1. Alcaniz, Chen, Gong , Yu , Zhang
21世纪第二个十年的宇宙学
Testing the Coincidence Problem of Dark Energy
Zhu, Zong-Hong
Beijing Normal University, Beijing , China
&
Alcaniz, Chen, Gong , Yu , Zhang

2. Introduction

3. Testing the severity of the coincidence problem
Using a phenomenological model to test the coincidence problem of dark energy
Chen, Z-HZ, Alcaniz, Gong, ApJ, 2010
A quantitative criteria for the coincidence problem
Zhang, Yu, Z-HZ, Gong, PLB, 2009
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4. ΛCDM model The simplest candidate for dark energy (DE)
Good agreement with observations
However, embarrassed by two problems:
Fine-tuning problem: Why so small? The observed value of the vacuum energy density is about 120 order of magnitude smaller than the theoretical one
Coincidence problem: Why now? Why the energy density of dark energy and dark matter happens to be of the same order now?
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5. Cosmological constant problem
Fine tuning
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6. Cosmological constant problem
log r
radiation (~1/a4)
Coincidence
matter
(~1/a3)
cosmological
constant (~constant)
quintessence problems: finetuning and a very light field (10^-33 eV)
-> can lead to long range forces and varying constants, especially with couplings
log a
imagination
dominated
radiation
dominated
matter
dominated
Lambda
dominated
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7. To solve or alleviate the coincidence problem:
Several possible approaches:
Anthropic principle
Dynamical component
Interacting models
solve [美] [sɑlv, sɔlv]; alleviate[美] [ə’livi,et]
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8. Testing the coincidence problem of DE I. A phenomenological model

9. Headspring of the model
In the ΛCDM scenario:
In a theory without coincidence problem:
Phenomenologically, setting
Let observations tell us its value !
Dalal et al PRL
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10. ξdenotes the severity of the coincidence problem
The key parameter: ξ
ξdenotes the severity of the coincidence problem
, corresponding to ΛCDM model
, corresponding to the self-similar solution without coincidence problem
, making the coincidence problem less severe
denote[美] [dɪ’not]
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11. The basic equations (i)
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12. ♠ : indicating that the energy is transferred from DM to DEQ
: denoting the standard cosmology without interaction between DM and DE
: denoting the non-standard cosmology with interaction between DM and DE
♠ : indicating that the energy is transferred from DM to DE
♠ : indicating that the energy is transferred from DE to DM
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13. The basic equations (ii)
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14. Constraints from SNe + BAO + CMB
Chen, Z-HZ, Alcaniz, Gong, ApJ, 2010
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15. Constraints from the transition redshift
Z.-H.Z & Fujimoto, ApJ, 2004
Z.-H.Z & Alcaniz, ApJ, 2005
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16. Constraints from the transition redshift
Chen, Z-HZ, Alcaniz, Gong, ApJ, 2010
isopleth [‘aisəupleθ]
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17. Testing coincidence problem I: summary
ΛCDM model remains a good agreement with the recent observational data
Coincidence problem indeed exists and is quite severe
The theoretical constrains from the transition redshift zT show that
♣ if the transition from deceleration to acceleration happens at the redshift zT > 0.73, the interaction between DE and DM should be taken into account
♣ if it happens at the redshift zT ≤ 0.73, we can not confirm whether the interaction is necessary by using the transition redshift only
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18. Testing the coincidence problem of DE
II. A quantitative criteria

19. In terms of the parameter r,
Introduction
In terms of the parameter r,
the coincidence problem says why r becomes order of 1 now.
If the current value of r which is order of 1 is independent of initial conditions,
then the coincidence problem is alleviated.
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20. For quintessence model without interaction
Introduction
The resolution of the coincidence problem lies on the attractor solution.
For quintessence model without interaction
the attractor solution with acceleration is the scaling solution with r = 0
So the interaction between DM and DE is proposed to get nonzero r attractor solution.
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21. To solve the coincidence problem
Introduction
To solve the coincidence problem
r should not vary too much through the whole history of the universe
in addition to having attractor solution
During most of the history of the universe, DM and DE evolve almost in the same way
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22. Interaction models
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23. The attractor for interaction model
For IQT and IPT models with constant
, the attractor solution is
Chimento et al., 2003
Olivares et al., 2008
Campo et al., 2008
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24. The attractor for interaction model
The attractor solution:
Zhang & Z-HZ, PRD, 2006
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25. Basic equations
Defining ,
&
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26. r = u/v as a function of ln(1 + z)
ICG model is a better model
Zhang, Yu, Z-HZ, Gong, PLB, 2009
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27. A quantitative criteria for coincidence
ICG model is a better model for overcoming the coincidence problem
But in what degree ?
We need a quantitative criteria for the selection.
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28. A quantitative criteria for coincidence
Dividing the coincidence problem into two smaller problems:
The coincidence between the value of re at early time and that of r0 at present
The coincidence between r0 and the attractor value (if it exists) rf
Indicating the early coincidence
Indicating the late coincidence
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29. A quantitative criteria for coincidence
The closer to 1, Ce or Cf is, the better the coincidence problem is overcome
We can’t define the index of the coincidence as CeCf
Ce and Cf maybe varies in the opposite direction, making the the index approach 1
e.g., if Ce = 1010 and Cf = 10−10, then CeCf = 1.
Introducing a function:
Defining a proper index of coincidence C in the whole history of the universe
coincidence problem less severe
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30. A quantitative criteria for coincidence
Taking z = 100 as “early universe”
The fixed point of r : or
Lead to negative rs
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31. A quantitative criteria for coincidence
If w is a function of cosmic time,
like the case in the Chaplygin gas model
taking the value of w as lim z→−1 w for late time
For the ICG model
taking c = 0.06, A′= 0.4
according to observations (Zhang & Z-HZ, PRD, 2006)
6.705
Zhang, Yu, Z-HZ, Gong, PLB, 2009
2019/1/10
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32. Testing coincidence problem II: summary
ICG model is a better model than IQT and IPT for overcoming the coincidence problem
In term of the coincidence index C
ICG is smaller than that for the IQT and IPT by six orders of magnitude
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33. Thanks for all your patience!
&
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