Formula of the Universe
Vladimír Skalský
Faculty of Material Sciences and Technology of the Slovak University of Technology,
917 24 Trnava, Slovakia
Leon M. Lederman, the prize-winner of the Nobel Prize in physics 1988, summarised
efforts of the cosmologists to the one succinct sentence: “Our ultimate goal is to
explain the entire Universe in a single, simple formula that you can wear on your
T-shirt.”
The Wilkinson Microwave Anisotropy Probe (WMAP) measurements determined
[1]
the present cosmological time of the Universe
t 0 (13 .7 0.2) 10 9 yr (1)
and
the present value of the Hubble parameter
4
H 0 71 1 1
3 km s Mpc . (2)
From the relations (2) and (3) it results:
1
H0 . (3)
t0
The Friedmann-Robertson-Walker equations (FRW equations) can be written as:
8 G a 2 a 2 c 2
a2
kc2 , (4a)
3 3
8 Gp a 2
2aa a 2
kc2 a 2 c 2 , (4b)
c2
p , (4c)
where a is the gauge factor; , mass density; k, curvature index; , cosmological
constant; p, pressure; , state equation constant; and , energy density.
The WMAP measurements and the FRW equations make it possible to carry out
the Lederman half-joke, half-serious demarcated goal.
The FRW equations (4a), (4b) and (4c) fulfil the restrictive condition, determined
by the relation (3), only with k = 0, = 0 and = –1/3 [2].
From the FRW equations (4a), (4b) and (4c) with k = 0, = 0 and = –1/3 result
relations for the fundamental parameters of our Universe in the first (linear)
approximation:
2Gm
a ct 2 , (5)
c
where t is the cosmological time; and m, mass.
If we substitute the constants in the last member of the relations (5) by
1
the Schwarzschild gravitational constant
2G
K (6)
c2
we can rewrite them in the form:
a ct Km , (7)
which represents the formally simplest possible description (“the formula”) of our
observed relativistic Universe in the first (linearly, Newtonian or classical-
mechanical) approximation [2].
Any other simplification of “the Universe formula” – without losing its physical
meaning – is principally not possible!
References
[1] Bennett, C. L., et al.: First Year Wilkinson Microwave Anisotropy Probe (WMAP)
Observations: Preliminary Maps and Basic Results, http://lambda.gsfc.nasa.gov/
[2] Skalský, V.: The Universe as a vacuum fluctuation, The Slovak University of
Technology Press, Bratislava, 2002.
2