CC BY
26
UDC 530.1; 539.1
Quasi-Rip universe induced by the fluid with inhomogeneous equation of state.
I. Brevik1, V. V. Obukhov2, A. V. Timoshkin2
1 Department of Energy and Process Engineering,
Norwegian University of Science and Technology, N-7491 Trondheim, Norway.
2 Department of Theoretical Physics, Tomsk State Pedagogical University, Tomsk, 634061, Russia.
E-mail: [email protected], [email protected], [email protected]
We investigate a specific model for a dark energy which lead to the Quasi-Rip cosmology. In the Quasi-Rip model the equation of state parameter w is less than — 1 in the first stage, but then in the second stage is larger than —1. The conditions for the appearance the Quasi-Rip in the terms of the parameters equation of state are received.
Keywords: dark energy, cosmological constant, equation of state, bound structures.
1 Introduction
The discovery accelerated expansion of the universe led to the appearance the new theoretical models in the cosmology (for recent review see [1,2]) and significantly-changed our view of the fate of the universe. Recent observations suggest that the universe is dominated by a negative-pressure component named dark energy (dark fluid). Such quintessence/phantom dark energy proposed to explain the cosmic acceleration should have the strong negative pressure. It can be characterized by an equation of state parameter w, which is the ratio of the pressure to the density: w = -p. Its equation of state parameter w is smaller than —1.
The condition w < —1 corresponds to a dark energy density that monotonically increases with time t and scale factor a. There are the some interesting possible scenarios concerning the fate of the universe, including Big Rip [3-4], Little Rip [5-12], Pseudo-Rip [13] models. These models are based on the assumption, that the dark energy density p is a monotonically increasing function.
In this paper we are interested to study the cosmo-
p
tonically increases (w < —1) in the first stage and then monotonically decreases (w > —1). At first stage it takes the place the disintegration of bound structures, but then at the second stage the disintegration process will stop, and the already disintegrated structures have the possibility to be recombined. This scenario in the cosmology was called the Quasi-Rip [14]. Note, that p
plausible, and it is more difficult to make any sort of general statement about such models.
The aim of this article is to examine the influence of dark fluid equation of state explicitly dependent on scale factor w and A to the occurrence of the QuasiRip.
2 Dark fluid with inhomogeneous equation of state in the Quasi-Rip model
Let us consider an explicit model of the Quasi-Rip.
p
ap
[14]:
p = poa
a—3 ln a
(i)
where p = p0 at fixed time t0, a and ft are both constants. The derivative of the energy density with respect to cosmic time t is equal:
p' = pH (a — 2ft ln a)
(2)
where H = aa is the Hubble rate. We assume, that our universe is filled with an ideal fluid (dark energy) obeying an inhomogeneous equation of state [15]:
p = w (a) p + A (a)
(3)
where w (a) Mid A (a) depend on the scale factor a, P is the pressure. Let us write down the energy conservation law:
p' + 3H (p + p) = 0 (4)
Taking into account (2-4) we obtain: p (a — 2ft ln a) + p (1 + w (a))+A(a)=0 (5)
w (a)
A
to the square of the energy density, that is:
A (a) = 7p0a2(a—3 ln a), (6)
where y is a some constant. Using (6), one obtains:
w (a) = — 1 — Yp0aa 3 ln a + 2ft ln a — a
(7)
I. Brevik, V. V. Obukhov, A. V. Timoshkin. Quasi-Rip universe induced by the fluid.
ft > 0 p mum. It is at a = exp 23, then the parameter is equal:
’(a) = — 1 — Yp02 (8)
The Quasi-Rip model has an unique feature different from Big Rip, Little Rip and Pseudo-Rip. All these models arise from the assumption, that dark en-
„ . , n ■ , 1 ■ er§y density is monotonically increasing. They lead
Consequently, if we take an ideal fluid, obeying an e „ , , , , , ,
^ ,/x, , , , to the dissolution of all bound structures. As distinct
equation of state (3) and (5), then obtain the solution, c ,, , , . ^ .
, , , , X ' ^ tvt , , ^ from these models m Quasi-Rip model this assumption
which realize the Quasi-Rip (1). Note, that such Quasi- ■ , , ^ ■ , -u-i-j. a u u -u
^ ^ , is broken. Our universe has a possibility to be rebuilt
Rip is caused exceptionally with cosmological constant r, ,, ■ T j. i u u -u. r\
. , , / x , a,i after the rip. In present work we have built the Quasi-
AA
, , w Rip universe induced by the dark fluid with mhomoge-
w (a)
^ 7 neous equation of state. It is shown, that the Quasi
j Rip cosmology can be caused exceptionally with the
----a3lna—a, (9) cosmological constant or the parameter . It would be
3p0
j- j- nr u ■ ■ be mapped with dark energy fluid cosmology mimick-
Dnstant. We obtain the expression: , , r r i -n 1
mg string-landscape features [16J. From another side,
j the role of viscosity in Rip cosmology may be also rel-
A (a) = —p0a“ 3 ln a (a — 2ft ln a) — 3 (10) evant in Quasi-Rip picture [17
w
future behaviour of our universe depends on the par-
aft
the equation of state (3), which gives the Quasi-Rip. helpful discussions.
References
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Received 01.10.2012
if. Вревик, В. В. Обухов, А. В. Тимошкин Вселенная Quasi-Rip, индуцированная жидкостью с неоднородным уравнением состояния
Исследована специфическая модель темной энергии, которая приводит к Quasi-Rip космологии. В модели Quasi-Rip параметр w на первой стадии эволюции меньше — 1, а затем, на второй стадии эволюции, больше —1. Получены условия для возникновения Quasi-Rip в терминах параметров уравнения состояния.
Ключевые слова: темная энергия, космологическая постоянная, уравнение состояния, граничные структуры. Бревик И., профессор.
Норвежский университет науки и технологии.
Трондхейм, Норвегия, N-7491 E-mail: [email protected]
Обухов В. В., доктор физико-математических наук, профессор.
Томский государственный педагогический университет.
Ул. Киевская, 60, Томск, Россия, 634061.
E-mail: [email protected]
Тимошкин А. В., кандидат физико-математических наук, доцент.
Томский государственный педагогический университет.
Ул. Киевская, 60, Томск, Россия, 634061.
E-mail: [email protected]
