion, it may help in understanding the internal reference to the above relations, we would like to say acceleration. Proceeding further, till today, no cosmo- that, 11

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1) Earth, Solar family, Milky way and all other ga- 3 0.6831c laxies are living inside the proposed Machian Tpl  (53) k GM universe. B pl 2) There is matter and space outside the proposed Comparing this with Hawking’s relation, it is differ- ing by the factor numerical 0.6831. In may be noted growing and rotating Machian universe. that, in our earlier publications [3,12], we tried to 3) The growing and rotating Machian universe al- develop models of black hole cosmology with mod- ways sucks matter inward and thus it grows on ified Hawking’s temperature relation as, with increasing suction rate. 4) At poles, inward matter flow rate is maximum 3 c and at equator, inward matter flow rate is zero. Tt  Thus, starting from poles to equator, inward 8kGB MM t pl (54) matter flow rate gradually decreases. where M c3 2 GH t t  21. To develop practical methods for understanding growing Machian universe In those publications our aim was to couple Hubble parameter and cosmic temperature without cosmic We would like to propose the following points rotation. In some situations, we were forced to as- for understanding cosmic singularity. sume the equality of Hubble parameter and angular velocity. By doing so, we could be able to match cur- 1) To study cosmic anisotropy on very large rent Hubble radius and Hubble age. But, our idea of MOND’s approach of dark matter analysis and advo- cosmic distances. cated [39] Birch’s cosmic angular velocity are not 2) To believe, to understand and to study the working for the case of H   . Hence, in this pa- consequences of cosmic rotation. 0 0 per, we are forced to accommodate 146.3 c H 3) To develop high precision cosmic gyros-  0  copes. radius 146.3 1H0  . With future observations and 4) To study galactic mean temperature and to advanced telescopes, it may be possible to see far estimate the galactic dark mass. distant galaxies. For example, the oldest stars in the 5) To correlate galactic rotations and cosmic Milky Way are nearly as old as the current universe rotation. itself. Based on this observation, by considering very old galaxies compared to Milky Way, there is a pos- 6) To find oldest galaxies like EGSY8p7 sibility of observing very old stars beyond our current whose age is closer to or greater than 13.8 observable radius which may help in understanding billion years. the actual cosmic radius and age. 7) To study very high energy cosmic gravitons. 8) To study cosmic dipole magnetic moment 23. Discussion on galactic flat rotation curves and and its related properties. galactic dark matter estimation

22. Discussion on cosmic temperature, angular 1) With reference to maximum possible (current) velocity, radius and age cosmic angular acceleration, MOND relation can be rewritten as follows. Relation (11) is very similar to the famous Hawk- ing’s black hole temperature formula [62]. This is V 4 G  27.28 Mc   due to the similarities in between Mach’s relation for Grot0  Gvis 0  0 (55) increasing cosmic radii and Schwarzschild radius of a 1.2 1010 m.sec -2  black hole. For the Planck scale, cosmic temperature where,    27.28 c  can be expressed as, 0  2) On comparison, percentage of dark mass in MOND model seems to be constant at 12

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(26.28/27.28)x100 = 96.33% whereas in our ap- As per the observational data [65], for Milky proach, dark matter percentage increases with Way, starting from a radius of 60 kpc, rotation increasing (visible) mass and radius of galaxy. It speed seems to decrease gradually [66,67]. Us- is very interesting to note that, MOND’s ap- ing the current dwarf galaxy population, very proach implicitly seems to support the cosmological estimation of 95% invisible matter and 5% recently predicted [64] edge of the Milky Way visible matter. It needs further study. halo is 292 61 kpc. This is a very support. 3) By minimizing the errors in estimating the visi- 8) In near future, by thoroughly studying the galac- ble mass of galaxy and by properly choosing the tic dark mass distribution and corresponding effective radius of galaxy, accuracy can be im- deviations, variations in flat rotation speeds can proved in estimating the dark mass of a galaxy. be analyzed in a systematic approach. Very rent Point to be noted is that, there is no correlation studies conducted on super spiral galaxies with between photometric mass estimations and pa- Southern African Large Telescope (SALT) suggest high rotation speeds in the range of rametric mass estimations. Similarly, in some (240 to 570) km/sec indicating a dynamical cases, including Milky Way, there is no correla- masse range of (0.6 to 4) 1012 M [68]. It may tion between MSTG mass estimations and  MOND mass estimations. It needs a careful be noted that, with a visual galactic mass of 0.64 1012M  1.5510 12 M , estimated analysis.     4) Staring from the lowest massive galaxy, (DDO flat rotation speed is 539 km/sec. This is a good 154) to the highest massive galaxy (NGC 2841), support for our proposal pertaining to most dark mass seems to increase from 2.7 to 49.3 massive galaxies having fast rotation speeds. times respectively and needs further study. Ap- Considering a visual mass of 0.98 0.1 of plying this idea to Sun like stars, dark mass ratio logM dark  mentioned in Table-1 of Ref. [68], is close to 0.0001. corresponding flat rotation speeds can be fitted 5) As per the recent studies [63], Virial mass of well. Milky Way is 1.280.97 10 12 M and its cor- 9) We are also working on developing alternative 0.48  relations for estimating  X  . On lower responding upper limit is 2.25 1012 M . Based Gdark 0  side, by studying the ultra faint dwarf galaxies it on proposed relations, for Milky Way [49], es- seems possible to fine tune X dark . timated flat rotation speed is 199.6 km/sec and 10) Interesting point to be noted is that, for small its corresponding total mass is galaxies whose mass is less than 3.5×1038 kg , 25.5 10.6 1010M  2.7 10 12 M . This is    their dark mass seems to be less than their visu- a good fit and strong support for our proposal. al mass. Whether it is - ‘correct or not’ - can be confirmed with their galactic rotational curves. Based on relation (34), estimated angular ve- For a galaxy of visual mass 106M , galactic locity of whole Milky Way is  17 -1 flat rotation speed seems to be 5.0 km/sec. It 2.2 10 rad.sec . It is for observational test- needs further investigation with respect to least ing [39] and further study. Sun is located at 25 massive galaxy, Segue2. According to Evan N. kpc from the Milky Way center and is having a Kirby et al [69]: “Either Segue 2 would be the rotational period of 240 million years. So, for first of a vast class of new galaxies to be dis- the whole Milky Way of radius 290 kpc, our covered with very low luminosities and very proposal can be given a chance [64]. low dark matter content, or it would have to represent a rare case of a dark matter halo that is 6) For Milky Way, its corresponding ‘visual’ and typically too small to host a galaxy but, for ‘effective’ radii are 11.5 kpc and 293.66 kpc. Corresponding geometric radius is 58.1 km/sec. 13

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some reason, managed to form a small number mic entities and like matter, space cannot travel faster of stars over at least 100 Myr.” than speed of light. 10) Relation (34) seems to be very simple in repre- Flatness problem can be understood well with sentation, easy to follow and simple to visualize Machian radius of the current universe. Considering and analyze MONDin approach connected with light speed expansion, inflation and dark energy concepts can be relinquished. Based on relations (4) and galactic structures and cosmic structure. (8), Hubble parameter can be estimated independent of galactic distances and their red shifts. 24. Discussion on the nature of dark matter Even though, cosmic horizon is assumed to be expanding at light speed, based on relations (47) and We would like to appeal that, when 95% of total (52), it seems possible to have internal acceleration cosmic mass is believed to be in the form of dark nature having interactions only with gravitation, it below the cosmic horizon and seems to be a conse- may not be logical to attribute its nature to any quence of Hubble’s law for increasing time periods. known or known any elementary particle supposed to Even though, estimated cosmic radius is 146.3 times be originating from interactions involved with visible the Hubble radius, estimated angular velocity is mass spectrum. 146.3 times less than the Hubble parameter and is As current cosmic temperature is at 2.7 K, recently it has been suggested that, galactic cold hy- directly helping in estimating galactic dark masses drogen can be considered as dark matter [70,71]. with relations (21) to (41). Since hydrogen is the basic building block of visible Further study and advanced telescopes may matter, this proposal can be given a chance. If so, 95% help in thoroughly exploring the cosmic and galactic of the cosmic mass must be explained with a suitable structures in a broad view based on the concepts of mechanism with respect to current sub zero tempera- Quantum Cosmology. In this context, relation (8) can tures, past high temperatures and dark matter needed be given some consideration. for the formation and evolution of galaxies. For example, based our approach, estimated dark mass of current Milky Way is 24.5 times of its visible mass. It Acknowledgements needs a reasonable mechanism for generating the required dark matter distribution. Author Seshavatharam is grateful to Dr. E.T. Tatum If dark matter is really having a different na- for guiding with his valuable scientific thoughts on ture and if one is willing to study and understand the ‘light speed expansion’ and ‘Flat Space Cosmology’. mechanism of transformation of dark mass to Hydro- Author Seshavatharam is indebted to professors shri gen atoms, it may give some clue. Applying our idea M. Nagaphani Sarma, Chairman, shri K.V. Krishna to Sun and Proton, their current dark masses are Murthy, founder Chairman, Institute of Scientific Research in Vedas (I-SERVE), Hyderabad, India and 1.5 1026 kg and 3.6 10-60 kg respectively. With Shri K.V.R.S. Murthy, former scientist IICT (CSIR), these magnitudes, it is possible to say that, at atomic Govt. of India, Director, Research and Development, level, at present, dark matter influence is negligible. I-SERVE, for their valuable guidance and great Even for Sun like massive stars, dark matter is having support in developing this subject. a very little role. This can be confirmed with current gravitational observations. We are thinking in this References direction. [1] Friedmann A (1999) On the Curvature of Space. 25. Conclusion General Relativity and Gravitation. 31(12): 1991- 2000. Considering the points and relations proposed in [2] Hawking S.W. A Brief History of Time. Bantam sections (2) to (24), our model can be recommended for further research. We would like to emphasize the Dell Publishing Group. (1988) point that, ‘space’ and ‘matter’ are inseparable cos-

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[3] Seshavatharam UVS (2010) Physics of rotating and tiers of Astronomy, Astrophysics and Cosmology expanding black hole universe. Progress in Physics. 1(1): 16-23. 4:7-14. [14] Seshavatharam UVS, Lakshminarayana S (2016) [4] Seshavatharam UVS (2012) The Primordial Cos- Cosmologically Strengthening Hydrogen Atom in mic Black Hole and the Cosmic Axis of Evil. Inter- Black Hole Universe. J. Nucl. Phy. Mat. Sci. Rad. national Journal of Astronomy. 1(2): 20-37. A. 3(2): 265–278. [5] Seshavatharam UVS, Lakshminarayana S (2013) [15] Seshavatharam UVS and Lakshminarayana S (2016) Applications of Hubble Volume in Atomic Physics, On the possible role of continuous light speed ex- Nuclear Physics, Particle Physics, Quantum Phys- pansion in black hole & Gravastar cosmology. ics and Cosmic Physics. J. Nucl. Phy. Mat. Sci. Rad. Prespacetime Journal. 7(3):584-600. A. 1(1):45-60. [16] Seshavatharam UVS. Lakshminarayana S. (2018) [6] Seshavatharam UVS, Lakshminarayana S (2014) Toy Model of Evolving and Spinning Quantum Friedman Cosmology: Reconsideration and New Cosmology – A Review. International Journal of Results. International Journal of Astronomy, Astro- Astronomy, Astrophysics and Space Science. physics and Space Science. 1(2):16-26. 5(1):1-13. [7] Seshavatharam UVS, Lakshminarayana S (2014) [17] Seshavatharam UVS, Lakshminarayana S (2019) On the Evolving Black Holes and Black Hole Cos- A first step in evolving quantum cosmology. Jour- mology-Scale Independent Quantum Gravity Ap- nal of Physics: Conf. Series 1251: 012045. proach. Frontiers of Astronomy, Astrophysics and [18] Seshavatharam UVS, Lakshminarayana S (2019) Cosmology, 1(1):1-15. An Outline Picture of a Growing and Rotating [8] Seshavatharam UVS, Lakshminarayana S (2015) Planck Universe with Emerging Dark Foam. Asian Black Hole Cosmology with Propelling Lambda Journal of Research and Reviews in Physics. 2(2): Term & Hindu Cosmic Age. Prespacetime Journal. 1-13. 6( 9):850-874. [19] Seshavatharam UVS, Lakshminarayana S (2019) A [9] Seshavatharam UVS, Lakshminarayana S (2015) Practical Model of Godel–Planck–Hubble–Birch Role of Mach’s Principle and Quantum Gravity in Universe. Athens Journal of Sciences. 6(3):211-230. Understanding Cosmic Evolution and Cosmic Red- [20] Seshavatharam UVS and Lakshminarayana S. shift. Frontiers of Astronomy, Astrophysics and (2020) Light speed expansion and rotation of a Cosmology. 1(1): 24-30. primordial cosmic black hole universe having in- [10] Seshavatharam, UVS, Tatum, E.T and Lakshmina- ternal acceleration. International Astronomy and rayana, S. On the role of gravitational self energy Astrophysics Research Journal. 2(2): 9-27. density in spherical flat space quantum cosmology. [21] Bojowald M. Quantum cosmology: A review. Rep. Journal of Applied Physical Science International. Prog. Phys. 2015;78:023901. Vol.: 4, Issue.: 4, 228-236 (2015) [22] Nielsen JT, Guffanti A and Sarkar S (2016) Mar- [11] Seshavatharam UVS. Lakshminarayana S. (2015) ginal evidence for cosmic acceleration from type Ia Applications of light speed expansion and gravita- supernovae. Scientific Reports 6: 35596 tional self-energy density in black hole cosmology. [23] Wei JJ, Wu XF, Melia F, Maier RS (2015) Com- International Journal of Advanced Astronomy, 3 (2) parative analysis of the Supernova Legacy Survey 123-128. sample with ΛCDM and the Rh=ct Universe. The [12] Tatum ET, Seshavatharam UVS and Lakshmina- Astronomical Journal. 149:102. rayana S (2015) The basics of flat space cosmology. [24] Melia F, Fatuzzo M (2016) The epoch of reioniza- International Journal of Astronomy and Astrophys- tion in the R_h=ct universe. Monthly Notices of ics. 5:116-124. Royal Astronomical Society. 456(4): 3422-3431 [13] Seshavatharam UVS, Lakshminarayana S (2015) [25] Arved Sapar (2019) A perpetual mass-generating Primordial hot evolving black holes and the Planckian universe. Proceedings of the Estonian evolved primordial cold black hole universe. Fron- Academy of Sciences. 68(1):1-12. 15

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