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 (zhuzh@bnu.edu.cn) Beijing Normal University, Beijing 100875, China & Alcaniz, Chen, Gong , Yu , Zhang

Introduction

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 2019/1/10 2010-2020的宇宙学

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? 2019/1/10 2010-2020的宇宙学

Cosmological constant problem Fine tuning 2019/1/10 2010-2020的宇宙学

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 2019/1/10 2010-2020的宇宙学

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] 2019/1/10 2010-2020的宇宙学

Testing the coincidence problem of DE I. A phenomenological model

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. 2001 PRL 2019/1/10 2010-2020的宇宙学

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] 2019/1/10 2010-2020的宇宙学

The basic equations (i) 2019/1/10 2010-2020的宇宙学

♠ : indicating that the energy is transferred from DM to DE Q : 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 2019/1/10 2010-2020的宇宙学

The basic equations (ii) 2019/1/10 2010-2020的宇宙学

Constraints from SNe + BAO + CMB Chen, Z-HZ, Alcaniz, Gong, ApJ, 2010 465.719 2019/1/10 2010-2020的宇宙学

Constraints from the transition redshift Z.-H.Z & Fujimoto, ApJ, 2004 Z.-H.Z & Alcaniz, ApJ, 2005 2019/1/10 2010-2020的宇宙学

Constraints from the transition redshift Chen, Z-HZ, Alcaniz, Gong, ApJ, 2010 isopleth [‘aisəupleθ] 2019/1/10 2010-2020的宇宙学

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 2019/1/10 2010-2020的宇宙学

Testing the coincidence problem of DE II. A quantitative criteria

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. 2019/1/10 2010-2020的宇宙学

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. 2019/1/10 2010-2020的宇宙学

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 2019/1/10 2010-2020的宇宙学

Interaction models 2019/1/10 2010-2020的宇宙学

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 2019/1/10 2010-2020的宇宙学

The attractor for interaction model The attractor solution: Zhang & Z-HZ, PRD, 2006 2019/1/10 2010-2020的宇宙学

Basic equations Defining , & 2019/1/10 2010-2020的宇宙学

r = u/v as a function of ln(1 + z) ICG model is a better model Zhang, Yu, Z-HZ, Gong, PLB, 2009 2019/1/10 2010-2020的宇宙学

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. 2019/1/10 2010-2020的宇宙学

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 2019/1/10 2010-2020的宇宙学

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 2019/1/10 2010-2020的宇宙学

A quantitative criteria for coincidence Taking z = 100 as “early universe” The fixed point of r : or Lead to negative rs 2019/1/10 2010-2020的宇宙学

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 2010-2020的宇宙学

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 2019/1/10 2010-2020的宇宙学

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