Quasi-Rip: A New Type of Rip Model without Cosmic Doomsday

1. Quasi-Rip: A New Type of Rip Model without Cosmic Doomsday Based on Wei et al., Phys.Rev. D86 (2012) 083003 Hao Wei School of Physics Beijing Institute of Technology USTC , Hefei , 20 June 2013

2. 在过去 20 年里，北大保安队先后有 500 余名保安考学深造，有的考取大专或本科学历，有的甚至考上重点大学的研究生，有的毕业后当上了大学老师。（人民日报海外版 2013 年 5 月） 我国三大无敌武器：城管、临时工、保安

3. 笑话一枚 有一次进入北大校门时被保安拦住， 被问了三个哲学上的终极问题： • 你是谁？ • 你从哪里来？ • 你往哪里去？

5. Caldwellet al., Phys. Rev. Lett. 91, 071301 (2003)

6. Besides the traditional Big Bang, Big Crunch, and Big Rip, many novel singularities have been considered in the literature, such as Sudden singularities, Generalized sudden singularities, Quiescent singularities, Big Boost, Big Brake, Big Freeze, w singularities, Inaccessible singularities, Directional singularities Nojiri et al., Phys. Rev. D 71, 063004 (2005)

7. Of course, singularities usually are not desirable in physics. Therefore, other possible fates of our universe are also considered in the literature, such as the cyclic/oscillatory cosmology. Recently, some interesting scenarios concerning the fate of the universe attracted much attention in the community, namely the so-called “Little Rip” and “Pseudo-Rip”. If the cosmic energy density will remain constant or monotonically increase in the future, then all the possible fates of our universe can be divided into four categories based on the time asymptotics of the Hubble parameter Framptonet al., Phys. Rev. D 85, 083001 (2012)

8. Little Rip Dark energy density increases with time (so that the EoS satisfies w < −1), but w → −1 asymptotically, such that there is no future singularity. Such models can display arbitrarily rapid expansion in the near future, leading to the destruction of all bound structures (“little rip”). Framptonet al., Phys. Rev. D 84, 063003 (2011)

9. 3.8 × 10117 Gyr 1.3 × 1033 Gyr 1.6 × 109 Gyr 9.2 × 104 Gyr Pseudo-Rip Framptonet al., Phys. Rev. D 85, 083001 (2012)

10. 38 Gyr 39 Gyr 40 Gyr 45 Gyr Framptonet al., Phys. Rev. D 85, 083001 (2012)

11. Quasi-Rip It is worth noting that all the Big Rip, Little Rip and Pseudo-Rip arise from the assumption that the dark energy density is monotonically increasing, i.e., the dark energy is phantom-like We consider the case of the dark energy density monotonically increases (namely w < −1) in the first stage and then monotonically decreases (namely w > −1) in the second stage (this is the case of the so-called “quintom B” dark energy). It can be expected that in the first stage some or all bound structures will be dissociated (similar to the case of Pseudo-Rip), but then the disintegration process will stop, and the already disintegrated structures have the possibility to be recombined in the second stage. Wei et al., Phys.Rev. D86, 083003 (2012)

12. Quintom Quintom 最早由张新民等人提出，Feng, Wang, Zhang , Phys. Lett. B 607, 35 (2005) [astro-ph/0404224] EoS of DE can cross the so-called phantom divide

13. Huterer, Cooray, Phys. Rev. D71, 023506 (2005) [astro-ph/0404062]

14. Alam, Sahni, Starobinsky, JCAP 0406, 008 (2004) [astro-ph/0403687]

15. Zhao et al., Phys.Rev.Lett. 109, 171301 (2012)

16. Li, Xia, Zhang, arXiv:1303.3428

17. The Disintegration of Bound Structures “inertial force” A bound structure dissociates when the inertial force Finert (dominated by dark energy) is equal to the force Fbound holding together this bound structure

18. Nesseris, Perivolaropoulos, Phys. Rev. D 70, 123529 (2004) However, if the bound structure is massive enough to significantly affect the local spacetime metric, it is not accurate to express Finert in terms of FRW metric. To be more accurate, in the Newtonian limit, the interpolating metric of the local spacetime is given by The radial equation of motion for a test particle in the Newtonian limit reads

19. the time-dependent effective potential The bound structure dissociates when the minimum of the time-dependent effective potential (including the centrifugal term) disappears.

20. This equation has a real solution only for So, the bound structure dissociates when or equivalently Ω0 and h will be determined by the observational data

21. Since the current observational data are in the epoch a < 1, we cannot ignore the contribution from pressureless matter in this stage, although it can be safely ignored in the above discussions when the universe is dominated by DE.

22. An explicit model of Quasi-Rip Our task is to construct an explicit function ρ(a), which monotonically increases (namely w < −1) in the first stage and then monotonically decreases (namely w > −1) in the second stage. A naive idea is to use a piecewise function, which is phantom-like in the first sector and is quintessence-like in the second sector. Then, we can refine this naive idea with a smooth function β> 0 is required to ensure it has a maximum

25. It is easy to see that the most distinct feature of Quasi-Rip is that the inertial force monotonically decreases in the second stage. Eventually, it will become lower than all the thresholds to disintegrate the bound structure. Therefore, the already disintegrated structures have the possibility to be recombined in the second stage. This is the unique feature of Quasi-Rip different from Big Rip, Little Rip and Pseudo-Rip. Our universe has a chance to be rebuilt from the ashes after the terrible rip. This might be the last hope in the “hopeless” rip.

26. Remarks • The current observational data cannot tightly tell what is the true fate of our universe. • The explicit model of Quasi-Rip considered here is the simplest case. One can construct other more complicated ρ(a) to implement the Quasi-Rip. • Issues concerning the stability in the phantom phase. • The oscillatory Quasi-Rip model driven by the oscillatory quintom dark energy.

27. Thanks! Blessed be the Lord, who daily loadeth us with benefits, even the God of our salvation. (Psalms 68:19)