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9 .1
Alternative ideas i
n cosmolog y
JA YA NT V . NA RL IK AR
Inter-University Centre for Astronomy and Astrophysics,
Pune
It i s show n tha t i n cosmology , a
s i n th e res t o f science , th e evolutio n o
f
observational evidenc e an
d theoretica l concept
s ha s ofte n le d t o th e accep -
tance o f idea s tha t wer e onc e considere d outlandish
. Fre d Hoyl e himsel f wa s
responsible fo r generatin g severa
l suc h ideas , althoug h h
e wa s muc h ahea d
of hi s time . Her e som e o f thos e idea s ar e outlined , idea
s tha t wer e though t
to be unrealisti c a
t th e time they were proposed , bu
t whic h hav e no w bee n
assimilated into mainstream
cosmology. A general commen t tha
t emerge s
from such examples i
s tha t highl y creativ e individual s wh
o ar e fa r ahea d
of thei r tim e d o no t ge t th e recognitio n the
y deserv e onc e thei r idea s ar e
accepted as standard .
Introduction
The origina l titl
e suggeste d fo
r m y contributio n t
o th e meetin g dedi
-
cated to the memor y o
f Fre d Hoyl e ha d bee n 'Alternativ e cosmologies'
. I changed
it t o th e presen t titl e fo r th e followin g reason
. Ther e hav e bee n occasiona l re
-
views o f alternativ e cosmologie
s fro m tim e t o time , th e mos t recen t on e bein g
by myself an d Padmanabha n (2001)
. Fre d himsel f ha d bee n th e originato r o
f a
few alternative
cosmologies. However , i
n th e presen t context , whil e highlightin g
his contribution s t
o cosmolog y i
t i s mor e interesting to
look at idea s o n specific
topics o f cosmologica l interest
rather tha n a t cosmologica l model
s pe r se .
In the decade followin g th
e observation s o
f th e microwav e backgroun
d ra -
diation by Penzias an d Wilso n (1965) , mos t cosmologist s mad
e u p thei r mind s
that th e so<alle d Big-Ban g cosmolog
y provide s th e correc t framewor k i
n whic h
The Scientifi c Legac y o f Fre d Hoyle , ed . D . Gough .
Published by Cambridge Universit y Press
. © Cambridge Universit
y Pres s 2004 , 127
Alternative ideas i n cosmolog y 12
9
to describe th e histor y an d large-scal e structur
e o f th e Universe . Althoug
h ther e
existed a rang e o f possibl e model s withi n thi s framework , the
y becom e collec -
tively known as 'standar d cosmology'
. An y othe r cosmologica l mode
l tha t di d no t
fall withi n th e standar d framewor
k wa s identifie d a
s 'non-standar d cosmology'
.
A revie w entitle d 'Non-standar d cosmologies
' b y mysel f an d Kembhav i (1979
)
summarized how such models deal t wit h th e variou s theoretica l concept
s i n
cosmology and the available observationa
l data .
However, i n th e 1980 s th e adjectiv e 'non-standard
' (whic h ha s somewha t neg
-
ative connotations ) wa
s replace d b y 'alternative' , i
t bein g presume d tha
t th e
alternative was wit h respec t t o standar d cosmology .
Nevertheless, th e adjectiv e 'standard
' i s itsel f a misnomer, sinc
e i t implie s
something stable an d invarian t wit
h respec t t o whic h other s ca n b e measured .
(The dictionar y meanin
g o f 'standard ' i
s typicall y 'o
f recognize d authorit
y o r
prevalence'.) I n a highly critical articl e o n cosmolog y Disne
y (2000 ) ha s give n
reasons a s t o wh y thi s adjectiv e i s inappropriat e i
n th e sens e i n whic h i t i s use d
in the context o f cosmology . Indeed
, h e ha s argue d tha t th e standar d mode
l i n
cosmology is nowher e a
s secur e an d laboratory-teste d a
s th e standard model i
n
particle physics.
That th e standar d cosmolog
y ha s evolve d considerabl y i
n th e fou r decade s
since th e 1960 s i s see n fro m th e variou s ne w concept s i t ha s acquire d durin g
that period , namely , inflation , dar
k matter , non-baryoni c matter
, cosmologica l
constant o r quintessenc e o
r dar k energy , ne w physic s involvin g mor
e than four
dimensions, etc . Indeed , idea s tha t wer e onc e considere d 'non-standard
' hav e
now become acceptable a
s 'standard' .
It make s sens e therefor e t
o concentrat e her
e o n such alternative
ideas i n
cosmology, particularl y thos
e wit h whos e origi n Fre d Hoyl e wa s associated . A
s I
propose t o show , thes e idea s wer e no t accepte d a
t th e tim e the y wer e proposed ,
but graduall y foun
d thei r way into the 'standard ' categor
y as cosmology
evolved.
Before proceedin g further
, however , i
t i s instructiv e t
o tak e a brief loo k a t th e
historical evolutio n o
f cosmologica l idea
s fro m earlie r times .
From 9.2 Aristarchus t
o Hubbl e
For viewin g histor
y on e ma y defin e 'standard ' a
t an y epoc h a s repre -
senting ideas believe d b
y th e majorit y a
t tha t epoch , whil e 'alternative ' woul
d
stand for idea s significantl y differen
t fro m th e standar d on
e (prevailin g a
t th e
time) bu t believe d b y a minority. A
s wil l shortl y b e seen , thi s distinctio n betwee
n
'standard' an d 'alternative ' i
s epoch-dependent . A
n ide a fallin g withi n th e alter -
native baske t a t epoc h t might wel l b e transferred to
the standard basket a t a
later epoc h t + A(
A >
0). Naturally , i
f A » huma n life-span , the
n w e hav e t o
conclude tha t th e originator(s ) o
f th e alternativ e idea(s
) faile d t o ge t credi t fo r
them while stil l alive .
Take Aristarchu s (c.
310-230 BC), for example, who
argued that the Earth
not
only spins abou t it s axis , bu t i t als o goe s aroun d th e Sun . T o prov e hi s point ,
he propose d wha
t i s toda y know n a s th e parallax method fo
r measurin g distance
s
of nearb y stars . Th e tes t faile d no t becaus e th e underlyin g hypothesi
s wa s fals e
but becaus e th e stella r distance s wer
e underestimate d an
d th e observationa l
techniques wer e no t sensitiv e enoug h t o measur e th e actua l parallax .
The standar d cosmolog
y o f thos e time s firml y believe d a geocentric universe
.
That belie f remained intact til
l Copernicu s (A
D 1473-1543 ) appeare
d o n th e
scene. However , it
took nearly a centur y befor e hi s alternativ e ide
a o f th e helio -
centric cosmology
became accepted. Thu
s fo r Copernicus , A
= 10 0 yr . S o fa r a s
Aristarchus i s concerned , hi
s contributio n ha
s bee n belatedl y recognize
d rela -
tively recently. Hi s bus t i n hi s home-tow n o
f Samo s carrie s th e inscription :
Aristarchus o f Samos..
. 320-23 0 BC..
. Firs t t o discove r th e Eart h
revolves aroun d th e Sun..
. Copernicu s copie
d Aristarchu s 153
0 AD..
,
Shall w e sa y tha t A(Aristarchus ) =
23 centuries?
While th e heliocentri c theor
y becam e standard , i
t to o ha d it s factua l limita -
tions. B y th e beginnin g o
f th e twentiet h century
, Herschel' s pictur
e o f th e Su n
close t o th e centr e o f th e Galax y ha d becom e standard , an
d wa s adopte d b y J . C .
Kapteyn in what ha d becom e know n a s th e 'Kaptey n universe'
. Harlo w Shapley' s
measurements o f distribution s an
d distance s o
f globula r clusters , however , le
d
to the realization
that th e Su n mus t b e wel l awa y (~8-1 0 kpc ) fro m th e Galacti c
Centre. I n thi s cas e on e ma y se t A at ~1 0 years , an d Shaple y coul d ge t th e credi t
during his lifetime .
An alternative
idea that rouse d considerabl e passio
n an d controvers y bega
n
with Immanuel Kan
t (1724-1804) , an
d i s know n a s Kant' s 'islan d universe ' hy
-
pothesis. Thi s hypothesi s envisage
d th e Univers e a
s a limitless system
, lik e a
vast ocean , i n whic h galaxie s lik e ou r Milk y Wa y existe d lik e islands . Obser -
vations ha d indee d reveale d a
number o f nebulae , cloud-lik e fain
t bu t lumi -
nous systems , som
e o f whic h (lik e th e Andromed a Nebula
) wer e claime d b y a
small minorit y t
o b e distan t galaxies , th
e Kantia n islands . Th e standar d vie w t o
which eve n Shaple y subscribe d was
, however , tha
t everything observed
till tha t
date was par t o f ou r Milky Way, whic
h wa s envisage d a
s th e Grea t Galaxy . Th e
above alternative claim
was dismisse d a
s unfactual . See
, fo r example , th
e follow -
ing extract fro m th e popula r 190 5 boo k calle d Th e System of th e Stars by Agnes
Clerke:
The questio n whethe
r nebula e ar e externa l galaxie s hardl y an y longe r
needs discussion . I
t ha s bee n answere d b
y th e progres s o f research . N
o
competent thinker , wit
h th e whol e o f th e availabl e evidenc
e befor e
him, ca n now , i t i s saf e t o say , maintai n an
y singl e nebul a t o b e a star
system of co-ordinat e ran
k wit h th e Milk y Way..
.
The not e o f finalit y an d certaint y indicate
s th e confidenc e fel
t b y th e majorit y
in the correctnes s o
f th e standar d picture
. Withi n tw o decades , however , thi
s
view had to be abandone d i
n th e fac e o f growin g evidenc e agains
t i t an d th e
lack o f dat a i n it s favour . Le t u s firs t loo k a t th e latter .
The mor e accurat e metho
d o f measurin g th
e distances using
the period -
luminosity relation for th e Cepheids , whic
h ha d bee n introduce d earlier
, wa s
applied by Hubble (1926 ) t o M3 1 an d M33 . H e foun d 5 0 variable s i n M31 , o f
which 40 were cepheids , an
d 3 5 cepheid s i n M33 . In addition, ther
e wer e know n
to be nin e i n NGC6822 , an
d Shaple y ha d measure d 10
5 in the Smal l Magellani c
Cloud (SMC).
Of course, Hubble realize
d an d stresse d tha t thes e distances would
be affecte d
by any change i n th e zer o poin t o f th e period-luminosit y relatio
n a s i t ha d bee n
derived by Shapley. Still
, th e ver y larg e distance s derive
d fo r th e spiral s wer e
compatible wit h man y attempts to
determine th e prope r motion of th
e spirals ,
which ha d alway s le d t o nul l result s ( a velocit y o f 100 0 k m s"
transverse t 1
o
the lin e o f sigh t woul d correspond to
an annual prope r motio n o f th e orde r o f
0".0007, a value fa r belo w wha t coul d b e measured) .
However, ther e wa s a stumbling bloc
k which led
many to question
these
large distances . Thi
s aros e fro m th e claim s b y A . va n Maane n (1916-30 ) a
t Moun t
Wilson to have determine d prope
r motion s i n th e spiral arms o
f a number o
f
nearby spiral galaxie s includin
g M33 , M81 , M101 , NGC2403 , 4051
, 4736 , 5055 ,
and 5195. A t a n indicativ e distanc
e o f 10 light year 6
s a n annua l motio n ~0".01 ,
which was o f th e orde r o f wha t wa s bein g claimed , correspond s t
o a velocity of
~15000 km s"
. Thu 1
s va n Maanen' s result
s corresponde d t
o period s o f rotatio n
of th e spirals , i f the y were assumed
to have size s simila r t o th e Milk y Way , o f th e
order 10 years o 7
r less , implyin g ejectio
n o f matte r o n simila r timescales , s
o tha t
the spiral s woul d disintegrat e i
n time s o f thi s order . However , late
r observation s
could not confir m thes e claims , an d the y graduall y fade
d away .
Side b y sid e wit h th e lac k o f confirmatio n o
f prope r motions , th e ne w metho d
of measurin g distance
s usin g th e Cephei d variable s le
d Hubbl e t o th e conclusio n
that nebula e lik e th e Andromed a Nebul
a (M31) , M33 , an d severa l other s li e wel l
beyond the Galaxy . An d s o th e Kantia n islan d univers e hypothesi s bega
n t o gai n
credibility. I f w e dat e thi s chang e o f paradig m t
o hav e take n plac e i n th e mi d
1920s, the n A(Kant ) = 1.5 centuries.
Alternative idea s i n cosmolog y 13
1
The abov e historica l backgroun
d ma y b e kep t i n min d whil e evaluatin g th
e
cosmological contribution s o
f Fre d Hoyle .
93 Interaction
of particl e physic s wit h cosmolog y
It i s generall y assume
d tha t particle physicists an
d cosmologist s firs
t
got togethe r i
n th e 1980s , th e latte r usin g idea s fro m particl e physic s a t ver y
high energy in order t o addres s issue s lik e th e origi n an d evolutio n o
f large -
scale structure . However
, th e firs t cosmolog y t
o dra w heavil y o n particl e physic s
was th e Steady-Stat e cosmology
, which explored
this frontie r are
a i n 195 8 a t
the Pari s Symposiu m o
n Radi o Astronomy . Th
e 'ho t universe ' o
f Gol d an d Hoyl e
(1959) wa s th e outcome . Briefly
, th e ide a wa s a s follows .
In the Steady-Stat e cosmology
, th e Univers e maintain
s a steady densit y despit e
expansion, b y continuou s creatio
n o f matter . Th e amoun t o f matte r expecte d t o
be produce d wa
s estimate d t
o b e extremel y small
, a t a rate ~10~
g cm" 46
s~ 3
. 1
Nevertheless, th e questio n was
, i n wha t for m di d thi s ne w matte r appear
? Gol d
and Hoyle propose d th
e hypothesi s tha
t th e create d matte r wa s i n th e for m o f
neutrons. Th e creation of neutron
s doe s no t violat e an y standard conservation
laws o f particl e physic s excep t th e constanc y o
f th e numbe r o
f baryons . Al -
though this wa s considere d a
n objectio n i
n 1958 , toda y th e numbe r o f baryon s
is n o longe r regarde d a
s strictl y invariant . Indeed
, a s w e shal l se e later , scenar -
ios based on non-conservation
of baryon s ar
e bein g propose d i
n th e contex t o f
the ver y earl y Univers e t
o account for th
e observe d numbe
r o f baryon s i n th e
Universe.
In the Gold-Hoyl e pictur
e th e create d neutro n undergoe s a
beta decay :
n->- p + e + v .
(9.1)
The conservatio n o
f energ y an d momentu m result
s i n th e electro n takin g u p
most of the kineti c energ y and thereby
acquiring a hig h kineti c temperatur e
of ~10 K. Gol 9
d an d Hoyl e argue d tha t suc h a high temperature
produced inho-
mogeneously would lead to the workin g o
f hea t engine s betwee n th e ho t an d
cold regions, whic
h provid e pressur e gradient
s tha t resul t i n th e formatio n o
f
condensations o f siz e >
50 Mpc. I t wa s already known
that pur e gravitationa l
forces ar e no t abl e t o provid e a satisfactory
picture o f galax y formatio n i
n a n
expanding universe. Th
e temperatur e gradient
s se t u p i n th e ho t univers e o f
Gold an d Hoyl e hel p i n thi s process .
The resultin g system
, however , i
s no t a single galaxy , bu t a supercluster o
f
galaxies containin g ~10
-10 3
members. Suc 4
h large-scal e inhomogeneitie
s i n th e
distribution of galaxie s cautio n u s agains t applyin g th
e cosmologica l principl
e
too rigorously. Fo
r example , i
f w e ar e i n a particular supercluster
, w e expec t t o
see a preponderance o
f galaxie s o f age s simila r t o tha t o f our s i n ou r neigh -
bourhood out t o sa y 2 0 o r 3 0 Mpc . Thu s i t wil l no t b e surprisin g i
f ou r lo -
cal sampl e yield s a n averag e ag e muc h large r tha n th e universa l averag
e o f
(SHo)- « 3 1
x 10%
years. J
Although newly created electrons hav
e a kinetic temperature
of ~10 K, 9
the temperatur e tend
s t o dro p becaus e o f expansion . Th
e averag e tempera -
ture i s three-fifth s o
f thi s value , tha t is , aroun d 6 x 10 K. I 8
t wa s suggeste d
by Hoyle i n 196 3 tha t suc h a hot intergalacti c mediu
m woul d generat e th e
observed X-ray background . However
, quantitativ e estimate
s b y R . J . Goul d
soon showed that th e expecte d X-ra
y backgroun d i
n th e ho t univers e woul d
be considerabl y highe
r tha n wha t is actually
observed, thu s makin g the hot
universe untenable . Th
e present-da y backgroun
d measurements , however
, d o
not rul e ou t suc h a hot univers e fo
r h « 0.5 0
. Astrophysicist s toda
y are, how-
ever, incline d t
o loo k fo r othe r explanation s fo
r th e origi n o f th e X-ra y back -
ground.
Although it i s no w discredited , th
e ho t univers e mode l wa s th e firs t exercis e i n
linking particle physic s (neutro n decay ) t o th e formatio n o
f large-scal e structures
in the Universe .
Notice, however , th
e differenc e i
n approac h her
e fro m th e standar d astroparti
-
cle physics . Th e latte r relie s o n unteste d extrapolatio n o
f particl e physic s couple d
with assumed
initial condition s fo
r seedin g large-scal e structure
and seeks t o ar -
rive a t th e presen t hierarch y o
f structure s throug
h severa l regime s o f evolution ,
neither al l directl y observabl e no
r analyticall y calculable
. Th e forme r take s th e
process o f bet a decay , whic h i s wel l teste d i n th e laborator y an
d build s o n i t i n
timescales o f th e orde r o f th e present-da y expansion
, t o arriv e a t th e supercluste r
scale structure .
In the 1960 s cosmologist s by-and-larg
e ha d no t gon e beyon d classica l gravit y
to address th
e proble m o
f structur e formation
; no r ha d the y (a s see n i n th e
following section) gon
e t o th e exten t o f acceptin g structur
e o n th e scal e o f
superclusters. Th e appea l t o a particle physics interactio n i
n th e abov e mode l wa s
therefore viewe d wit h scepticism , and
the outcome in the
form of supercluster s
was considere d irrelevan
t t o cosmology .
It i s somewha t ironica
l tha t toda y cosmologist s accep
t uncriticall y concepts
like GUT s an d supersymmetry , a
phase transitio n a
t 10 GeV, non-baryoni 1 6
c dar k
matter (col d o r hot) as foundation s o
n whic h t o buil d th e evolutio n o
f th e Uni -
verse acros s a decrease o
f 8 7 orders of magnitude in
density and 29 orders o f
magnitude in temperature, whe
n none of the physics of
the initial epochs is
tested in
a laboratory.
Moreover, supercluster s are
no longer under a
taboo, but are wel l
accepted. Thu s i n thi s case , w e hav e A = 2 0 year s fo r Fred .
Alternative idea s i n cosmolog y 13
3
9.4 The rol e o f supercluster s i
n radi o sourc e count s
In 19 6 1 Marti n Ryl e an d hi s colleague s a
t th e Mullar d Radi o Astronom y
Observatory in Cambridge announce
d th e result s o f th e 4 C radi o sourc e survey ,
claiming that th e sourc e count s ha d a super-Euclidean
slope tha t disprove d th
e
Steady-State theory . I n a uniform distribution
of source s i n a Euclidean
universe
the numbe r N
of source s brighte r tha n flu x densit y S goes a s S"
- 1
, That 5
is, i n
the log N - log S plo t th e slop e o f th e numbe r coun t N(
> S ) curv e wil l b e -1.5 .
Ryle reporte d a
slope o f -1.8 , wherea s th
e Steady-Stat e theor
y wa s expecte d t
o
give a slope beginnin g wit
h -1.
5 a t hig h S, and flattening
at lowe r value s o f S .
In January of 1961 , Ryl e state d thes e point s t o clai m tha t th e Steady-Stat e theor
y
was disproved .
I ha d joine d a s Fred' s researc h studen t barel y si x month s earlier , an d h e aske d
me t o develo p a counter t o Ryle' s clai m alon g th e followin g lines
:
(a) Assum e tha
t th e Univers e i
s inhomogeneou s o
n th e scal e ~50Mp c o
f
superclusters. Thu s ther e wil l b e mor e galaxie s i n a supercluster, an
d
fewer (ideall y zero
) i n th e voi d outsid e it .
(b) Assum e tha
t a galaxy becomes a
radio sourc e a s i t ages , i.e . th e
probability P tha t th e galax y become s a radio source increase s wit
h
age T.
He suggeste d a
n empirica l formul
a P a exp(4Hr) .
The supercluste r ide
a ha d com e fro m th e Gold-Hoyl e ho
t univers e model
.
The notio n o f age-dependenc e o
f a radio sourc e propert y wa s base d o n th e then -
available indication s tha
t radi o source s do not aris e fro m collidin g galaxie
s
but ar e generall y associate
d wit h elliptica l galaxie
s (whic h wer e considere d
older tha n spirals) . I n an y case , Fre d Hoyl e ha d maintaine d th
e reasonabl e
stand that on e shoul d no t dra w cosmologica l conclusion
s fro m population s
of source s whos
e physic s wa s stil l unknown . Eve
n toda y th e power-hous e o
f
a doubl e radi o sourc e an d th e genesi s o f it s jet s ar e hardl y wel l under -
stood.
With these postulates, whic
h i n n o wa y altere d th e basi c tenet s o f th e Steady -
State cosmology , w
e wer e abl e t o demonstrat e tha
t a n 'average ' lo
g N - lo g S
curve wil l hav e a super-Euclidean
slope a t hig h flu x level s a s foun d b y Ryl e
et al.
(Hoyle an d Narlika r 1961)
.
The poin t tha t Fre d wishe d t o emphasiz e wa
s that , becaus e o f supercluster -
scale inhomogeneity , th
e slop e o f th e lo g J V - log S curv e fluctuate s a
t larg e
values o f S depending
on the location of th
e observer , althoug
h a t lo w S it
settles dow n t o th e cosmologica l sub-Euclidea
n valu e predicte d analytically
. Thi s
expectation was late r confirme d observationally
by deeper survey s (Kellerman n
and Wall 1987) .
To demonstrat e thi
s fluctuation , Fre
d an d I thought o
f carryin g ou t N-bod y
Monte Carl o simulation s o
n a n electroni c computer
. Th e Cambridg e EDSA
C wa s
manifestly inadequate fo
r thi s computation , bu
t Fre d ha d acces s onc e a week
to an IBM 7090 in London. S
o wit h a few weekly visits t o Londo n I was abl e t o
carry ou t thi s demonstration . Thi
s wa s probably the firs
t compute r simulatio
n
in cosmology
(Hoyle an d Narlika r 1962) .
A grea t dea l wa s mad e o f th e steepnes s o
f th e lo g N - lo g S curve a t hig h
flux end , wit h the claim that it implies evolution
, whic h is inconsistent wit
h
the Steady-Stat e cosmology
. Kellerman n an
d Wal l (1987 ) hav e commente d o
n
how the effec t wa s blow n ou t o f proportion, being
confined to about 50 0 rela -
tively nearby sources. Indeed
, i f th e resul t wa s cosmologicall y significant
then
one mus t demonstrat e tha
t th e sourc e populatio n ha
s evolve d ove r th e perio d
covered by the survey . Fo r testin g evolutio n on
e need s t o kno w th e redshift s
of thes e sources . Ver y fe w redshift s wer
e know n i n 1961-2 . B y th e mi d 1980s ,
however, mos t source s i n th e SC R catalogu e ha
d their redshifts determined
. Us -
ing this additiona l informatio
n DasGupt a e
t al.
(1988) wer e abl e t o sho w tha t n o
evolution was necessar y fo
r th e consistenc y o
f mos t Friedman n model
s (wit h
A = 0), wit h th e source-coun t dat
a a s pe r th e 3C R catalogue . DasGupt
a (1988 )
later showe d als o tha t eve n th e Steady-Stat e cosmolog
y wa s consisten t wit
h th e
SCR source count . Simila r complet e redshif
t dat a for the 4C survey
are not yet
available for carrying
out suc h analysis .
In the 1960 s th e concep t o f supercluster s wa
s no t 'standard' , an
d mos t cosmol -
ogists believe d tha
t th e Univers e wa
s homogeneou s o
n scale s large r tha n cluster s
of galaxie s (~
5 Mpc) . Th e idea that th e Univers e ca
n b e inhomogeneou s o
n th e
supercluster scal e introduce s a
larger degre e o f fluctuations in
the predicte d
values o f observationa l test
s o f homogeneou s cosmology
. Evidenc e existe
d fro m
the studie s o f Abel l (1958) , d e Vaucouleur s (1961)
, Shan e an d Wirtane n (1954
) o n
superclusters, bu t nobod y believe d tha t th e Univers e coul
d b e inhomogeneou s
on such a larg e scale . Th e 'complication ' introduce
d b y inhomogeneit y o
n th e
scale o f supercluster s (~5
0 Mpc ) wa s therefor e fel
t unnecessar y i
n th e opinio n
of man y theoreticians , an
d certainl y a
high price t o pa y i n orde r t o kee p th e
Steady-State theor y alive . I t wa s som e tw o decade s later , i n th e 1980s , tha t th e
existence o f supercluster s an
d void s o n scale s o f 50-10 0 Mp c becam e par t o f
standard cosmology. Thu
s i n thi s instance , I
would set A = 2 5 year s fo r Hoyle' s
belief i n superclusters .
I no w retur n t o th e interactio n betwee
n cosmolog y an
d particl e physics .
9.5 Non-conservatio n o
f baryon s an d negativ e stres s energ y
I understan d tha
t Fre d had sent his first manuscrip t on
the Steady-Stat e
cosmology to a wel l know n physic s journal . I t wa s rejecte d there presumably
because physicist s looke
d upo n continuou s creatio
n a s a violation
of th e la w o f
conservation of matte r an d energy . (Th e reaso n fo r rejectio n cite
d b y th e journal ,
however, wa s a curious one , namel y tha t i t wa s facin g shortag e o
f paper.
) H e
subsequently sent i t t o th e astronom y journa
l MNRAS . I n fact , unlike the versio
n
of Bond i an d Gol d (1948) , th e versio n o f Steady-Stat e cosmolog
y advocate d b
y
Fred Hoyle (1948 ) does not violat e th e abov e conservatio n law
. There , a scalar
field of negativ e energ
y an d pressur e wa
s used , a n ide a tha t physicist s foun
d
abhorrent. I t i s significan t tha
t th e ide a i s no w gainin g popularity , se
e it s recen t
'rediscovery' b y Steinhard t an
d Turo k (2002) . Thu s on e coul d argu e tha t A S 5 0
years fo r thi s ide a originall y propose
d b y Hoyle .
The Gold-Hoyl e ho
t univers e mode
l ha d continuou s creatio
n o f neutrons .
In general Hoyl e believe d tha t baryon s (i n preferenc e t
o antibaryons ) woul
d b e
created. Thi s break s th e baryon-numbe r conservatio
n la w a s wel l a s baryon -
antibaryon symmetry, whic
h wer e considere d sacrosanc
t i n th e 1960s . Thu s
when our pape r (Hoyl e an d Narlika r 1966a
) o n non-conservatio n o
f baryon s i n
cosmology came u p th e physicist s wh
o too k not e o f i t argue d tha t th e ide a
violated the abov e principles .
Again it i s significan t tha
t wit h th e approac h t
o Gran d Unifie d Theorie s
particle physicists themselve
s foun d thes e principle s n
o longe r necessary . Indee
d
they were highl y constrainin g t
o Big-Ban g cosmolog y i
f on e wishe d t o explai n
the observe d baryon-antibaryo
n asymmetr y an
d th e baryo n t o photo n ratio . I n
the end , high-energ y particl
e physicist s hav
e droppe d thes e symmetries .
On one occasio n Fre
d Hoyl e himsel f answere d th
e criticis m o
n baryo n non -
conservation by stating that thi s i s th e consequence of broke
n symmetr y whic
h
perpetuates itself . Th e C-fiel d whic h mediate s i
n th e creatio n proces s ma y hav e
internal degree s o
f freedo m tha t favou r matte r ove r antimatter . Sinc
e i n late r
(post-1964) version s o
f th e C-field , actio n a t a distance formulatio
n wa s use d
(see Hoyl e an d Narlika r 1964) , on e coul d argu e tha t th e informatio n o
f broke n
symmetry in one spacetim e even
t coul d b e carrie d alon g ligh t cone s t o th e
future and thus spread all ove
r th e Universe .
If w e dat e th e notio n o f baryon non-conservation
in cosmology
to the Hoyle -
Narlikar pape r o f 1966 , an d loo k a t th e 197 9 publicatio n b
y Steve n Weinber g
(entitled 'Baryon-lepton
non-conserving processes'), w
e ma y se t A = 1 3 year s fo r
this idea . I n fac t al l thre e o f th e trilog y o f paper s publishe d b
y Hoyl e an d m e
in 1966 hav e foun d echoe s i n subsequen t year
s a s w e shal l se e i n th e followin g
two sections.
Inflation 9.6 and
the bubbl e univers e
I no w com e t o th e fiel d theor y wit h which Hoyle an
d I worked in order t o
derive th e physica l propertie s o
f th e Steady-Stat e univers
e relate d t o gravit y an d
matter creation . Th
e C-fiel d theory , a s i t i s called , wa s i n fac t base d o n th e scalar -
field formulation
provided b y M . H . L Pryce i n 196 1 a s a private communication.
Like Hoyle' s origina l approach , th
e C-fiel d theor y als o involve d addin g mor e
terms t o th e standar d relativisti
c Einstein-Hilber t actio
n t o represen t th
e phe -
nomenon of creatio n o
f matter . Usin g Occam' s razor , th e additiona l fiel
d t o b e
introduced was a scalar fiel d wit h zer o mass and zero charge . W e denot e thi s
field by C an d it s derivativ e wit
h respec t t o th e spacetim e coordinate
x' b y C . f
The actio n i s the n give n b y (wit h c — spee d o f light) ,
A = -—
/ f CiC'^gd
K-^ 4
/C.da'. a
(9.2)
The additiona l term
s (thir d an d fourth ) o n th e right-han d sid
e ar e th e C-fiel d
terms. Not e tha t th e last term of (9.2 ) i s path-independent . I
f w e consider the
world line of particl e a between
the en d point s A I an d A , w 2
e hav e
C
i:
da'=C(A j
)-C(A 2
). 1
(9.3)
Normally such path-independent term
s d o no t contribut e t
o an y physic s deriv -
able from the action principle. S
o wh y includ e suc h a term?
The answer t o
this questio n lie
s i n th e notio n o f 'broken ' worl d lines . A theory that discusse s
creation (or annihilation ) o
f matte r pe r s e mus t hav e worl d line s wit h finit e be -
ginnings o r end s (o r both) . Th e C-fiel d interactio n ter
m pick s ou t precisel y thes e
end points o f particl e worl d lines . I f w e var y th e worl d line s o f a and consider
the change i n th e actio n A in a volum e containin g th
e poin t A
! wher e th e worl d
line begins, w e ge t a t A I (whic h i s no w varied )
da
1
— gj k - Cf c =
0. a ds
(9.4)
This relatio n tell
s u s tha t overall energy an
d momentum are conserved
at th e point
of creation.
The 4-momentu m o
f th e create d particl e i s compensate d b
y th e 4 -
momentum of the C-field. Clearly
, to achieve
this balanc e the
C-field must hav e
negative energy. W e shal l retur n t o thi s point later. W
e als o not e that , sinc e th e
interaction term i s path-independent , th
e equatio n o
f motio n o f a is stil l tha t
of a geodesic. Th
e Pryc e formulatio n i
s therefor e a
masterly way of dealin g wit h
creation (and annihilation) o
f matte r withou t violatin g th
e conservatio n laws
.
The constan t /
in the action (9.2) i s a coupling
constant. Th e variatio n o
f C
gives the source
equation in the form
C&
= cf-'n , (9.5 )
where n i s th e numbe r o f ne t creatio n event s pe r uni t prope r 4-volume .
Alternative ideas i n cosmolog y 13
7
Finally, th e variatio n o
f g leads t jk
o th e modifie d Einstei
n fiel d equations
where Tj is the matte r tenso r whil e
(9.6) (9.7)
Again we note that T
°° < (
0 fo r / > 0 . Thu s th e C-fiel d ha s a negative
energy
density that produce s a
repulsive gravitational effect
. I t i s thi s repulsiv e forc
e
that drive s th e expansio n o
f th e Universe . Th
e abov e effec t ma y resolv e on e
difficulty usually associated
with the quantum theory of negativ e energ
y fields .
Because suc h field s hav e n o lowes t energ y state , the y normally do
not for m stabl e
systems. A cascading
into lower an d lowe r energ y state s woul d inevitabl y occu
r i f
we pertur b th e fiel d i n a given state of negativ e energy
. However , thi
s conclusion
is altere d i f w e includ e th e feedbac k o
f (9.7 ) o n spacetim e geometr
y throug h
(9.6). Thi s feedbac k result s i n th e expansio n o
f spac e an d i n th e lowerin g o
f th e
magnitude of fiel d energy . Thes e tw o effect s ten d t o wor k i n opposit e direction s
and help stabilize th e system .
Using the Robertson-Walker line
element an d th e assumption that a
typical
particle created by the C-field has mass m, w e ge t th e followin g equation
s ou t
of th e abov e set :
C = me , 2
ma )
(9.9) (9.10)
S + kc 2 2
(9.11)
It i s eas y t o verif y tha t th e steady-stat e solutio
n follow s fro m thes e equation s fo
r
3-Tin „ T
k = 0, S = e
", p H
= A (9,12) , =
Notice tha t bot h H O an d p are 0
given in terms o f th e elementar y creatio
n process :
that is, in term s of the couplin g constan
t / and the mass of the particl e created .
Thus th e Hoyl e approac h provides
the quantitative
information lacking in the
deductive approac h vi
a th e Perfec t Cosmologica l Principl
e o f Bond i an d Gold .
138 Jayan t V
. Narlika r
A first-orde r perturbatio
n o f th e abov e equation s an
d o f th e steady-stat e so
-
lution also tells u s tha t th e solutio n i s stable . Indeed , a stability
analysis bring s
out th e ke y rol e playe d b y th e creation process. Thi
s tell s u s tha t th e create d
particles hav e their world
lines alon g the normals to
the surface s C = constant .
Hoyle ha s argue d tha t suc h a result give s a physical justificatio
n fo r th e Wey l
postulate; i t tell s u s wh y th e worl d line s o f th e fundamenta l observer
s ar e or -
thogonal t o a special famil y o f spacelik e hypersurfaces
. I n th e C -field cosmolog y
these hypersurface s are
not jus t abstrac t notion s but are see n to have a physical
basis. W e therefor e argue
d tha t eve n i f th e Univers e wa
s considerably different
from the homogeneou s an
d isotropi c for
m i n th e remot e past , th e creatio n pro -
cess woul d driv e i t t o tha t stat e eventually . Years
later thi s ide a resurface d i
n
the contex t o
f inflatio n a s th e 'cosmi c no-hai r conjecture' , namel
y tha t a n infla -
tionary universe wipe
s out the initia l irregularitie s and
leads to homogeneity
and isotropy. I
t ha s bee n recognize d b
y Barro w an d Stei n Schabe s (1984 ) tha t
this notion is ver
y simila r t o th e abov e resul t derive d b y u s i n th e earl y sixtie s
(Hoyle an d Narlika r 1963
; A - 2 1 years!) .
However, a s i t turne d out , Fre d ha d anticipate d th
e ver y ide a o f inflatio n i
n
the mi d 1960s . Thi s wa s publishe d i
n a paper wit h mysel f a s coautho r (Hoyl e an d
Narlikar 1966b ) wher e w e discusse d th
e effec t o f raisin g th e couplin g constan
t
/ b y ~10 . A 20
s th e formula e (9.12
) show , w e woul d the n hav e a Steady-State
universe o f ver y larg e densit y (p ^ 1CT 0
g cm~ 8
) an 3
d ver y shor t timescal e (H,,"
~ 1
1 year!) . I f i n suc h a dense universe creation
is switche d of
f i n a local region ,
that is , i f w e locall y hav e a phase transitio n fro
m th e creativ e t o th e non-creativ e
mode:
C<
=0 ,
then this loca l regio n wil l expan d accordin g t
o th e formul a
oc S(t) 1 1 +
(9.13) (9.14)
where t i an d t o ar e constants . Not
e tha t thi s i s th e 'non-singular ' analogue
of
the Einstein-d e Sitte
r mode l o f standar d cosmolog y (no
w mor e popularl y know
n
by the parameter s £2
tter = ma
1, &A = 0) , whic h ha s S(t ) a t . Indeed 2/3
, fo r smal l
to, th e solutio n rapidl y approache s th
e Einstein-d e Sitte
r form . Bein g les s dens e
than the surroundings , such
a regio n wil l simulat e a
n ai r bubbl e i n water .
Although the basi c physic s i s different , th
e similarit y betwee
n thi s mode l an d
the inflationar y mode
l tha t cam e int o fashio n 1 5 year s late r i s obvious . I n bot h
models a phase transitio n create
s th e bubbl e tha t expand s int o th e oute r d e
Sitter spacetime . I
n th e Steady-Stat e universe
, suc h bubble s coul d aris e i n man y
places a t differen t epoch s fro m t = -o o t o t = +00 .
According to this model , thi s bubbl e i s al l tha t w e se e wit h ou r survey s o f
galaxies, quasar s an d s o on . Henc e ou r observation s tel
l u s mor e abou t thi s
unsteady perturbation
than about th e ambien t Steady-Stat e universe
. Ther e are ,
however, observabl e effect
s tha t giv e indications of th
e hig h valu e o f / . Fo r
example, w e showe d tha t particle creation i
s enhanced near already
existing
massive object s an d tha t th e resultin g energ
y spectru m o
f th e particle s woul
d
simulate tha t o f high-energ y cosmi
c rays . Th e actua l energ y densit y o f cosmi c
rays require s th
e hig h valu e o f / chosen here.
Thus takin g Fred' s anticipation of inflatio
n i n 1966 , w e ma y se t A = 1 5 years .
9.7 Nucle i o
f galaxie s
The followin g extrac
t fro m th e abstrac t o f th e Hoyl e an d Narlika r (1966c )
paper wil l indicat e Fred' s idea s i n th e mi d 1960 s o n th e dynamic s o
f galax y
formation:
We sugges t tha t the condensation of...galaxie
s depend s on the
presence o f inhomogeneities , i
n particula r tha
t a galaxy is forme d
around a central mass concentration
. Becaus e th e Einstein-d e Sitte
r
expansion la w i s th e limitin g cas e betwee n th e expansion to
infinity at
finite velocit y an
d a fall-back
situation, i n which the expansio
n stop s
at som e minimu m bu
t finit e density , a central condensatio n wit
h
mass appreciabl y les
s tha n tha t of the associate d galax
y suffice s to
prevent continuin g expansion
. A mass o f 10 M 9
, fo G
r example , wil
l
restrain a total mass o
f ~10 M 12
from Q
expanding beyond normal
galactic dimensions..
.
In the mi d 1960 s th e notio n o f a massive blac k hol e a t th e nucleu s o f a galaxy had
not receive d 'standar
d sanction"
, an d s o th e ide a remaine d relativel
y unknown ,
especially because i t wa s propose d i
n th e contex t o f a Steady-State universe
. I
briefly elaborate o
n th e ide a tha t th e abov e abstrac t indicates , whil
e stressin g
that th e argument s wer
e mad e i n th e mi d 1960s .
The cosmologica l basi
s o f thi s work was discussed
in the preceding paper
(Hoyle an d Narlika r 1966b) , whic h suppose d tha
t th e Universe , o
r a portion of
it, expand s fro
m a n initiall y steady-stat e situation
with p ~ 10~
g cm~ 8
, H" 3
~ 1
10 cm, tha 1 8
t creatio n i s effectivel y zero
during this expansion , an
d tha t th e
Einstein-de Sitte r expansio n la
w hold s i n firs t approximation .
The Newtonia n analogu
e o f th e Einstein-d e Sitte
r la w i s give n b y
f = 2GM/r 2
, (9.15)
in which r i s th e radia l coordinat e o
f a n elemen t o f materia l define d b y th e
condition that i n a spherically
symmetric situation
about r = 0 , th e mas s inte -
rior t o r is M . Fo r a given sample o f materia l M remains constan
t an d f -»• 0
only as r ->
oo. Equatio n (9.15
) i s a n integra l o f th e second-orde r Newtonia
n
equations, an d th e fac t tha t n o constan t o
f integratio n appear
s represent s th
e
analogue of th e Einstein-d e Sitte
r law .
Next, conside r th
e Newtonia n proble
m o f a n objec t o f mas s //
placed at th e
origin r = 0, all conditions at
a particula r momen
t for a particula r elemen
t of
the cloud being the same as before . Denot e th e valu e o f r at thi s momen t b y r . 0
Then f a t thi s momen t i s (2GM/r ) 0
, a 1/2
s before , an d th e subsequen t motio
n o f
the element i
n questio n i s determined by
2G/J.
r (9.16) 0
The outwar d velocit
y drop s t o zero , an d th e elemen t subsequentl y fall
s bac k
towards r = 0 . Th e maximu m radia
l distanc e r reached max
by the element i
s
given by
r ax = m
(1 + (M/M)}t"o , (9-17 )
and for sufficientl y larg
e M//LI , r ~ Mr max
/M, s 0
o tha t th e fractiona l increas
e
r /r max
, abov 0
e th e radiu s r at whic 0
h th e elemen t ha d th e sam e radia l motio n
as i n th e Einstein-d e Sitte
r case , i s jus t M//it . Thi s facto r i s large r fo r element s
more distant fro m /j.
than for th e inne r part s o f th e cloud , s o th e oute r part s
recede proportionatel y furthe
r tha n th e inne r parts .
What determine s th
e particula r momen
t a t whic h th e Einstein-d e Sitte
r con -
dition, r = (2GM/r) , hold 1/2
s fo r an y particula r sampl
e o f material
? T o com e t o
grips wit h thi s importan t questio
n w e mus t conside r th e relativisti c formulatio
n
of th e problem .
A complet e solutio
n o f a local gravitationa l proble
m ca n b e represente d a
s
a powe r serie s i n th e dimensionles s paramete
r 2G(
M + fi)/r, whic h mus t b e
<5C 1 , thi s bein g wha t w e mea n b y a 'local problem' . Th
e Newtonia n solutio
n i s
of cours e th e firs t ter m i n thi s series . However , i
t i s clea r tha t w e canno t us e
the Newtonia n solutio
n for the effec t of p. if the second-orde r ter
m in 2GM/r
exceeds th e first-orde r ter
m i n 2G/z/r , a s i s possibl e whe n /z/
M <g
; 1 . Henc e th e
Newtonian equations fo
r th e effec t o f /i , namel y equation s (9.16
) an d (9.17) ,
cannot b e use d unles s th e momen t fo r whic h w e us e r = r , r 0
= (2GM/r ) 0
, i 1/2
s
such that 2G/z /2 GM
\
\ I 0
(9.18)
By takin g equalit y i
n (9.18 ) w e d o indee d defin e a particular valu
e o f r ,
corresponding to a specifie d M
, namely , (9.19)
The situatio n i
s tha t th e Newtonia n calculatio
n fo r th e effec t of/
n ca n b e applie d
to the subsequent motio
n o f a n elemen t o f materia l suc h tha t th e specifie d M
lies interio r t o it . Bu t ca n w e us e (2GM/r )i a 0
s th e starting velocity
in this
calculation? No t i n general , becaus e i n genera l th e clou d wil l hav e a t leas t smal l
fluctuations fro m th e Einstein-d e Sitte
r expansion . W
e shal l confin e ourselve s
here to the case i n whic h th e condition s r
* r , r 0
= (2GM/r )*, wit 0
h r given 0
by
equation (9.19), hol d fo r al l M .
From equations (9.17
) an d (9.19 ) w e hav e
^r
~2GM 0 M
/M I M (9.20)
This resul t ha s a number o
f interestin g consequences
. Se t r equal t max
o a typical
galactic radiu s r = 3 max
x 10 cm. The 22
n equatio n (9.20 ) lead s t o
~5 xl 0
5 -
(9.21)
where M is th o
e sola r mass . A central objec
t o f mas s fi = 1 0 M 9
gives M G
=
5 x 10 M 1 1
, whil 0
e fi = 10 M 7
gives M 0
= 2 x 10 M 10
. I Q
t i s o f interes t tha t th e
central condensation s presen
t i n massiv e elliptica l galaxie s ar e know n t o b e o f
order 10 M 9
, an O
d tha t th e tota l masse s ar e believe d t o b e ~10 M 12
. 0
Suppose tha t during expansion
stars ar e forme d fro m gas . Th e star s wil l
continue to occupy the full volum e correspondin g t
o thei r maximu m extensio
n
from the centre, s o tha t th e mas s o f th e star s interio r t o r is give n b y settin g
'"max =r in equation
(9.21). Numerically , w
e hav e
. (9 22)
in whic h r is in kiloparsecs. Evidently
, the mean star densit y at distance
r fro m
the centre is proportiona l t
o M/r , i.e. 3
, t o r~5 . S o lon g a s th e star s hav e every -
where th e sam e luminosit y function
, th e emissivit y pe
r uni t volum e a t distanc e
r i s proportiona l t
o r
~J . Thi s determine s th
e ligh t distributio n i
n a spherical
elliptical galaxy .
To obtain the projected
intensity distribution
we first not e tha t th e abov e
considerations can be applie d to values ofr beyond
normal galacti c dimensions .
There i s n o uppe r limi t t o r so long as w e ar e dealin g wit h a single conden-
sation. Thi s agree s wit h observation , i
n tha t n o ultimat e maximu m radiu
s ha s
