Stability of the holographic description of the Universe
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Regular Article - Theoretical Physics
Stability of the holographic description of the Universe P. Huang1,a , Y.C. Huang1,2,3 1
Institute of Theoretical Physics, Beijing University of Technology, Beijing 100022, China Kavli Institute for Theoretical Physics China at the Chinese Academy of Sciences, Beijing 100080, China 3 CCAST (World Laboratory), Beijing 100080, China 2
Received: 8 January 2013 / Revised: 18 February 2013 / Published online: 27 March 2013 © Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2013
Abstract We investigate the stability of the holographic description of the universe. By treating the perturbation globally, we discover that this description is stable, which is support for the holographic description of the universe.
1 Introduction The cosmological constant problem [1] is a longstanding problem in theoretical physics. Evidence from Type SN Ia [2, 3], CMB [4] and SDSS [5] shows that the current universe is accelerating, which can be explained by dark energy (a generalization of the cosmological constant). There are various models about dark energy [6–18], and the holographic dark energy (HDE) model [13–18] has an intrinsic advantage over the other models in that it does not need finetuning of the parameters or an ad hoc mechanism to cancel the zero-point energy of the vacuum. The key point in the HDE model is that in quantum field theory, due to the limit made by the formation of a black hole, an ultraviolet (UV) cut-off is related to an infrared (IR) cut-off [13]. Thus, if one labels ρD as the quantum zero-point energy density caused by an UV cut-off, the total energy in a region of size L should not exceed the mass of a black hole of the same size, that is, L3 ρD ≤ LMp2 , so one has ρD = 3C 2 Mp2 L−2 , here, C is a numerical constant introduced for convenience and Mp is the reduced Planck mass. If one supposes that there is no interaction between dark energy and matter, an inevitable result is to use the future event horizon for IR cut-off; only by doing this can we deduce the correct equation of state to obtain an accelerated universe. The holographic dark energy model developed from this viewpoint is as follows [15]: ρD = 3C 2 Mp2 L−2 E , a e-mail:
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(1)
where C is a positive numerical parameter which is in favor of C = 1 [14, 15], Mp is the reduced Planck mass, LE = r (t) E (t) = a(t)rE (t), the definition of rE (t) is 0 E √ dr 2 = Ra(t) 1−kr ∞ dt t a(t) , RE (t) is the future event horizon, k = 1, 0, −1 corresponds to closed, flat and open universe, respectively. Though it is well in agreement with cosmological observation [19], using the event horizon for the large scale cut-off in this HDE model is thought to cause causality problem, see [20] for further reading. Recently, Li et al. deduced this HDE model from action principle [21], and thus, as they claimed, solved the causality problem. HDE model can be understood in terms of the holographic principle [22–24]. Such a basic principle should be universal and is not only for a specia
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