Acta Physica Academiae Scientiarum Hungaricae, Tomus 22 ( 1 - - 4 ) , pp. 51--58 (1967)

THE HOT MODEL OF THE U N I V E R S E AND THE ELEMENTARY PARTICLES By

Y. B. ZELDOVICH ACADEMY OF SCIENCES USSR, MOSCOW, USSB.

The recent radioastronomical observations strong]y s u p p o r t t h e h o t model of the Universe. The implications of this model ate discussed, and, in particular, a h estimation is given for t h e n u m b e r density of t h e quarks.

1. The observational basis The observations made b y r a d i o a s t r o n o m e r s during the last y e a r have shown t h a t the h o t model of the Universe is the correet one. These observations revealed the existence of a P l a n c k s p e c t r u m of black b o d y equilibrium radiation with t h e t e m p e r a t u r e 3 ~177 0,3 ~ K, isotropic in all directions and filling all space. This radiation is superimposed on the light of the stars m o s t l y in the visible p a r t of the s p e c t r u m , and of n o n t h e r m a l radio-sources prevailing at ~ > 50 cm. The m e a s u r e m e n t s were m a d e b y r a d i o m e t h o d s at ~ = 20 cm, 7,3 cm, 3 cm and 0,25 cm. T h e last point belongs to ?~c~lkT ~ 2. I t is i n d e p e n d e n t l y checked b y the m e a s u r e m e n t of p o p u l a t i o n ratio of two n e a r b y states of the molecule CN. T h e bolometric and colour t e m p e r a t u r e s at different wavelengths coincide and gire 3 ~ 0,3 o. At 7 cm t h e b l a c k b o d y i n t e n s i t y is some 102 more, at 0,25 some 105 more t h a n the calculated i n t e n s i t y due to k n o w n sources (stars, radiosources, quasistellar sources). T h e i n t e g r a t e d density of electromagnetic r a d i a t i o n of t h e b l a c k b o d y spectrum at 3 ~ K is 6 9 10 -13 erg/cm 3. I t exceeds b y a f a c t o r of 30 or 50 the m e a n density of r a d i a t i o n of k n o w n sources. The m e a n m a t t e r density in the Universe is still little k n o w n . The density of m a t t e r in the forro of galaxies is said to be 5 9 10 -3i g/cm 2 including visible stars, gas, dust and all other forms of invisible m a t t e r . This d e n s i t y is e v a l u a t e d b y the dynamics of galaxies as g r a v i t a t i o n a l l y b o u n d systems. Cosmological evidence does n o t exclude a m e a n d e n s i t y of 2 9 10 -29 g/cm 3. The greater p a r t of ir in this case should be in the forro of a highly ionized highly transp a r e n t i n t e r g a l a c t i c plasma at 105 -- 106 ~ h e a t e d b y cosmic rays. Of course ~*

Acta Physica Academiae Sciemiarurn Hungarir

22, J967

52

Y. B. ZELDOVICH

this plasma is not in equilibrium with the 3 ~ radiation, but is cooling very slowly. Neither the radiation from stars of other discrete sourees, nor the radiation of the hypothetical plasma can gire the 3 ~ blackbody radiation.

2. The hot model The only possible past state of the Universe, compatible with the observed situation is the so-called hot model first p u t forward by GEORGE GAMOW in 1947. The eosmological t h e o r y of A. A. FRI~DMAN (1922--24) whieh ineorporates the Hubble red shift and expansion gire the following pieture: there was a mo men t t : 0 (1010 years ago) when the density was infinite; from this m o men t begins the general expansion. The expansion is isotropic and uniform: all directions in spaee ate alike. The mean density of baryons decreases like R -3, where R is the linear scale. The density of q u a n t a decreases in the same way like R -a. But at the same time the wavelength of quanta ~ increases like R , so their energy E r -~ = ~c/~. decreases like R -1. T he overall energy density of quanta decreases like e~, = n y E~, = R - 4 = a T 4 .

This is perfectly in aceord with the Iaw of adiabatic expansion. The e n t r o p y per baryon is given b y S - 9 e~, ~

T','-J

4

aT a

--, 3 nb

so S = const corresponds to

n~/3

Th e dimensionless S divided by Boltzmann k (entropy per baryon) t od ay is of the order of 10 s -- 109. This means t h a t the number of quant a per b ar y o n is of the same order of magnitude. Then for the distant past, when the energy of quanta was far greater, we obtain the pieture of a quite uniform plasma with overwhelming number and energy of quanta. The electrons and ions constituting " o r d i n a r y m a t t e r " , from whieh stars and planets are built, were a small minority at this stage (t < 105 years). Only at a later stage the temperature of the radiation drops in the eourse of expansion, the eleetrons and ions go into neutral atoms, gravitational instability gathers t hem together in elusters, from whieh galaxies and stars ate formed -- in short, the present period of astronomieal evolution begins. We shall not follow these questions further.

3. Nuclear reactions and the primordial composition Let us return to the ver y beginning, with very high temperatures. The energy density as a function of time is given by the equations of mechanics Acta Physica Academiae Scien$iarum Hungaricae 22, 1967

53

THE ttOT /dODEL OF T H E UNIVEBE

quite independently of the composition of plasma: e

Q.

. C2

3 . . 32zl G t 2

.

5.105 [~] . t2

g

, [t] = see.

cm 3

The only assumption is t ha t of isotropic and uniform expansion. At very high density the time of the equilibrium adjustment is much smaller than the time of considerable diminution of the density. So to the first approximation the expansion goes through a succession of equilibrium states. The equilibrium at some moment for example when t = 10 -3 sec, T = 30 MeV, does not depend on previous states. So one can foresee t h a t at this moment there are no measurable quantities of antibaryons, excited states (resonances) and mesons. There ate quanta, electrons, positrons, neutrinos and antineutrinos of both sorts in commensurable quantities. Contrary to this, the number of baryons is small (10 - s - 10 -9 of the mentioned particles), the equilibrium e+ q - n ~ p q - ' t ' e , e-q-pZn-4-~e is rapidly established so t hat n / p = - =

e--Am'c'~/KT ~

1 ,

During the expansion at T ~ 1 MeV, t ~ 1 sec, the reaetion tate is no longer great enough. The eomposition 16~ N, 840/0 P i s "queIlched" i.e. is not much altered during subsequent expansion by the mentioned reactions. By subsequent nuclear reactions of the t ype N + P = D-I- 7,; P + D : H e 3 + ~ ; D+D=He3+N; He 3 + N : - - T +

D+D:T+P; P, T + D :

HO 91

T+P=HO+~; He 3 + D =

HO+D

one should obtain 70% H and 30% H O (by weight), with 10 -4 -- 10 -5 of D and He 3. Some astrophysicists claim t h a t observations confirm this composition, but there ate rumours of old stars with a smaller helium content. The investigation of helium content is very difficult, owing to its high potential of ionization and excitation from ground state. At least the observations do not disprove the hot model, and the evidence from the 3 ~ radiation is of overwhelming importance.

4. " R e l i c t " t h e r m a l n e u t r i n o s a n d their d e t e c t i o n

Near the m om ent when N +_~ P equilibrium is quenched, the reaetion e+-4 - e - ~ _ v e + Ve also beeomes slow. I t has no immediate consequences Acta Physica .4cademiae Scientiarum Hungarica6 22, 1967

54

Y.B. ZELDOVICH

because the t e m p e r a t u r e of i n d e p e n d e n t Ve, ~'e and e +, e - 9, drops in the same t e m p o when e +, e - ate relativistic, at T > 0 , 5 M a V . B u t later when e -+ disappears at T < m - c 2, their e n e r g y is p u m p e d into 9', t h e drop o f ~ - t e m p e r a t u r e is r e t a r d e d , eompared with the drop o f v - t e m p e r a t u r e . As a result n o w T~~ = / ~ l Ÿ- ) T y . T o d a y , when the T e = 3 o, the t h e o r y predicts t h a t there shall be an equilibr i u m distribution of Vj'e and also of v,~, corresponding b o t h to the t e m p e r a t u r e

T e ~ 2 ~ K.* Their e n e r g y d e n s i t y is of the order of 1,5 9 10 -t3 erg/em 3 = 0,1 eV/cm 3, the mean energy is E 5 9 10 -4 eV, the n u m b e r density n ~ 200 1/cm 3. The experimental investigation of these neutrinos is of the u t m o s t i m p o r t a n c e a s a direct p r o o f of the v e r y basis of m o d e r n cosmology. B u t the t a s k is immensely difficult. The various m e t h o d s for investigating cosmic n e u t r i n o s is reviewed in the r e p o r t of G. MARX at the B a l a t o n school. So we m a k e only a few remarks. T h e energy flux of solar neutrinos is e s t i m a t e d to be 5 % of the t o t a l e n e r g y flux (108 erg/cm 2 sec) i.e. 5 9 104 erg/cm 2 sec; it gives the energy d e n s i t y 5 9 104 c -1 = 10 -6 erg/cm 3. B u t the energy of solar neutrinos is of the order of 2 MeV so their n u m b e r density at the E a r t h is n ~ 1 cm -3. As is well k n o w n , there ate feasible projects for detecting solar neutrions. T h e main difficulty in our case arises a s a result of the v e r y small e n e r g y of cosmologic• ( " r e l i c t " ) neutrinos. I r has been proposed to determine the effects near the e n d p o i n t E o of s p e c t r u m in t r i t i u m decay. A t E ~ E o - - k T , where T = 2 o, k T - - 2 9 10 -4 eV, t h e electron n u m b e r shall be h a l f as small c o m p a r e d with the n o r m a l t h e o r y (Kurie plot). B u t it appears n o w a group of electrons with e n e r g y higher t h a n E 0 f r o m v q- T -----He z + e - . T h e i r / ~ - - E 0 ~ 6 k T = 10-3 their n u m b e r is the same as the n n m b e r of missing eleetrons from the o t h e r side of E 0, A N = - 3 / T~---/3N

I EoJ

~-~ 3 9 10 -24 N for t r i t i u m - h e l i u m decay where N is the n u m b e r of n o r m a l electrons. One should speculate on w h a t effect relict neutrinos have on cosmic rays of artificially accelerated particles. The relict neutrinos single out the frame of reference in which the n e a r b y galaxies are at rest; only in this f r a m e t h e y are isotropic and w i t h / ~ ~-~ 10 -3 eV. I n the frame of a relativistic particle with E• = 919 MpC2; 91= (1--~2) -~'2 the v~ a p p e a r as a gegenstream, with E ~-~ ~ 8 9 10 -3 eV, with t h e density of the order of n = n o 91 and effective angular spread O ~-~ ~-1. The increase of d e n s i t y is c o m p e n s a t e d b y the * D u r i n g t h e s t a y a t B a l a t o n , a n i n t e r e s t i n g r e m a r k w a s m a d e in a d i s c u s s i o n w i t h Gv.RSHTEI~: t h e m a s s of vt~ is k n o w n o n l y to be s m a l l e r t h a n 2 MeV b y p a r t i c l e p h y s i c s . B u t c o s m o l o g i e a l e v i d e n e e p e r h a p s could p u t a m u c h m o r e s t r i n g e n t l i m i t , m (v~) < > m e / w o = 5 K e V , b e e a u s e in t h e o p p o s i t e case t h e d e n s i t y of t h e t e s t m a s s of v• ~~ w'ould be t o o g r e a t , m o r e t h a n t h e a l l o w e d 2 = 4 9 10-29. Acta Physir

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Scientiarurn Hungarir

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THE HOT MODEL OF THE UNIVERSE

55

relativistic time dilatation, when one calculates the n u m b e r of interactions per unit length of p a t h in the l a b o r a t o r y frame. The non-specific scatterings on neutrinos ate far smaller t h a n the similar scattering of t h e particle on t h e r m a l e l e c t r o m a g n e t i c q u a n t a . For t h e specific reaction P @ v ~-- N -4- e § one m u s t have P with E = 10 ls eV in l a b o r a t o r y frame, and still the equilibrium n e u t r o n c o n t e n t is only 10 ls of the protons, ir only i n t e r a c t i o n with relict neutrinos is considered. The effect of the smaller n u m b e r of more energetic stellar neutrinos is overwhelming. P e r h a p s the collective coherent effects are more promising: for a neutrino with E N 10 -3 eV, the w a v e l e n g t h ~ ~ 0,1 cm, all t h e electrons of a macroscopic v o l u m e scatter in the same phase, and the v i n t e r a c t i o n with the nuclei is of second order and does not c o m p e n s a t e the electrons. These effects are best described b y the notion of the refractive index of o r d i n a r y m a t t e r for neutrinos. Let us s t a r t from the i n t e r a c t i o n t I a m i h o n i a n , H i n t ~ g~eO~)e~~Oto, (after Fierz t r a n s f o r m a t i o n ) single out 0 - - - - ? 4 and sum the c o n t r i b u t i o n of all electrons ~~?~Ve = ~~ where n~ the electron density, cm -3. So the energy of a neutrino with given impulse p = Eo/c is a h e r e d in m a t t e r b y the a m o u n t A E ~--gne. h correspouds to the i n d e x of refraction ~ such t h a t : zJ~/= ~ - - 1

zJE -

-

-

Eo

-

-

g -n~ ~ 10 -9 for no ---- 6 . 1 0 24 (gold) a n d E 0 = 10-3eV. E0

The sign of (~ -- 1) is opposite for v and ~. P e r h a p s one should search for the low e n e r g y excitations b y neutrinos in a solid cooled down to T ~ 10 K. F o r p h o n o n e x c i t a t i o n ir is the m o m e n t u m of neutrinos which is limiting more t h a n their energy. Finally, on a u n i f o r m l y m o v i n g macroscopic particle of r ~-~ Ÿ N 0,1 cm a force of the t y p e of friction is expected.

F = - - ~ ~ r ~v

(2n) ~,

r

so t h a t the inverse time of deceleration of the order 1 _ [ F

= 3 . 1 0 -42sec -1

l! ~ ~ - ~ ~, because zJn ~-~ ~, as it m u s t be for coherent effects]. The

same

time ~ characterizes the onset of B r o w n i a n motion, corresponding to 2 o, of Acta Physica Academiae Sr

Hungaricar 22, 1967

56

Y.B. ZELDOVICH

t h e particle due solely to the i n t e r a e t i o n w i t h relict neutrinos. Obviously, t h e s e effects are quite u n o b s e r v a b l e .

5. Quarks in the hot model L e t us assume t h a t q u a r k s e x i s t a s

n o r m a l h e a v y (m) particles and

a n t i p a r t i c l e s w i t h one sort (fo r e x a m p l e q w i t h z = ~- -2- e w i t h ~ with - - -2- e1 3 3 stable against w e a k i n t e r a c t i o n . At t h e v e r y beginning, w h e n k T >~ mc 2 t h e y were as n u m e r o u s as a n y o t h e r particles. D u r i n g cooling down their e q u i l i b r i u m e o n c e n t r a t i o n drops:

I k T 13/21mCl~e_mC~q nq = n~ ~ [ mc 2 ] ,---~-]

B u t t h e n comes a m o m e n t w h e n the r e a c t i o n r a t e of the e s t a b l i s h m e n t of e q u i l i b r i u m is too small, t h e r e m a i n i n g q a n d ~ ate " q u e n c h e d " . T h e i r conc e n t r a t i o n is f u r t h e r diminished only b y t h e general expansion, the r a t i o of q/2, q/v or q/P, N (short for n f f n ~ . . . ) tends to a finite limit. T h e q u a r k s are s t r o n g l y i n t e r a c t i n g a n d t h e small t a t e of t h e reactions leading to t h e disa p p e a r a n c e of q u a r k s is due to the fact t h a t one m u s t h a v e always t w o q or q a n d ~ for the reaction q -~- q = B + ~ (B for b a r y o n s ) or q + ~ = energy. So e v e r y one q of q is stable, b u t on the o t h e r side, triple encounters 3 q = B ~-}- e n e r g y , 3 ~ = B -4- e n e r g y are not necessary. 1 T h e inverse t i m e of b i m o l e c u l a r r e a c t i o n - - = avnq, where a is crossT

section, v velocity, nr c o n c e n t r a t i o n . This t e n d s to zero with nq --> 0 . 1 1 So t h e r e exists ah nq which m a k e s - - _ < , ti being the h y d r o d y n a m i c t i m e of expansion. T h e c o r r e s p o n d i n g nq/P is c o n s e r v e d a f t e r w a r d s (up to a n u m e r i c a l coefficient) b e c a u s e during t h e e x p a n s i o n

d (nq/P) __ dt

av (nq/P) 2 P

a n d t h e S P d t = f t a'2 dt does n o t diverge on t h e t = ~ side. W h a t is i m p o r t a n t ti

is t h a t the condition of q u e n c h i n g singles out a definite he---- n I . Acta Physica Academiae Scivntiarum Hungaricae 22, 1967

T H E HOT MODEL OF T H E U N I V E R S E

57

The equilibrium nq depends e x p o n e n t i a l l y on the mass of the quark. B u t if nq -~ n 1 is defined, it means t h a t the m o m e n t of quenching t 1 and the characteristic t e m p e r a t u r e T 1 adjust themselves to the mass M. So the resulting n 1 does not d e p e n d exponentially on M. The h y d r o d y n a m i c time t 1 ~ 1/89 because ~ ~-~--l/Gt 2, t = VG/~. B y the quenching condition

n I ~-~--

1 ~.~ VC..

ti

If~r~,~

(~ct~c- - ( b y

t h e order of m a g n i t u d e ) , t h e n b y

dimension a r g u m e n t

V

/

ni = 1 Gm~2 ~ 1 0 -~9, N1 hc 2

where N 1 is the n u m b e r density of all other kinds of particles (7, ~. . . . ) at the m o m e n t of quenching. B u t the n u m b e r density of b a r y o n s remaining after cooling is also a small p a r t of all kinds of particles, of the order of 10 -9. So the model predicts t h a t primordial m a t t e r contains some 10 -10 quarks per b a r y o n ! Of course we ha,ce lost here logarithmic factors of the t y p e (In Gm2/?~c)-l~--~-0,01 b u t the result is still impressive, because, for example, the ratio of gold to h y d r o g e n is now of the order of 10 -12. The result a b o u t quarks quenching is due to OKU~, PIKELNER and the author. One m u s t acknowledge t h a t at the time of their work, the hot model had not been p r o v e d correct b y r a d i o a s t r o n o m e r s , so in the original paper there are two e x t r e m e figures -- for the hot and for the cold model. Now the higher one (for the hot model) should be taken. The b u r n i n g out of quarks in stars is not v e r y great (see the original papers). T h e last work b y DOMOKOS and i n d e p e n d e n t l y done b y FEI~BSRG and al. has shown t h a t the q u a r k p r o d u c t i o n in cosmic r a y encounters is small. So the search for relict cosmological quarks appears to be more appealing - - ir quarks exist at all, of course!

6. The c h a r g e - - q u a s i - s y m m e t r y

o f the U n i v e r s e

T h e r e ate no signs of charge s y m m e t r y in the c o n t e m p o r a r y state of the Universe. T h e a t t e m p t s at a t h e o r y of charge s y m m e t r i c a l Universe with spontaneous division of m a t t e r and a n t i m a t t e r are artificial and not in accordance with general cosmological t h e o r y . .4eta Physica ,4cademiae Scientiarum Hungaricae 22, 1967

58

Y. B. ZELDOVICH

I n m y opinion this a s y m m e t r y of state ( p r e v a l e n c e of " m a t t e r " o v e r a n t i m a t t e r ) does n o t in a n y w a y c o n t r a d i c t t h e k n o w n s y m m e t r y of properties of particles and antiparticles. B u t in t h e h o t m o d e l of t h e U n i v e r s e t h e r e is ah enigma: e a r l y a t T ~,~ Mvc2, t h e r e were a n t i b a r y o n s , so t h a t a p p r o x i m a t e l y B/B:

1 + 10 -s.

T h e e a r l y s t a t e was almost eharge s y m m e t r i e a l , b u t the small d e p a r t u r e (of t h e o r d e r of l0 -s) f r o m full s y m m e t r y is of the u t m o s t i m p o r t a n e e for the p r e s e n t state. Such a s i t u a t i o n seems v e r y s t r a n g e . P e r h a p s m o r e a p p e a l i n g is t h e a s s u m p t i o n t h a t t h e r e was a p r e v i o u s h i s t o r y a t t < 0, before t h e singular s t a t e of t~-- 0, ~ = c~, T = c~. One eould a s s u m e t h a t at t < 0, t h e r e was no charge s y m m e t r y j u s t as now. N o r m a l m a t t e r prevailed. B y some nuelear r e a e t i o n s and o t h e r proeesses t h e m a t t e r was heated. D u r i n g the implosion at t < 0 the pairs B , / ~ were b o r n q u i t e n a t u r a l l y , t h e exeess of B o v e r /~ r e m a i n i n g . This exeess also r e m a i n s w h e n at t----- 0 t h e implosion at t < 0 is r e v e r s e d to t h e e x p a n s i o n at t > 0 . Sueh a eosmologieal t h e o r y has r e e e n t l y b e e n e l a b o r a t e d . T h e diffieult p o i n t is of eourse n e a r t = 0 w h e r e at high densities general r e l a t i v i t y is i n t i m a t e l y tied w i t h q u a n t u m m e e h a n i e s . I t is t h e b e a u t i f u l w o r k of ROLAr~D ]~iJTVSS w h i e h is t h e basis of ALBERT EI~STEI~'S general r e l a t i v i t y a n d t h r o u g h this of m o d e r n cosmology. I t is a great h o n o u r to m a k e this r e p o r t to a conference held b y t h e R o l a n d E6tviSs Society. B u t ir is also a t r i b u t e to t h e m e m o r y of t h e g r e a t H u n g a r i a n Physicist. LITERATURE (exhaustive eitation is given in the quoted surveys) a) General eosmglogical baekground: YA. B. ZELDOVtC~,Advances in Astronomy and Astrophysics (Kopal eclit.) Vol. III., 1965. The hot Universe -- a review YA. B. ZELDOVlC~t, Uspehi Phys. Nauk, 89, 647, 1966. Original measurements: A. A. P~.~rzlAs and K. W. WIL$ON, Astrophys. Journ., 142, 419, 1965. Interpretation: DICKE et al., ibid. 142, 414, 1965. b) Neutrinos: G. MAnX -- this volume. S. WEINBERG, Phys. Rey., 128, 1457, 1962. c) Quarks: L. B. OKUN, S. B. PIKELNERand YA. B. ZELDOVmH,Phys. Lett., 17, 164, 1965. Uspehi Phys. Nauk, 87, 113, 1965. FoPHqX~I MO~EYlb BCEJIEHH0Ÿ H 3YIEMEHTAPHbIE qACTH~bI H. I3. 3E.rlbjXOBHq

Pe3~oMe Ho~bte paaa0acTp0HoMnqecnne Ha6n~aenaa aana n0aaep>xKy r0pnqefi Moaenn BceO£ C.rle~CTBii~l 9T0~ bl0ae~IH, II, B qaCTHOCTII, aaeTca 0tteHKa IUIOTH0CTII qHcna KBapKoB,

J/eHH0~.

.Acta Physiea .,4cademiae Seientiarum tlungaricae 22, 1967