1 Light Speed Expansion and Rotation of a Primordial

LIGHT SPEED EXPANSION AND ROTATION OF A PRIMORDIAL BLACK HOLE UNIVERSE HAVING INTERNAL ACCELERATION

Abstract: With reference to primordial black holes, an attempt has been made to develop a practical model of cosmology. Main features of this integrated model are: eternal role of Planck scale, light speed expansion and rotation of a primordial cosmic black hole, slow thermal cooling, internal acceleration and anisotropy. At any stage of cosmic expansion, there exists a tight correlation between cosmic angular velocity and cosmic temperature. At

H0  70 km/Mpc/sec, present cosmic radius seems to be 140.56 times higher than the Hubble radius, angular velocity seems to be 140.56 times smaller than the Hubble parameter and cosmic age seems to be 140.56 times the Hubble age. Current cosmic graviton wave length seems to be around 4.9 mm. This model is free from ‘big bang’, ‘inflation’, ‘dark energy’, ‘flatness’ and ‘red shift’ issues.

Keywords:Planck scale; Primordial Black hole; Speed of light; Dark matter; Deep frozen matter; Relativistic mass of a galaxy; cosmic anisotropy; Internal acceleration; Cosmic graviton wavelength;

1. Introduction possible ways. As of now, theoretically and observa- tionally, with respect to inflation, isotropy, expansion We would like to emphasize the fact that, the basic speed, dark matter, dark energy and rotation, whole principles of cosmology were developed when the subject of cosmology is being driven into many con- subject of cosmology was in its budding stage. troversies and dividing cosmologists into various Friedmann made two simple assumptions about the groups with difference of opinions. On the other hand, universe [1,2]. They can be stated in the following very unfortunate thing is that, quantum cosmology way. point of view, ‘as a whole’, progress is very poor [17]. Instead of discussing about the controversies, we would like to propose a new model which can pave a new way for understanding and correlating astro- 1) When viewed at large enough scales, un- physical and cosmological observations in terms of iverse appears the same in every direction. quantum mechanics and general theory of relativity 2) When viewed at large enough scales, un- in a broad sense. It needs further study. iverse appears the same from every location. With three simplified assumptions, an at-

tempt has been made to develop a practical model of In this context, Hawking expressed that [2]: “There is the universe. As so many galaxies are rotating and all no scientific evidence for the Friedmann’s second the cosmic observations are being carried out with assumption. We believe it only on the grounds of photons, we consider a light speed expanding [11- modesty: it would be most remarkable if the universe 16],[18-22] and light speed rotating universe. As ga- looked the same in every direction around us, but not laxies are the key building blocks of the evolving around other points in the universe”. universe and as all galaxies constitute massive rotating black holes at their centers, we consider a grow- In our earlier and recent published papers ing and rotating black hole universe model [3-16]. [3-16] we tried to highlight the basic drawbacks of That is why we call it as a practical model. Interest- big bang, inflation and galactic red shift in various ing point to be noted is that, our model is absolutely

free from ‘cosmic red shift’ concept. Most important point to be noted is that, we have developed a very tight quantum gravity relation for correlating cosmic 1) Mass and size pertaining to pre and post big temperature and Hubble parameter independent of bang [15,16,23] are unclear. galactic red shifts and galactic distances. It can be 2) Whether Planck scale is associated with big applied to different time periods of the past. bang or big bang is associated with Planck scale is also unclear. 3) As there exist no clear reasons for understanding the occurrence of exponential expansion, 2. Reasons for choosing light speed cosmologists are having different opinions on cosmic inflation [24].

4) So far, it has not yet been possible to establish Based on the following reasons, we consider solid connection between Planck scale and cur- light speed as a special feature of cosmic expansion rent physical parameters of the observable un- and rotation. iverse. 5) At any given cosmic time, the product of currently believed ‘critical density’ and ‘Hubble volume’ gives a characteristic cosmic mass, and 1) All cosmic observations are being studied with can be called as ‘Hubble mass’. Of interest, the photons. Schwarzschild radius of this ‘Hubble mass’ ap- 2) It is well believed that gravity propagates with pears to coincide with the currently believed light speed. ‘Hubble length’. Most cosmologists believe that 3) It is well established that electromagnetic inte- this is merely a coincidence. Here we wish to raction propagates with light speed. emphasize the possibility that this coincidence 4) It is well proved that, light speed is the ultimate might imply a deep inter-connection between speed of material particles. cosmic geometry and other cosmological physi- 5) So far, it has not yet been possible physically to cal phenomena. 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 maintains a closed boundary to have its strate and distinguish ‘space without matter’ and size minimum, it is having an option to follow ‘matter without space’. In this ambiguous situa- the “Schwarzschild radius” at that time. At any tion, without knowing the origins of ‘space’ and stage of cosmic evolution, if one is willing to ‘matter’, it is quite illogical to say that, space consider the ‘Schwarzschild radius’ of the ex- drags massive galaxies at super luminal speeds. panding black hole universe as its minimum 7) So far, either at microscopic level or at macros- possible radius, corresponding other characteris- copic level, it has not yet been possible to estab- tic cosmic physical parameters can be esti- lish a common understanding among quantum mated/predicted easily and can be compared mechanics and gravity. with time to time cosmological observations. 7) Whether universe is giving birth to black holes

or black hole is the seed of any universe is not 3. Reasons for considering universe as a pri- yet clear [25]. When the early universe was able mordial growing and rotating black hole to create a number of galactic black holes or primordial black holes, it may not be a big problem for the whole universe to behave like a big primordial evolving black hole. With reference Based on the following reasons, we consider a to the current concepts of modern cosmology, primordial growing and rotating black hole universe. probability of ‘this’ to happen may be zero, but its possibility cannot be ruled out. 2

8) Formation scheme of primordial black holes is entirely different from stellar black holes [26] and early stage quantum fluctuations seem to 5. Three simple assumptions play a vital role in understanding the nature of

primordial black holes. 9) Whether galactic central halos are primordial We propose the following three assumptions. black holes or gravitationally collapsed objects is not yet clear [27]. Assumption-1: Right from the beginning of Planck 10) So far, it has not yet been possible to establish a scale, as a growing black hole, universe is expanding limiting mass range for stellar black holes and with speed of light and rotating with speed of light primordial black holes. from and about the cosmic center. It can be expressed with,

2GM c 4. List of symbols R t (1) t 2 c t

At any stage of cosmic evolution, c3  Mt (2) 2Gt 1) Cosmic time = t

2) Cosmic Hubble parameter = Ht

3) Cosmic angular velocity =t Assumption-2: At any stage of cosmic evolution, 4) Ratio of Hubble parameter to angular velocity = ratio of Hubble parameter to angular velocity can be expressed as, t

5) Cosmic radius = Rt H H pl t 1ln (3) 6) Cosmic mass = M t  t ttH 7) Cosmic volume = t 8) Cosmic temperature = T t cc351 where H 9.2746 1042 sec -1 9) Galactic distance from cosmic center = r pl  gal t 22GMpl G 10) Galactic receding speed from cosmic center = c and M   . r pl G gal t 11) Increment in expansion distance =  d exp t 12) Distance from cosmic center = r d t Assumption-3: Right from the beginning of Planck scale, at any stage of cosmic expansion, cosmic mat- 13) Wave length of cosmic graviton = gw  t ter energy density and thermal energy density are 14) Frequency of cosmic graviton =  equal in magnitude and can be expressed as follows.  gw t

Note: Planck scale symbols can be understood with a 4 3 Let, Cosmic volume = ttR (4) subscript ‘pl’ and current symbols can be understood 3 with a subscript of ‘0’. 3

45 235c  kT44 t  Bt 3  Based on relations (2) and (4), cosmic matter energy 8 G  235  density can be expressed as, 45  c c t    3  8 Gc    45 246c  t   3  2 5  8 Gc mat c c 4  t  R3  246  t 45 t  c G tt23G     8 3 Gc  G 3  (5)   55 22 1  33ccc 3t c  246    45 t  c c 3     8GR 88GG  32  tt t  8 G G  2  45246c cGc 4 26  t    32G 26  84 GGc  Thus, 22 412 3  45 cc c   2 34  c 22 22 32 G GG2 t 4  mat  33 cHc1   aT tt t(6) t  88GG2  45 412c  t t     3422 32 GMpl M t  (8)

6. Expressions for cosmic temperature and age Hence,

Rewriting relation (6) with respect to the radiation 24 1  kB 33 a  454 cc 0.4615 energy density constant, 33 and considering   15 c Tt  (9)  32 3 kG MM kG MM relation (2), cosmic temperature can be estimated in BtplBtpl the following way [11,13,28].

As universe is always expanding with speed of light,

Based on assumption (3) and relations (4) and (6), Rt  ct. Hence,

R 1  t tt (10) cH 24kT 43 22 c tt Bt t 33 (7) 15 c 8G

7. Current values at H0  70 km/Mpc/sec

By proceeding in the following way, a very simple expression for cosmic temperature can be obtained. Considering H  70 km/Mpc/sec, 0

The first experimental evidence of the Universe H pl 0 1  ln  140.5632 (11) rotation was done by Birch in 1982 evidently [29]. H0  According to Birch, there appears to be strong evidence that the Universe is anisotropic on a large scale, 1 H pl H producing position angle offsets in the polarization  H 1ln 0 00 (12) and brightness distributions of radio sources. These H00 can probably be explained on the basis of a rotation 20  1.61394 10 rad/sec of the Universe with an angular velocity of approx- 13 imately 10 rad/year. In our model, current cosmic angular velocity is 5.0932 1013 rad/year. Observa-  cc tional effects of current cosmic rotation can be un- R00 00H (13) derstood with the works of Obukhov [30], Godlowski  1.85752 1028 m [31], Longo [32] and Chechin [33]. Yuri N. Obukhov says: “Whether our universe is rotating or not, it is of fundamental interest to understand the interrelation between rotation and other 3 c 55 aspects of cosmological models as well as to under- M0 1.251 10 kg (14) 2G0 stand the observational significance of an overall rotation”. According to Michael Longo the universe has a net angular momentum and was born in a spin. 0.4615 c3 Whittaker says [34]: “however, that any of the T  2.72761 K (15) 0 mathematical-physical theories that have been put kGBpl MM0 forward to explain spin (rotation) in the universe has yet won complete and universal acceptance; but

progress has been so rapid in recent years that it is reasonable to hope for a not long-delayed solution of 1 0 t0  1963.4 Billion years (16) this fundamental problem of cosmology”.  H 00 According to T. Valery and S. V. Timkov, current universe is rotating with light speed and angular

velocity equal to the current Hubble parameter [35]. 8. Cosmic rotation and current cosmic rotation- Very recent and advanced studies of Lior Shamir al kinetic energy suggest [36] that, the distribution of galaxy spin directions in SDSS and Pan-STARRS shows patterns in the asymmetry between galaxies with opposite spin directions and can be considered as an evidence for 8.1 Cosmic rotation large-scale anisotropy and an indication for a rotating universe.

As ‘spin’ is a basic property of quantum mechan- 8.2 Cosmic rotational kinetic energy ics, from the subject point of quantum gravity, universe must have ‘rotation’. If it is assumed that, universe is a black hole, it is quite natural to expect ‘cosmic rotation’. Recent observations clearly indi- Current total matter density, cate the possibility of ‘light speed’ spinning black holes.

3 Formation of galactic halos and galactic enve- c 4 3 tot R0 lopes might be absorbing some of the frozen matter 0 23G (17) t on a regular basis. Galaxy which constitutes many -31 3 4.659 10 kg/m stars with high temperatures will try to heat the frozen matter in a short run. After a long run, old galaxies that constitute cold stars can have more frozen matter. Galaxies that constitute young stars can have As current matter density is very very small, consi- less frozen matter. Either an old galaxy or a new ga- dering current universe as a thin spherical shell, its laxy, galactic halos can absorb more frozen matter rotational kinetic energy can be estimated with a rela- due to their strong attractive nature. tion of the form,

11 1 KEIMRMc2222  rot 0 2300 00 0 3 0 (18) 9.2 Relativistic mass of a galaxy 2 where, IMR 2 0003

It may also be noted that, considering special theory of relativity, there is a possibility of relativistic 9. Understanding cosmic dark matter increase in galactic mass. Clearly speaking, galaxies having high receding speeds may have higher relativistic masses compared to galaxies having lower relativistic speeds. This kind of galactic mass increasing Dark mater [37] can be understood in two differ- mechanism seems to have an interesting role in un- ent ways. One way of understanding is based on derstanding actual galactic mass. But without under- thermal cooling of the universe [38]. Another way of standing the internal distribution mechanism of in- understanding is based on the receding galaxy’s increasing mass, it may not be possible to understand creasing relativistic mass. or distinguish the mass of galactic halo and total mass of stars enveloped by the galaxy. Very complicated point to be understood is – ‘nature’ of increasing 9.1 Deep frozen mass of a galaxy mass – whether the increased mass constitutes new kind of particles or a kind of inertia or currently believed dark matter.

Current cosmic temperature is 2.727 K and current cosmic age is 1963.4billion years. Based on these points, starting from the formation of hydrogen 10. To fit observed dark matter density and ba- (3000 K), formation of condensed star dust [39] ryonic matter density (1100 K) and the melting point of hydrogen (14 K) on wards, it is possible to guess that, most of the cosmic matter can be in the form of very deep frozen With reference to the recombination point of 3000 K , state. In general, at sub zero temperatures, matter can star dust condensation temperature of 1100 K, ob- show inability for photonic interactions. Frozen cos- served baryonic matter density and dark matter densi- mic matter can be qualitatively considered as the cur- ty [40] can be fitted with the following relations. rently believed dark matter. Heating effects caused by so many stars, some of the frozen matter exposed to star heat might have been converted to visible matter continuously. 10.1 Current baryonic matter density

baryonic matter and dark matter start to form in the envelope of galaxies. It needs further study. Current baryonic matter density can be fitted with the following relation.

11. To understand cosmic redshift associated with cosmic current and past temperatures 22 3300HH 3 00 bar   0 88GG 8  G (19) 3H 2 With reference to the light emitted from first hydro- 3.93 10-28 kg/m 3  4.27% of 0  gen atoms, we define the following two ad hoc rela- 8G tions.

3000 K where,   ln 1 6.0 R 2.725 K Let, x 1lnt (22) t  Rpl

where Rpl is the Planck scale cosmic radius. 10.2 Current dark matter density

Zxx exp0 t 1(23)

Current dark matter density can be fitted with the Based on these two ad hoc definitions, it is poss- following relation. ible to show that,

   RR0 t  Z exp 1 ln  1 ln  1 22 RR   33HH 3 pl  pl 2200  00  dar 0    88GG 8  G   RR  (20)  exp ln0 lnt 1  24 2   RRpl pl -27 3 3H0  2.36 10 kg/m  25.61% of   8G  RR   exp ln00 1 1  RRtt  2  2 3000 K where   ln 1 36.0 2.725 K With respect to the proposed assumptions, it is clear that at any stage of cosmic expansion, dar 3000 K 0  ln  1 (21)  2.725 K bar 0 

1) Cosmic radius is inversely proportional to cosmic angular velocity. In a trial-error method we have developed these rela- 2) Cosmic angular velocity is directly propor- tions. Interesting point to be noted is that, at a tem- tional to squared cosmic temperature. perature of 1100 K, the factor 3000 K  ln 1 0. From this it can be inter- 1100 K  Hence, preted that, from 1100 K onwards, condensates of

2 With reference to current cosmic mass and Planck RTT0 ttt Z 1111(25) mass, wave length of current gravitational waves [42] RT T 2 t 000 can be obtained as follows.

whereTt is the past cosmic temperature and T is the current cosmic temperature. 0 Our idea is that, at any stage of cosmic evolution, ‘evolving universe’ is an ‘internal accelerating’ ob- ject and wavelength of cosmic graviton is equal to the T 2 times the geometric mean of radius of universe at Z 1 t (26)  time t and Planck scale radius. It can be expressed as, T0

12. To understand Hubble’s law and to locate the Based on this idea, at present, cosmic center 2GMM 0 pl gw22RR0 pl  0 c2 (28)

Based on first assumption and special theory of rela- 4GMM0 pl tivity, from and about the cosmic center, for any ma-  0.0048687 m c2 terialistic galaxy, its current receding speed can be understood in the following way. Corresponding frequency and energy can be expressed as,

cc   gw  rgal  0 0 1 gw 2 RR0 pl vcrrH  0 gal000R  gal00  gal (29) 00 c3 61.5755 GHz (27) 4GMM0 pl

In this way qualitatively Hubble’s [41] law can be cc3 understood. Since 0 is known, by knowing the ac- E  gw 0 (30) tual galactic receding speed, its distance from the 2GMM00pl RR pl cosmic center can be estimated. By estimating the  0.000254656 eV cosmic radial distances of galaxies along with their locations, it seems possible to locate the cosmic center. If any galaxy’s actual receding speed is found to 14. Understanding cosmic anisotropy be faster than speed of light, our model can be falsi- fied.

As universe is always expanding at speed of light, at any stage of expansion, cosmic boundary expands by 13. To estimate current cosmic gravitational wave 8 length 310 m in one second. In between the cosmic center and cosmic boundary, expansion distance covered in one second can be expressed as,

r  d t 8 vrgal  gal  R d 310  m(31) ttt221 exp t R   (32) t vrR gal gal t2 tt11

where, where,

 d = Increment in expansion distance at time t . exp t vgal  and vgal  = Galactic receding speeds t1 t2 rd = Distance from cosmic center at time t. t corresponding to tt12,  respectively where

R = Cosmic radius at time t . vvgal   gal  . t tt21

Clearly speaking, rgal  and rgal  = Galactic distances corres- t1 t2

ponding to tt12,  respectively where 1) Distance moved near to cosmic boundary is rrgal   gal  . more compared to distance moved near to cos- tt21 mic center. 2) Rate of volume change near to cosmic boundary is higher than the rate of volume change near to R and R = Theoretical cosmic radii corres- cosmic center. t1 t2

3) Anisotropy [36,43] gradually increases from ponding to tt12,  respectively where cosmic center to cosmic boundary. RR .  tt21

15. Understanding (internal) cosmic acceleration Clearly speaking,

According toSaul Perlmutter, Adam Riess and Brian Schmidt, observable universe is accelerating [44,45]. 1) Within the cosmic horizon, second by Clearly speaking, expansion of the universe is such second, galactic receding speeds are increas- that the velocity at which a distant galaxy is receding ing and resemble a kind of internal cosmic from the observer is continuously increasing with acceleration. time. It can be understood in the following way. 2) Acceleration seems to be higher near to cosmic center and gradually reaches to zero at horizon. 3) Hubble’s law pertaining to two increasing Based on relation (27) and with reference to two periods seems to be a natural consequence time periods tt , ratio of galactic receding 21 of internal cosmic acceleration. speeds can be expressed as, 4) Cosmic horizon is always expanding at speed of light. 9

ponding to a temperature of 1010 K is 4.61 sec.It needs further study. Estimated cosmic age corres- 16. To relinquish dark energy ponding to 3000 K is 1.6223 106 years. This estimation is 4.27 times higher than the current estimation of 3.8 105 years. Clearly speaking, starting from the If it is assumed that, universe is always expanding with speed of light, then, considering ‘dark ener- Planck scale, without considering ‘inflation’ like gy’ like concepts need not be required [46]. Proceed- cooling pattern, our model follows a slow thermal ing further, till today, no cosmological observation or cooling pattern throughout the cosmic evolution. no ground based experiment could shed light on the physical nature of dark energy. 19. Inferences of growing cosmic singularity

17. Understanding cosmic age Based on the proposed assumptions and with

reference to the above relations, we would like to say Observable cosmic radius is just 2.2 times the Hubble that, radius and corresponding cosmic age is 1/H . Our 0 model result of cosmic radius is 140.5 times the Hubble radius and corresponding light speed cosmic 1) Earth, Solar family, Milky way and all other galaxies are living inside the proposed black hole age is 140.5 times 1/H0 . In this way, our model universe. result of cosmic age can be justified. We would like 2) There is matter and space outside the proposed to emphasize that, growing and rotating primordial black hole universe. 3) The growing and rotating primordial black hole 1) Modern cosmological observations are limited universe always sucks matter inward and thus it to 2.2 times the Hubble radius and needs further grows on with increasing suction rate. study. 4) At poles, inward matter flow rate is maximum 2) Time is a dynamic and emerging cosmic para- and at equator, inward matter flow rate is zero. meter. Thus, starting from poles to equator, inward 3) Cosmic age depends on the model under con- matter flow rate gradually decreases. sideration. 4) One should not worry about the absolute age of cosmic age. 20. To develop practical methods for understanding growing cosmic singularity

18. Understanding nucleosynthesis

We would like to propose the following points for understanding cosmic singularity. Based on relations (1) to (16) and by assuming appropriate density range or temperature range that is required for formation of nucleons and atoms, cosmic 1) To study cosmic anisotropy on very large physical parameters pertaining to nucleosynthesis can cosmic distances. be understood [47]. For example, cosmic age corres- 10

2) To believe, to understand and to study the seems essential to develop new techniques for mea- consequences of cosmic rotation. suring cosmic radius and angular velocity. 3) To develop high precision cosmic gyros- copes. 4) To study galactic mean temperature and to COMPETING INTERESTS DISCLAIMER: estimate the galactic dark mass. 5) To study and to map the relativistic masses Authors have declared that no competing interests of receding galaxies with reference to their exist. The products used for this research are com- star rotation curves. This approach may help monly and predominantly use products in our area of in inferring the galactic receding speeds in- research and country. There is absolutely no conflict directly. of interest between the authors and producers of the 6) To correlate galactic rotations and cosmic products because we do not intend to use these prod- rotation. ucts as an avenue for any litigation but for the ad- 7) To find oldest galaxies like EGSY8p7 vancement of knowledge. Also, the research was not whose age is closer to or greater than 13.8 funded by the producing company rather it was billion years. funded by personal efforts of the authors. 8) To study very high energy cosmic gravitons. 9) To study cosmic dipole magnetic moment References and its related properties.

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