# Presentation: 237922

**Dissecting**** ****Dark Energy**

**Eric Linder **
**Lawrence Berkeley National Laboratory**

## Our Tools

**Expansion rate of the universe**** a(t) **
**ds****2 ****= ********dt****2****+a****2****(t)[dr****2****/(1-kr****2****)+r****2****d********2****]**
**   ****Einstein equation***** ***
**(å/a)****2**** = H****2**** = (8********/3) ********m**** + ********H****2****(z)**
**	****	****         ****= (8********/3) ********m**** + C exp{********dlna [1+****w(z)****]}**
**Growth rate of density fluctuations***** *****g(z)**** ****= (********m****/********m****)/a **

**Poisson equation**** ********2********(a)****=4********Ga****2 ********m****= 4********G********m****(0) g(a)**

## Tying HEP to Cosmology

**Accurate to 3% in EOS back to *****z=1.7***** (vs. 27% for *****w******1*****). **
**Accurate to 0.2% in distance back to *****z******lss******=1100*****!**

**Linder *****Phys.Rev.Lett.***** 2003 following ****	****	****Corasaniti & Copeland 2003**

***w(a) = w******0******+w******a******(1-a)***

## All w, All the time

**Suppose we admit our ignorance:**
**	****H****2**** = (8********/3) ********m**** + ********H****2****(z)**
**Effective equation of state:**
**w(z) = -1 + (1/3) d ln(********H****2****) / d ln(1+z)**
**Modifications of the expansion history are equivalent to time variation w(z).****  ****Period.**** **

**Time variation w**** ́ is a critical clue to fundamental physics.**
**Alterations to Friedmann framework ******** *****w(z)***

- gravitational extensions or high energy physics

- Linder 2003

## The world is w(z)

**Don’t care if it’s braneworld, cardassian, vacuum metamorphosis, chaplygin, etc. **

**Simple, robust parametrization**
**    ****w(a)=w****0****+w****a****(1-a)**
**Braneworld**** ****[DDG]**** ****vs.**** ****(w****0****,w****a****)=(-0.78,0.32)**
**Vacuum metamorph**** ****vs.**** ****(w****0****,w****a****)=(-1,-3)**
**Also agree on m(z) to 0.01 mag out to z=2**

## Revealing Physics

**Some details of the underlying physics are not in w(z).**** **
**N****eed an underlying theory - ********? beyond Einstein gravity?**
**     ****Growth history and expansion history work together. **

**w****0****=-0.78 w****a****=0.32**

- Linder 2004
*cf.* Lue, Scoccimarro, Starkman  Phys. Rev. D69 (2004) 124015       for braneworld perturbations

## Questions

**How does ****a(t)**** teach us something fundamental (beyond w(z))? **
**Benchmarks:**** à la energy scale for inflation models; rule out theories tying DE to inflation; scalar tensor ********2****; slow roll parameters of V(********) like linear potential**
**Predictive power:**** Albrecht-Skordis-Burgess w(z); naturalness constraints ; flatness and w(z) **
**w<-1: ****Crossing w=-1**** with hybrid quintessence**
**Other tools:**** astronomy (strong gravity, solar system), accelerator, tabletop experiments**

## Lambda, Quintessence, or Not?

**Lambda, Quintessence, or Not?**

**Many models asymptote to w=-1, making distinction from ******** difficult.  Can models cross w=-1? *****(Yes, if w<-1 exists.)***

**All models match CMB power spectrum for ********CDM**

## Naturalness and w ́

**Consider the analogy with inflation. **
**Tilt**** ****n=1**** (Harrison-Zel’dovich) is roughly predicted; profound if n=1 exactly (deSitter, limited dynamics). **
**Same:**** ****w=-1**** exactly is profound, but w≈-1 maybe not too surprising. Small deviation w********-1 important so precision sought. **
**However,**** while n=0.97, constant without running, is possible, *****w=-0.97 constant is almost ridiculous*****. **
**Thus, searching for**** ****w ́**** ****is critical even if find w very near -1. **

## Predictions & Benchmarks

**Linear potential ****[Linde 1986]**
**V(********)=V****0****+******
**leads to collapsing universe, can constrain t****c**

**curves of ******

**Would like predictions of w(z)**** - or at least w ́. ****	****In progress for Albrecht-Skordis-Burgess model ****	****V(********) = (1+ ********/b + ********/b****2****) exp(-********)**

## Predictions & Benchmarks

**Extensions to gravitation**
**E.g. scalar-tensor theories: ****f/2********-********(********)********;************;********-V****	****	****Take linear coupling to Ricci scalar R: ****f/******** = F R**** ****	****Allow nonminimal coupling **
**	****	****F=1/(8********G)+ ********2**
**R-boost (note R********0 in radiation dominated epoch) gives large basin of attraction: solves fine tuning yet w ≈ -1. ****[Matarrese,Baccigalupi,Perrotta 2004]**
**But growth of mass fluctuations altered: S********0 since G ******** 1/F.**

## Questions

**How does ****a(t)**** teach us something fundamental (beyond w(z))? **
**Benchmarks:**** à la energy scale for inflation models; rule out theories tying DE to inflation; scalar tensor ********2****; slow roll parameters of V(********) like linear potential**
**Predictive power:**** Albrecht-Skordis-Burgess w(z); naturalness constraints ; flatness and w(z) **
**w<-1: ****Crossing w=-1**** with hybrid quintessence**
**Other tools:**** astronomy (strong gravity, solar system), accelerator, tabletop experiments**