Holographic and agegraphic dark energy models Yun Soo Myung Inje University, Gimhae, Korea

Contents 1. Introduction 2. Sourced Friedmann equations 3. Interacting holographic dark energy model 4. Agegraphic dark energy model 5. New agegraphic dark energy model 6. Discussions

1. Introduction

Introduction Main issue of the present cosmology :How to explain the present accelerating universe?  Candidates for DE with w<-1/3 1) cosmological constant (w=-1) 2) quintessence (w>=-1) 3) K-essence (w>=-1) 4) holographic dark energy (w>=-1) 5) phantom matter (w<-1)  Can we rule out a dynamical DE model?  Can we rule out the phantom phase of w<-1? phantom matter violates all the energy conservation laws.

Introduction Dark energy  a repulsive form of gravity in space  present 9 billion years ago.  its effect becomes more dominant as the universe expands. Einstein  the first person to realize that the empty space is not the space as nothingness.  introduce the cosmological constant to balance the universe against the inward pull of its own gravity.

Introduction-cosmological constant

Introduction-another models 1)Holographic dark energy density 2) Vacuum fluctuation energy density 3) Geometric mean of 4) Casimir energy of QM 5) Uncertainty of distance in holographic form cosmology distance in holographic form cosmology 6) Entanglement energy? ),3)Astro-ph/ , 4)gr-qc/ , 5) PLB469,243

Introduction-HDEM

Introduction-gravitational holography ** Gravitational Holography limits number of states accessible to a system including gravity. **Considering an infinite contribution to the vacuum energy is not correct when the gravity is present. **Projection from states in bulk-volume to states on covering surface  holographic principle.

Introduction-HDEM

2. Sourced Friedmann equations

Sourced Friedmann equations

Macroscopic mechanism for energy transfer in two-fluid model

Microscopic mechanism for energy transfer in two-fluid model

3. Interacting holographic dark energy model

Interacting holographic dark energy model

Interacting holographic dark energy model –density parameters

Interacting holographic dark energy model – effective EOS

Non-interacting holographic dark energy model-EOS

Interacting holographic dark energy model – comments After a long decaying, two are the new same fluid like cosmological constant.  It seems that there is no mechanism to generate a phantom phase by turning on an interaction between two fluids. by turning on an interaction between two fluids.

  Two quantities for the cosmological evolution : EOS and squared speed of sound velocity (SSV) 2) SSV evaluated to 0 th order determines the stability of background evolution: : stability of a first-order perturbation : instability of a first-order perturbation 3) Linear perturbation: 1) EOS determines the nature of background evolution

EOS and SSV for HDEM c=0.8c=1c=1.2 FEHFEH PHPH blow up and phantom phase unstable

EOS and SSV for Chaplygin gas and tachyon models Chaplygin gas model-stable Tachyon model-stable

4. Agegraphic dark energy model (ADEM) The Karolyhazy relation: ‘ The time-energy uncertainty in the Minkowiski spacetime: Vacuum energy density with the parameter : No causality problem. Problem for describing the matter-dominated universe in the par fast.

ADEM: non-interacting case   The first Friedmann equation:   continuity equation:   density parameter :

  Pressure:   EOS:   The evolution equation:   SSV: ADEM: non-interacting case

  Result of ADEM (solid  EOS, dashed  SSV) n=0.9n=1.2 n=2.0     No dark energy-dominated universe in the far future.   for n=0.9 (n<1.0), no phantom phase of.

  continuity equation:   The evolution equation:   EOS:   SSV: with ADEM: interacting case with

Interacting case using EOS (solid  EOS, dashed  SSV) n=0.9n=2.0 : phantom phase   n=1.2

  SSV:   Effective EOS: : no phantom phase   When using effective EOS, we find no phantom phase

5. New agegraphic dark energy model (NADEM) Vacuum energy density: No causality problem. Resolving problem for describing the matter-dominated universe in the par fast.

NADEM: non-interacting case with matter-dominated universe   EOS:   The evolution equation: Evolution is nontrivial because EOS is function of x and. SSV : SSV :

  Result of NADEM   whole evolution depends on the parameter critically. For EOS, n=2.6 nc= n=2.7

Region of evolution Considering the connection between x and z : Hence our region from x=-20( ) to x=20 ( ) covers the whole region of evolution.

  far past : : non-acceptable   far future : for all n, The squared speed is always negative for Result of NADEM

NADEM with matter-and radiation- dominated universes   continuity equation:   The evolution equation:   SSV:

  Result of NADEM   far past : radiation-dominated universe   far future : dark energy –dominated universe( ) For EOS, n= nc= n=

  Interacting case of NADEM with   continuity equation:   The evolution equation:   EOS:   SSV: with

  Result- No simulation   The evolution of the native EOS and the SSV are similar to NADEM except including the phantom phase.   When using effective EOS, we expect that No phantom phase. the whole evolution of the universe implies negative squared speed.

6. Discussions   Comparison between NADEM and HDEM NADEMHDEMRemark Far past Far future Matter-dominated U Dark energy -dominated U   The squared speed for ADEM is always negative, so it is classically unstable like HDEM with future event horizon.   The NADEM is no better than the HDEM for the description of the dark energy-dominated universe.

Discussions Similarity HDEM with particle horizon  ADEM HDEM with future event horizon  NADEM Comment For n>n c, NADEM could describe Matter (radiation)-dominated Universe.