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

Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 10 July 2020 doi:10.20944/preprints202007.0200.v1

A review on Reference [20]

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: With reference to Mach’s relation, an attempt has been made to develop a practical model of cosmology. Main features of this integrated model are: eternal role of Planck scale and Mach’s relation, light speed expansion and rotation, slow thermal cooling, internal acceleration and anisotropy. At any stage of cosmic expansion, there exists a tight correlation between gravitational self energy density, thermal energy density, cosmic angular velocity and Hubble parameter. In this model, total cosmic matter is dark matter only. During cosmic evolution, part of galactic dark matter is slowly transforming to visual mass. Magnitude of galactic dark mass is proportional to galactic visible mass 3 2 . Considering the current cosmic maximum angular acceleration, MOND’s approach implicitly seems to support the cosmological estimation of 95% invisible matter and 5% visible matter. 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. As per the reference data, their corresponding flat rotation speeds are 52 km/sec, 202.6 km/sec and 500 km/sec respectively. Within a range of (50 to 500) km/sec, these striking coincidences are strongly supporting our proposed concepts. We are working on collecting data for most of the galaxies and updating this draft with detailed tables and figures in our next revision. Proceeding further, applying our idea to Sun and Proton, their current dark masses are 1.5 1026 kg and 3.6 10-60 kg respectively. Current cosmic graviton wave length seems to be around 3.6 mm. 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 higher than the Hubble radius, angular velocity is 146.3 times smaller 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 distance galaxies and very old stars far beyond our Milk Way.

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

1. Introduction 2) When viewed at large enough scales, universe appears the same from every location. We would like to emphasize the fact that, the basic principles of cosmology were developed when the In this context, Hawking expressed that [2]: “There is subject of cosmology was in its budding stage. no scientific evidence for the Friedmann’s second Friedmann made two simple assumptions about the assumption. We believe it only on the grounds of universe [1,2]. They can be stated in the following modesty: it would be most remarkable if the universe way. looked the same in every direction around us, but not around other points in the universe”. 1) When viewed at large enough scales, universe appears the same in every direction. In our earlier and recent published papers [3-20] we tried to highlight the basic drawbacks of

[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]

big bang, inflation and galactic red shift in various With three simplified assumptions, an attempt possible ways. As of now, theoretically and observa- has been made to develop a practical model of the tionally, with respect to inflation, isotropy, expansion universe. As so many galaxies are rotating and all the speed, dark matter, dark energy and rotation, whole cosmic observations are being carried out with pho- subject of cosmology is being driven into many con- tons, we consider a light speed expanding [22-26] troversies and dividing cosmologists into various and light speed rotating universe. As galaxies are the groups with difference of opinions. On the other hand, key building blocks of the evolving universe and as very unfortunate thing is that, quantum cosmology all galaxies constitute massive rotating dark holes at point of view, ‘as a whole’, progress is very poor [21]. their centers, we consider a growing and rotating Ma- Instead of discussing about the controversies, we chian universe model [27-34]. That is why we call it would like to propose a new model which can pave a as a practical model. Interesting point to be noted is new way for understanding and correlating astro- that, our model is absolutely free from ‘cosmic red physical and cosmological observations in terms of shift’ concept. Most important point to be noted is quantum mechanics and general theory of relativity that, we have developed a very tight quantum gravity in a Machian view. It needs further study. relation for correlating cosmic temperature and Hub- ble parameter independent of galactic red shifts and With reference to our very recent publica- galactic distances. It can be applied to different time tion [20], in this version, periods 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 the define the Gamma parameter with stored on a two dimensional projection much like a the ratio of past and current temperatures holographic image [35,36]. The ‘holographic prin- [10,11]. It helps in estimating the Hubble para- ciple’ is a property of string theory and a supposed meter with a direct relation rather than trial- property of quantum gravity that states that the de- error approach. scription of a volume of space can be thought of as 4) Made an attempt to bring clarity in the estima- encoded on a lower-dimensional boundary. Based on tion of galactic dark matter. this concept, for the four dimensional spacetime un- 5) Tried to define a dark matter reference mass iverse, its three dimensional increasing volume can unit of 3.523 1038 kg in terms of current cos- 2 be set by Mach’s principle, GMt cR t   1. Clearly mic mass and Planck mass. speaking, information of the evolving universe, can 6) Tried to provide a clear procedure for under- GM standing galactic dark matter via Inverse square be extracted from R  t . With this proposal, at t 2 law and cosmic angular acceleration. c 7) Removed some topics pertaining to ‘Cold dark any stage of cosmic evolution, a closed and massive matter’ and ‘Relativistic dark matter” of galax- universe can be defined with its minimum possible ies. radius. One can find interesting technical discussion 8) Removed Tables and Figures in view of compil- on this relation by D.W.Sciama, R.H. Dicke, C. ing updated data on galactic visual masses and Brans and G. J. Whitrow [27-34]. rotational curves extended to increasing galactic 3. Reasons for choosing light speed radii. 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.

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A review on Reference [20]

Based on the following reasons, we consider 2) Mass and size pertaining to pre and post big light speed as a special feature of cosmic expansion bang [35] are unclear. and rotation. 3) Whether Planck scale is associated with big bang or big bang is associated with Planck scale 1) All cosmic observations are being studied with is also unclear. photons. 4) As there exist no clear reasons for understand- 2) It is well believed that gravity propagates with ing the occurrence of exponential expansion, light speed. cosmologists are having different opinions on 3) It is well established that electromagnetic inte- cosmic inflation [36]. raction propagates with light speed. 5) So far, it has not yet been possible to establish 4) It is well proved that, light speed is the ultimate solid connection between Planck scale and cur- speed of material particles. rent physical parameters of the observable un- 5) So far, it has not yet been possible physically to iverse. measure the actual galactic receding speeds. 6) At any stage of cosmic expansion, if the un- 6) So far, it has not yet been possible to demon- iverse wish to maintain a closed boundary to strate and distinguish ‘space without matter’ and have its size minimum, it is having an option to ‘matter without space’. In this ambiguous situa- 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 than the Schwarzschild radius of a black hole. ‘matter’, it is quite illogical to say that, space At any stage of cosmic evolution, if one is will- drags massive galaxies at super luminal speeds. ing to consider the ‘Machian radius’ of the 7) So far, either at microscopic level or at macros- evolving universe as its minimum possible ra- copic level, it has not yet been possible to estab- dius, corresponding other characteristic cosmic lish a common understanding among quantum physical parameters can be estimated/predicted mechanics and gravity. easily and can be compared with time to time cosmological observations. 4. Reasons for considering universe as a Machian Sphere 5. List of symbols

Based on the following reasons, we consider a Ma- At any stage of cosmic evolution, chian universe. 1) Cosmic time = t 1) Without a radial in-flow of matter in all direc- 2) Cosmic Hubble parameter = H t tions towards one specific point, one cannot expect a big crunch and without a big crunch, one 3) Cosmic angular velocity = t cannot expect a big bang. Really if there was a 4) Ratio of Hubble parameter to angular velocity = ‘big bang’ in the past, with reference to forma- t tion of big bang as predicted by GTR and with reference to the cosmic rate of expansion that 5) Cosmic radius = Rt

might had taken place simultaneously in all di- 6) Cosmic total dark mass = Mt rections at a ‘naturally selected rate’ about the 7) Cosmic volume =  point of big bang - ‘point’ of big bang can be t considered as the characteristic reference point 8) Cosmic temperature = Tt of cosmic expansion in all directions. Thinking 9) Galactic distance from cosmic center = r in this way, to some to some extent, point of big  Gdis t bang can be considered as a possible center of 10) Galactic receding speed from cosmic center = cosmic evolution. If so, thinking about a center r  less is universe is illogical. Gres t 3

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A review on Reference [20]

T  11) Increment in expansion distance = dexp  Ht pl   t 1 ln     (4)  T  t 12) Distance from cosmic center = r t t    d t

3 5 13) Wave length of cosmic graviton = gw  c c t where H   1.855 1043 sec -1 and pl GM G 14) Frequency of cosmic graviton =  pl   gw t c 15) Galactic star rotation speed = VGrot  M  . t pl G 16) Galactic angular velocity =   Grot t 17) Estimated visible mass of galaxy = M Assumption-3: Right from the beginning of Planck  Gvis t scale, at any stage of cosmic expansion, gravitational 18) Estimated total mass of galaxy = M  Gtot t self energy density and thermal energy density are 19) Estimated dark mass of galaxy = M equal in magnitude and can be expressed as follows.  Gdark t 20) Ratio of dark mass of galaxy and visible mass of 4 3  galaxy = Dark mass factor =  X  Let, Cosmic volume = t  R t  (5) Gdark t 3  X   Gdark t 21) %Dark mass of galaxy =  100 Based on relations (3) and (5), gravitational self 1 X   Gdark t  energy density can be expressed as,

Note: Planck scale symbols can be understood with a 2  c 2  2 2 subscript ‘pl’ and current symbols can be understood  gsc t3GM t4 3  9 t c   Rt   (6) with a subscript of ‘0’.  5R   3  20 G t t 

6. Three simple assumptions 2 2 9t c 4  aTt 0 (7) We propose the following three assumptions. 20G

Assumption-1: By following Mach’s principle, right 92c 2 t  aT 4 from the beginning of Planck scale, universe is ex- 20G t (8) panding with speed of light and rotating with speed of light from and about the cosmic center. It can be 7. Expressions for cosmic temperature and age expressed with, Rewriting relation (8) with respect to the radiation 2 2 4 GMt cR t (1)  k energy density constant, a  B and considering 15 3c 3 GM c  R t  (2) relation (3), cosmic temperature can be estimated in t 2 c t the following way. c3  Mt  (3) Based on assumption (3) and relation (8), G t 2kT 4 49  2 c 2 Assumption-2: At any stage of cosmic evolution, Bt t 3 3 (9) ratio of Hubble parameter to angular velocity can be 15 c 20G expressed as, 4

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A review on Reference [20]

By proceeding in the following way, a very simple c3 c H  1.85492  1043 sec -1 expression for cosmic temperature can be obtained. pl GM R pl pl (13) 135   2 3c 5  where R GM c2  Gc 3 1.6162 10  35 m k4 T 4  t  pl pl  B t 3   20  G  is the Planck length and the assumed radius con- 2 3 5  135  c c nected with the Planck mass. t     3   Planck scale cosmic temperature can be expressed as 20 G  c   2 4 6 1 4 135  t  c  2 2     9Hpl c 31 20 3  G c  T   9.67791 10 K   pl 20Ga  135  2 4c 6 G    (14) t   3    20 Gc  G   As per the 2015 Planck data (Planck Collaboration 2015) 1  135  2 4c 6 c  [37],  t   3  2   20 G G  2  The current value of the Hubble parameter is reported 135   2 4c 6 c   4 Gc2 6  to be: t    3  2   2 6  20  GG   4 Gc  Planck TT+low P:  67.31 0.96 km/sec/Mpc    2  2 4 12 3  Planck TE+low P:  67.73 0.92  km/sec/Mpc  135  c c  c         3  4     Planck TT,TE,EE+low P:  67.7 0.66  km/sec/Mpc 20  G G 2 Gt   135  4c 12     The current value of CMBR temperature is reported 3  4 2 2 to be: 20  G Mpl M t  (10) Planck TT + lowP + BAO:  2.722 0.027 K   Planck TT; TE; EE + low P + BAO:  2.718 0.021  K Hence, 

In this paper, for calculation purpose, we consider 1 3 3 T  2.722 K. Hence, 135 4 c 0.6831 c 0 T    t 3  (11) 20  kGMMB tpl kGMM B tpl Tpl   0 1 ln    146.3 (15) T  As universe is always expanding with speed of light, 0  

Rt  ct.Hence, 4 20GaTt 20 -1 0  1.4674 10 rad.sec (16) R 1  9c2 t t   t (12) c H t t H  2.14675  1018 sec -1 0 0 0 (17) 8. Current cosmic physical parameters at cur-  66.24 km/Mpc/sec rent cosmic temperature

Following assumptions, the Planck scale Hubble pa- c c  R0  0   rameter can be expressed as follows: 0H 0  (18)

 2.043  1028 m

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A review on Reference [20]

3 yet won complete and universal acceptance; but c 55 M0  2.751  10 kg (19) progress has been so rapid in recent years that it is G0 reasonable to hope for a not long-delayed solution of this fundamental problem of cosmology”. 1  t  0  2159.5 Billion years (20) According to T. Valery and S. V. Timkov, cur- 0  H 0 0 rent universe is rotating with light speed and angular velocity equal to the current Hubble parameter [45]. 9. Cosmic rotation Very recent and advanced studies of Lior Shamir

As ‘spin’ is a basic property of quantum mechan- suggest [46] that, the distribution of galaxy spin di- ics, from the subject point of quantum gravity, un- rections in SDSS and Pan-STARRS shows patterns in iverse must have ‘rotation’. If it is assumed that, un- the asymmetry between galaxies with opposite spin iverse is a Machian sphere, it is quite natural to ex- directions and can be considered as an evidence for pect ‘cosmic rotation’. large-scale anisotropy and an indication for a rotating Kurt G¨odel put lot of efforts in developing a universe. realistic universe models with rotation and expansion. 10. Understanding galactic dark matter and its His heuristic results were presented at International estimation Congress of Mathematics held at Cambridge (Massa- chusetts) from 30th August to 5th September 1950 As per modern cosmological observations, dark mat- [38]. ter seems to have a major role in understanding ga- The first experimental evidence of the Universe lactic rotational curves, gravitational lensing, galactic rotation was done by Birch in 1982 evidently [39]. evolution, galactic collisions, motion of galaxies According to Birch, there appears to be strong evi- within galaxy clusters and cosmic microwave fluc- dence that the Universe is anisotropic on a large scale, tuations [47,48]. In this context we propose our views producing position angle offsets in the polarization in the following way. and brightness distributions of radio sources. These can probably be explained on the basis of a rotation 1) Right from the beginning of Planck scale, ‘un- of the Universe with an angular velocity of approx- iverse’ is generating dark mass only. imately 1013 rad/year. In our model, current cosmic 2) Dark mass plays the complete role in the formation and evolution of galaxies. 13 angular velocity is 4.631 10 rad/year. Observa- 3) During cosmic evolution, for any galaxy, part of tional effects of current cosmic rotation can be un- dark mass slowly transforms to visual mass. derstood with the works of Obukhov [40], Godlowski 4) Visual mass fraction can be understood with the [41], Longo [42] and Chechin [43]. following kind of semi empirical relation. Yuri N. Obukhov says: “Whether our universe is rotating or not, it is of fundamental interest to under- 32  3H 2    3 H 2    t  t   tt   stand the interrelation between rotation and other vis t t      8GG 8t 8  G aspects of cosmological models as well as to under-      (21)   stand the observational significance of an overall 1 t where,     t   rotation”. 2  According to Michael Longo the universe has a 5) Current cosmic visual mass fraction can be un- net angular momentum and was born in a spin. derstood with the following relation. Whittaker says [44]: “however, that any of the mathematical-physical theories that have been put forward to explain spin (rotation) in the universe has 6

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2  2  MGtot   M Gdark   M Gvis  30 3H 0 0 0 0 vis   0    (28) 0 8G  8  G  1  X  M    Gdark 0  Gvis  0

 3H2  3 H 2 where, M = Current total mass of galaxy. 0 0  0.045 0 (22)  Gtot 0   0 8G  8  G 10) Current galactic dark mass percentage can be 1   where,  0   6.548 understood with the following relation. 0   2  6) Current galactic visual mass can be understood MGdark  %M  0  100 with the following relation. Gdark 0 M  Gtot 0 (29) 1 X Gdark 0 2 3   100 MGvis    M X   M Gdark  (23) 1 X  00 0  Gdark 0 

where M = Current visual mass of galaxy.  Gvis 0 11. To develop a MOND like relation for galactic flat orbiting speed with cosmic angular veloc- M = Dark mass of galaxy.  Gdark 0 ity and galactic total mass 1 3 4 M0 M pl  Even though MOND approach [49,50,51] was aimed M  3.523 1038 kg X 0 for understanding galactic rotation curves without 1  0  dark matter, with reference to the proposed current = Current semi empirical mass of reference [20]. cosmic angular velocity and relation (10), it is possi-

ble to fit the rotation curves and thereby galactic dark 7) By estimating the current galactic visual mass, masses can be inferred. current galactic dark mass can be understood with the following relations. Observed galactic flat rotation curves can be understood in the following way. At present, for any galaxy, 3 M  let, Gvis 0 (24) MGdark   0 M X 0 GM  GM  GM  V  G10  G 2 0  G 3 0 3 2 Grot 0 M M (25) rG1   r G 2   r G 3  Gdark 0 Gvis  0 0 0 0 (30)

8) Current galactic dark mass factor can be unders- where, tood with the following relation. V Current observed flat orbiting velocity of  Grot 0 = galactic star. MGdark   M Gvis  X 0  0 (26) r,, r r Gdark 0  G10 G 2 0 G 3  0 MGvis   M X  0 0  Increasing galctic distances from galactic center.  X  = Current total mass factor of galaxy. Gdark 0 M,, M M  G10 G 2 0 G 3  0  Increasing galctic masses at r , r , r . M X M (27) G1 0 G 2  0 G 3  0  Gdark0 Gdark 0 Gvis  0

9) Current galactic total mass can be understood with the following relation. 7

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A review on Reference [20]

Within a range of (50 to 500) km/sec, these striking MG1  M G 2  M G 3   0 0  0  Constant  coincidences are strongly supporting our proposed r r r  G1 0 G 2  0 G 3  0  concepts. We are working on collecting data for most Point to be noted is that, star’s orbiting velocity of the galaxies and updating this draft with detailed changes with changing galactic dark mass distribu- Tables and Figures in our next revision. tion and it needs further study and observational data for a number of galaxies. Let, In this way,

1) Current galactic angular velocity can be unders- G M  tood with the following relations. V  Gtot 0 Grot 0 (31) rGeffe  3 0 Grot     0 (35) where, Grot 0 G M Gtot 0 V  Observed current flat orbiting speed of  Grot 0 galactic star. where,  = Current galactic angular ve-  Grot 0 r  Current galctic effective radius. locity  Geffe 0 V   c  (36) G M  Grot0 Grot 0 0 r  Gtot 0 Writing Geffe  2 and eliminating 0 V 2) Based on relations (30), (33) and (34), effective Grot 0 radius of galaxy can be expressed as, r ,  Geffe 0 GM  GM  4 Gtot0 Gtot 0 (37) GM   v  rGeffe    Gtot0 Grot 0 0 c  (32) GMGtot  c0 0 2 G M 0 r Gtot 0 Geffe 0 3) Based on relation (30), as a special case, radius

of galaxy corresponding to its visual mass and Now, based on MOND approach, assume that, flat rotation speed, can be called as galactic

4 ‘visual radius’ and can be expressed as, vGrot  0  c (33) G M  0 Gtot 0 G M   M  Gvis0 Gvis 0 where, rGvis    0 GM c 1 X  c Gtot 0 0 Gdark 0  0 c0  Current possible maximum cosmic (38) angular acceleration. Thus, 4) Based on relations (30), (36) and (37), if dark V 4 GM c matter distribution is ‘as expected’, galaxy Grot0  Gtot  0 0 (34) should follow flat rotation speeds in between 4 GX1   Mc Gdark 0  Gvis  0 0 r and r A least, close to the geo-  Gvis 0  Geffe  0 . Based on this relation, estimated flat rotation speeds metric mean of rGvis  and rGeffe  rotation of DD168, Milky Way and UGC12591 are 49.96 0 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 corresponding flat rotation speeds km/sec respectively. 8

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G M  With respect to the proposed assumptions, it is Gvis 0 (39) rGgeom   rr Geffe Gvis   clear that at any stage of cosmic expansion, 0 0 0 c 0

5) Effective, geometric and visual radii can be ex- 1) Cosmic radius is inversely proportional to pressed with a common relation of the form, cosmic angular velocity. 2) Cosmic angular velocity is directly proportional to squared cosmic temperature. p G M  r1  X  Gvis 0 Gx0  Gdark  0  c0 (40) Hence, 1 1  where, p  ,0,   2 2  R TT2 Z 0 1t  1 t  1 t 1 (45) R T 2 T 6) With reference to MSTG and MOND approach- t 00 0 es [49], approximate galactic core radius can be expressed as, where Tt is the past cosmic temperature

and T0 is the current cosmic temperature. rGvis  1  GM r 0  vis (41) T Gcore 0    Z  1 t (46) 2 2  Xdark  1  c 0 T0

12. To understand cosmic redshift associated with 13. To understand Hubble’s law and to locate the cosmic current and past temperatures cosmic center

With reference to the light emitted from first hydro- Based on first assumption and special theory of rela- gen atoms, we define the following two ad hoc relativity, from and about the cosmic center, for any ma- tions. terialistic galaxy, its current receding speed can be R  Let, x  1  ln t  (42) understood in the following way. t   Rpl 

where R is the Planck scale cosmic radius. rGdis   pl v0  c Gres 0   R0   (47) Z  exp xx0 t  1 (43) 1  r  rH Gdis 00  Gdis  0 0 0  Based on these two ad hoc definitions, it is possible to show that, In this way qualitatively Hubble’s [53] law can be

understood. Since 0 is known, by knowing the ac-       tual galactic receding speed, its distance from the R0 Rt   Z exp 1  ln   1 ln     1 R   R   cosmic center can be estimated. By estimating the pl   pl     cosmic radial distances of galaxies along with their        R0 Rt  locations, it seems possible to locate the cosmic cen-  exp ln   ln      1  44  R   R   pl   pl    ter. If any galaxy’s actual receding speed is found to  be faster than speed of light, our model can be falsi- R   R   expln0    1 0 1  fied. Rt   R t  

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14. To estimate current cosmic gravitational wave where, length

dexp  = Increment in expansion distance at time t . With reference to current cosmic mass and Planck t mass, wave length of current gravitational waves [54] r = Distance from cosmic center at time t. can be obtained as follows.  d t

Our idea is that, at any stage of cosmic evolution, Rt = Cosmic radius at time t . ‘evolving universe’ is an ‘internal accelerating’ ob- ject and wavelength of cosmic graviton is equal to the Clearly speaking, 2 times the geometric mean of radius of universe at time t and Planck scale radius. It can be expressed as, 1) Distance moved near to cosmic boundary is more compared to distance moved near to cos- Based on this idea, at present, mic center. 2) Rate of volume change near to cosmic boundary G M M  is higher than the rate of volume change near to 0 pl  gw  2 R0 R pl  2  cosmic center. 0 c2    (48) 3) Anisotropy [46,55] gradually increases from cosmic center to cosmic boundary. 2G M0 M pl   0.00361 m 2 c 16. Understanding (internal) cosmic acceleration

Corresponding frequency and energy can be ex- According to Saul Perlmutter, Adam Riess and Brian pressed as, Schmidt, observable universe is accelerating [56,57]. Clearly speaking, expansion of the universe is such c c    that the velocity at which a distant galaxy is receding gw 0  2 R0 Rpl from the observer is continuously increasing with gw 0 (49) time. It can be understood in the following way. c3   83.033 GHz 2G M0 M pl Based on relation (47) and with reference to two

time periods t2 t 1  , ratio of galactic receding c3 c E    speeds can be expressed as, gw 0 2GMM0pl RR 0 pl (50)

v r   0.0003434 eV  Grest Gdis  ttR  2  2  1  (52)   vGres   r Gdis   R t 15. Understanding cosmic anisotropy t1 t 1 2  where, As universe is always expanding at speed of light, at

any stage of expansion, cosmic boundary expands by vGres  and vGres  = Galactic receding t1 t2 3 108 m in one second. In between the cosmic cen- speeds corresponding to t, t respectively ter and cosmic boundary, expansion distance covered  1 2 

in one second can be expressed as, where vGres   v Gres  . t2 t 1

rd  d t 3  108 m (51) exp t   Rt 10

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r and r = Galactic distances cor- 1) Modern cosmological observations are limited  Gdis t  Gdis t 1 2 to 2.2 times the Hubble radius and needs further responding to t1, t 2  respectively where study. r r . 2) Time is a dynamic and emerging cosmic para-  Gdist Gdis  t 2 1 meter. 3) Cosmic age depends on the model under con- R and R = Theoretical cosmic radii corres- t1 t2 sideration.

ponding to t1, t 2  respectively where 4) One should not worry about the absolute age of cosmic age. Rt R t .  2 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 [60]. For example, cosmic age corres- center 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 ponding to 3000 K is 1.78 106 years. This estima- internal cosmic acceleration. tion is 4.68 times higher than the current estimation 4) Cosmic horizon is always expanding at speed 5 of light. of 3.8 10 years. Clearly speaking, starting from the Planck scale, without considering ‘inflation’ like 17. To relinquish dark energy cooling pattern, our model follows a slow thermal cooling pattern throughout the cosmic evolution. If it is assumed that, universe is always expanding with speed of light, then, considering ‘dark ener- 20. Inferences of growing Machian universe gy’ like concepts need not be required [58,59]. If one 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, logical observation or no ground based experiment could shed light on the physical nature of dark energy. 1) Earth, Solar family, Milky way and all other galaxies are living inside the proposed Machian 18. Understanding cosmic age universe. 2) There is matter and space outside the proposed Observable cosmic radius is just 2.2 times the Hubble growing and rotating Machian universe. radius and corresponding cosmic age is 1/H0  . Our 3) The growing and rotating Machian universe al- model result of cosmic radius is 146.3 times the ways sucks matter inward and thus it grows on Hubble radius and corresponding light speed cosmic with increasing suction rate. age is 146.3 times 1/H  . In this way, our model 4) At poles, inward matter flow rate is maximum 0 and at equator, inward matter flow rate is zero. result of cosmic age can be justified. We would like Thus, starting from poles to equator, inward to emphasize that, matter flow rate gradually decreases.

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3 c 21. To develop practical methods for understand- Tt  8kG MM ing growing Machian universe B t pl (54) where M c3 2 GH We would like to propose the following points t t  for understanding cosmic singularity. In those publications our aim was to couple Hubble 1) To study cosmic anisotropy on very large parameter and cosmic temperature without cosmic cosmic distances. rotation. In some situations, we were forced to assume the equality of Hubble parameter and angular 2) To believe, to understand and to study the velocity. By doing so, we could able to match current consequences of cosmic rotation. Hubble radius and Hubble age. But, our idea of 3) To develop high precision cosmic gyros- MOND’s approach of dark matter analysis and advo- copes. cated [39] Birch’s cosmic angular velocity are not

4) To study galactic mean temperature and to working for the case of H0  0 . Hence, in this pa- estimate the galactic dark mass. per, we are forced to accommodate 146.3c H0  5) To study and to map the relativistic masses radius 146.3 1H  . With future observations and of receding galaxies with reference to their 0 advanced telescopes, it may be possible to see far star rotation curves. This approach may help distance galaxies. For example, the oldest stars in the in inferring the galactic receding speeds in- Milky Way are nearly as old as the current universe directly. itself. Based on this observation, by considering very 6) To correlate galactic rotations and cosmic old galaxies compared to Milky Way, there is a pos- rotation. sibility of observing very old stars which may help in 7) To find oldest galaxies like EGSY8p7 understanding the actual cosmic age. whose age is closer to or greater than 13.8 23. Discussion on galactic flat rotation curves and billion years. galactic dark matter estimation 8) To study very high energy cosmic gravitons.

9) To study cosmic dipole magnetic moment and its related properties. 1) With reference to maximum possible (current) cosmic angular acceleration, MOND relation 22. Discussion on cosmic temperature, angular can be rewritten as follows.

velocity, radius and age V 4 G  27.28 Mc   Grot0  Gvis 0  0 Relation (11) is very similar to the famous Hawk- (53) 1.2 1010 m.sec -2  ing’s black hole temperature formula [61]. This is where,  27.28   due to the similarities in between Mach’s relation for c0  increasing cosmic radii and Schwarzschild radius of a 2) On comparison, percentage of dark mass in black hole. For the Planck scale, cosmic temperature MOND model seems to be constant at can be expressed as, (26.28/27.28)x100 = 96.33% whereas in our ap- 0.6831 c3 proach, dark matter percentage increases with T   (53) increasing (visible) mass and radius of galaxy. It pl k GM B pl is very interesting to note that, MOND’s ap- Comparing this with Hawking’s relation, it is differ- proach implicitly seems to support the cosmo- ing by the factor numerical 0.6831. In may be noted logical estimation of 95% invisible matter and 5% that, in our earlier publications [3,12], we tried to visible matter. It needs further study. develop models of black hole cosmology with mod- 3) By minimizing the errors in estimating the visi- ified Hawking’s temperature relation as, ble mass of galaxy and by properly choosing the

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effective radius of galaxy, accuracy can be im- 3.179×1038 kg , their dark mass seems to be proved in estimating the dark mass of a galaxy. less than their visual mass. Whether it is - ‘cor- Point to be noted is that, there is no correlation rect or not’ - can be confirmed with their galac- between photometric mass estimations and pa- tic rotational curves. For a galaxy of visual rametric mass estimations. Similarly, in some mass 106M , galactic flat rotation speed seems  cases, including Milky Way, there is no corre- to be 5.14 km/sec. It needs further investigation lation between MSTG mass estimations and with respect to least massive galaxy, Segue2. MOND mass estimations. It needs a careful According to Evan N. Kirby et al [66]: “Either analysis. Segue 2 would be the first of a vast class of new 4) Staring from the lowest massive galaxy, (DDO galaxies to be discovered with very low lumi- nosities and very low dark matter content, or it 154) to the highest massive galaxy (NGC 2841), would have to represent a rare case of a dark dark mass seems to increase from 2.0 to 48.3 matter halo that is typically too small to host a times respectively and needs further study. Ap- galaxy but, for some reason, managed to form a plying this idea to Sun like stars, dark mass ratio small number of stars over at least 100 Myr.” is close to 0.0001. 10) Relation (36) seems to be very simple in repre- 5) As per the recent studies [62], Virial mass of sentation, easy to follow and simple to visualize 0.97 12 and analyze MONDin approach connected with Milky Way is 1.280.48  10M and its cor-  galactic structures and cosmic structure. responding upper limit is 2.25 1012 M . Based  on proposed relations, for Milky Way [49], es- 24. Discussion on the nature of dark matter timated flat rotation speed is 199.6 km/sec and its corresponding total mass is We would like to appeal that, when 95% of total cosmic mass is believed to be in the form of dark 25.5 10.6 1010M  2.7 10 12 M . This is    nature having interactions only with gravitation, it may not be logical to attribute its nature to any a good fit and strong support for our proposal. known or known any elementary particle guessed to Based on relation (36), estimated angular ve- be originating from interactions involved with visible locity of Milky Way is 2.2 1017 rad.sec -1 . It is mass spectrum. for observational testing [39] and further study. As current cosmic temperature is at 2.7 K, 6) For Milky Way, its corresponding ‘visual’ and recently it has been suggested that, galactic cold hydrogen can be considered as dark matter [67]. Since ‘effective’ radii are 11.5 kpc and 293.66 kpc. hydrogen is the basic building block of visible matter, Corresponding geometric radius is 58.1 km/sec. this proposal can be given a chance. If so, 95% of the As per the observational data [63], for Milky cosmic mass must be explained with a suitable me- Way, starting from a radius of 60 kpc, rotation chanism with respect to current sub zero temperatures, speed seems to decrease gradually [64,65]. past high temperatures and dark matter needed for the 7) In near future, by thoroughly studying the galac- formation and evolution of galaxies. For example, tic dark mass distribution and corresponding based our approach, estimated dark mass of current deviations, variations in flat rotation speeds can Milky Way is 24.5 times of its visible mass. It needs be analyzed in a systematic approach. a reasonable mechanism for generating the required 8) We are also working on developing alternative dark matter distribution. If dark matter is really having a different na- relations for estimating X . On lower  Gdark 0 ture and if one is willing to study and understand the side, by studying the ultra faint dwarf galaxies mechanism of transformation of dark mass to Hydro- it seems possible to fine tune X dark . gen atoms, it may give some clue. Applying our idea 9) Interesting point to be noted is that, for small to Sun and Proton, their current dark masses are galaxies whose mass is less than 1.5 1026 kg and 3.6 10-60 kg respectively. With 13

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these magnitudes, it is possible to say that, at atomic References level, at present, dark matter influence is negligible. Even for Sun like massive stars, dark matter is having [1] Friedmann A (1999) On the Curvature of Space. a very little role. This can be confirmed with current General Relativity and Gravitation. 31(12): gravitational observations. We are thinking in this 1991-2000. direction. [2] Hawking S.W. A Brief History of Time. Bantam

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