Why stop at 2/3?

(1)

August aorz Galley 52

CORRESPONDENCE To the Eilitors of 'The Obseraatory'

Wry stop ar %?

In

the discussion ofProfessorTurner's talk, Rev. Barber statesl that

"the

age

of

the Universe

could be

derived

&om

any

multiple

of

the Hubble

constant

from

/,

onwards." (Presumably he means the Hubble time,

not

its inverse, the

Hubbie

constant.)

In

the Einstein-de Sitter universe,

with

1.

:

o

and

O

:

r,

the age is % of the Hubble time, which is presumably why Barber mentions this fraction. However, this is not a

limiting

value; except for the fact that there is a

region of the ),-Q parameter space

in

which the age of the {Jniverse is

infinite

(2.e., there is

no

Big Bang), the age

of

the Universe expressed

in

units of

the

Hubble time is a very well-behaved

function

of

l,

and Q

with

no lower bound, neither at 2A

_\or

_at_{any other value (e.g.,}_Fig.

3 in ref.

z).

(The value of o occurs

for infinitely large (absolute) values

of),

(which is negative in such cases) andfor

Q (if

only one (absolute) value is

infinitely

large, the other is o).) To be sure, an age of the l-Iniverse of less than % the Hubble time implies l. < o, Cl

> r

or both.

Since the discussion is concerned

with

the possibiliry to "kick

in

an arbitrary A dark energy",

it

seems strange

to

constrain ). to be greater than o and

O

to be less than

l.

Of

course, cosmologists are now reasonably certain3

that

I

₌

o.73 and

()

₌

o'27

(and xhese seem

to

be the result

of

a real convergence,

not

iust

the popular values dujoura), but

in

a general discussion

ofwhat

could be, rather than what is,

it

is

important

to remember that there is no theoretical reason to

excludel<oorC)>r.

Yours faithfully, PHII r rP HeI,Brc 'l'homas-Mmn-Stra8e 9 D-63477 Maintal Germany helbig@asto. multhu.de zorz Mrch o3 References

(r)

Meeting of rhe Royal Astronomical Sociery, Tlu Obseroau4t, tl2, 64, 2012.

(z) P. Helbig, MNR4S,4zr,56r, zorz.

$)

E. Komatsu et al." ApJS, r9z, r8, 2orr.

(a) R. A. C. Croft & M. Dailey, MNRIS (submitted), rXiv:rrrz.3ro8.

18105/2012 08:20

|

Why stop at 2/3?

In

"the

of

could be

&om

multiple

of

the Hubble

/,

not

Hubbie

In

with

:

o

O

:

r,

limiting

in

infinite

no

of

in

units of

function

l,

with

\or

z).

of),

Q (if

infinitely

> r

with

in

it

to

O

l.

Of

that

I

=

()

=

o'27

to

of

not

in

ofwhat

it

important

excludel<oorC)>r.

(r)

$)

_\or

₌

₌