| dc.description.abstract |
Since the observations of Perlmutter and others, it is now an established fact that the
universe expands with an acceleration in the present epoch. In order to explain this
phenomenon Hemantha and de Silva modified the Einstein’s field equations
T G g ,0 T 0
: constant
G T g
; = ; − Λ ; = ⇒ ; =
Λ −
= + Λ
υ
µυ
υ
µυ
υ
µυ
υ
µυ
µυ µυ µυ
κ
κ
with the following variations.
g T 0
G 0 ( g T ) 0
Λ :-variable
;
;
;
;
Λ + =
= ⇒ Λ + =
υ
µυ µυ
υ
υ
µυ µυ
υ
µυ
κ
κ
Essentially they made Λ, the “Cosmological Constant”, a variable and replaced the
energy conservation by the conservation of the energy of the Λ field, matter and
radiation. According to the modified equations the energy of the Λ field and that of
matter and radiation are together conserved instead of the energy of the matter and
radiation only. This enables matter and radiation to be created from the Λ field during
the expansion of the universe during certain epochs. Conversely in certain other
epochs the matter and radiation contributes to the Λ field.
The modification leads to the following equations with respect to the Robertson -
Walker metric.
2 2
2
2 2
2
2
2
2
3 3
2
R c
R
R
k
c
R
R
R
R
R
kc
p
&
&& &
= +
Λ
+
+ + + = Λ
κρ
κ
67
3 0 2 2
=
Λ
+ +
+
R c
R
c
p
κ
ρ ρ
&
&
&
where dot ( & ) denotes differentiation with respect to cosmic time t.
The modified equations give rise to solutions representing acceleration during certain
epochs. We have found that with k=1, p =0, the modified equations are satisfied by
the solution R = a + b1 cos ωt + b2 cos 2 ωt. It is believed by Perlmutter and others
that the present acceleration epoch commenced at a redshift of 1.6. Taking that and
minimum of R=0, as boundary conditions, we find that 2 1
3( 10)
4
3
b = + b , a
= 2
2
2
1
8
b
b
b
+ . These conditions give a family of solutions representing an accelerating
universe, with b1 as the parameter. As an example, we give below a schematic
representation of the solution with b1=5x1030
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