# Presentation: 586305

**Dark Energy:   **
***Accelerating the Universe***** **

**Eric Linder**** **
**University of California, Berkeley**
**Lawrence Berkeley National Lab**

## Our Expanding Universe

- Simulation courtesy of Bertschinger & Ma

## Discovery!  Acceleration

## New Frontiers

**Beyond Einstein:**** What happens when gravity is no longer an attractive force?**

- Scientific American

**Discovery**** ****(****SCP,HiZ 1998****)****:**** ****70% of the universe acts this way! **
***Fundamentally new physics.****** Cosmology is the key.****** ***

## Cosmic Concordance

**Cosmic Concordance**

** *****Supernovae alone*****   ****	****       ******** Accelerating expansion**
** ******** ****> 0**
** *****CMB (plus LSS)***
****** ****Flat universe **
****** ******** ****> 0 **
** *****Any two of SN, CMB, LSS***
****** ****Dark energy ~75%**

## Frontiers of Cosmology

**95% of the universe is unknown!**

**Frontiers of Cosmology**

- STScI

**Us**

**Notes:**
What a frontier! 

## Dark Energy Is...

**Dark Energy Is...**

** ****70-75% of the energy density of the universe**
** ****Accelerating the expansion, like inflation at 10****-35****s**
** ****Determining the fate of the universe**

**!**** 70-75% of the energy density of the universe**
***95% of the universe unknown!***
**!**** Accelerating the expansion, like inflation at 10****-35****s**
***Repulsive gravity!***
**!**** Determining the fate of the universe**
***Fate of the universe!***

**Is this mysterious dark energy the original ****cosmological constant ********, a quantum zeropoint sea?**** **

## What’s the Matter with Energy?

**They are off by a factor of **

**1,000,000,000,000, 000,000,000,000, 000,000,000,000, 000,000,000,000, 000,000,000,000, 000,000,000,000, 000,000,000,000, 000,000,000,000, 000,000,000,000, 000,000,000,000.**

**This is modestly called the**** ****fine tuning**** ****problem.**** **

**Why not just bring back the cosmological constant (********)?**** **
**When physicists calculate how big ******** should be, they don’t quite get it right. **

## : Ugly Duckling

**Astrophysicist:**** **
**Einstein equations – **
******g****ab**
**      ********	****p = -******
**Naturally, ******** =const= ********PL**
**********= 10****120**
**Today  ****************M**

**Field Theorist: **
**Vacuum – Lorentz invariant**
**T****ab**** ****~********ab**** = diag { -1, 1, 1, 1}**
**        ********   ****p = -******
**Naturally, E****vac**** ****~**** 10****19 ****GeV**
**          ****E******** ****~**** (meV)****4**
******=0?**

** ****Fine Tuning Puzzle – why so small?**
** ****Coincidence Puzzle – why now?**

## Cosmic Coincidence

**Matter**

**Dark energy**

**Today**

**Think of the energy in ******** as the level of the quantum “sea”.  At most times in history, matter is either drowned or dry.**** **

**Cosmic Coincidence**

**Is this mysterious dark energy the original ****cosmological constant ********, a quantum zeropoint sea?**** **

## On Beyond !

***We need to explore further frontiers***** in high energy physics, gravitation, and cosmology.**
** **
**New quantum physics?**** ****Does nothing weigh something?**** ****Einstein’s cosmological constant****,**** Quintessence****, ****M/String theory**** *****	***
**New gravitational physics? ****Is nowhere somewhere?**** ****Quantum gravity, supergravity, extra dimensions?****	**
**	****   ****We need new, highly precise data**

***[Lecture 1]***

***[Lecture 3]***

***[Lecture 2]***

## Dark Energy – the Easy Way?

**Direct detection?**** **
**(*****Dark energy in solar system = 3 hours of sunlight*****).**** **
**Variations of fundamental constants:**** **
**lab and accelerator and universe.**** **
**Direct acceleration?**** **
**Redshift drift**** ****(Sandage 1959; Linder 1991,1997)**
**  ****dz=10****-8**** over 100 years**

## What Dark Energy Isn’t

**Is dark energy related to dark matter?**** Probably not.**
**DM: clumps around galaxies and clusters ****	****	****      ****	****   DE: smoothly distributed**
**DM: pressureless, dominated by rest mass****	****	****        ****	****   DE: strongly negative pressure, of order energy density**
**DM: important to evolution of universe since z****eq****: t=100,000 y DE: important to evolution of universe since t≈7 billion y**
**DM: interacts through gravity and (presumably) weak force DE: interacts only through gravity**
**DM: makes up 20% of total energy density today, 70% at z****dec**** DE: makes up 75% now, negligible amount at z****dec**

## What Dark Energy Isn’t

**Is dark energy related to inflation?**** Probably not.**
**Inflation: at energy scale around 10****24**** eV ****	****	****      ****	****	****    DE: at energy scale around 10****-3**** eV**
**  *****[Energy density goes as (scale)******4******, making the ratio 10******108******.]***** **
**Inflation: began at perhaps t****≈****10****-35**** s****	****	****        ****	****	****    ****	****    DE: acceleration began at t≈7 billion y**
**Is dark energy related to Casimir energy?**** Probably not.**
**Casimir: depends on physical boundaries ****	****	****	****	****    DE: universe has no physical boundaries **
**Casimir: can have positive pressure, depending on boundary geometry DE: negative pressure, universe has no physical boundaries **
**Casimir: detected effect arises from vector field (EM) ****	****	****    DE: not a vector field (no charge), maybe scalar field**
**Casimir: dies off rapidly with distance (~d****-4****)****	****    ****	****	****	****    DE: repulsion (tension) increases with distance**

## Dark Energy

**Dark energy is likely to be a   **
**fundamentally new **
**physical phenomenon.**

## Acceleration and Dark Energy

## Negative pressure

## Vacuum Energy

**Quantum physics**** predicts that the very structure of the vacuum should act like springs.**
**Space has a “****springiness****”, or tension, or ****vacuum energy**** with negative pressure. **

**Review --**** **
***Einstein*****: ****expansion acceleration**** depends on**** ********+3p**
***Thermodynamics*****: ****pressure p ****can be negative**
***Quantum Physics*****: ****vacuum energy**** has negative ****p**
**Supernova ****markers can map**** the expansion history, ****measure**** acceleration, ****detect**** vacuum energy.**

## Theory of Fields

**Scalar field:**

**Vector fields:**

**At every point in a field of grass, you can measure the height of the grass: a single number or scalar h(x).**

## Nature of Acceleration

**How much dark energy is there?  ****energy density**** **********
**How springy is it?  ****equation of state**** ****w**
**How does it vary with time (how stretchy)?****  ****w******

**How do we learn**** *****what***** ****it is, not just**** *****that***** ****it is?**** **
** ****Longer “lever arm” (higher redshift, more history)**
** ****Many more supernovae, more precisely**
** ****High accuracy**

## Scalar Field Theory

**Scalar field Lagrangian - **
**	****canonical, minimally coupled**
**L*********** *****= (1/2)(******************)****2 ****- V(**********)**** **
**Noether prescription ******** Energy-momentum tensor**
**T********=(2/********-g) [ ********(********-g ****L**** )/********g******** ****]**
**Perfect fluid form (from RW metric)**

**Energy density****  ************** = (1/2) *********** *****2**** + V(**********) ****+ (1/2)(**************)****2**** **
**Pressure**** ****	****	****p********** = (1/2) *********** *****2**** - V(**********) ****- (1/6)(**************)****2**** **

**.**

**.**

## Scalar Field Equation of State

**Continuity equation follows KG equation**
**[(1/2)*********** *****2****]  + 6H ****[(1/2)*********** *****2 ****] = -V**
****** ****- V + 3H (********+p) = -V**
**d********/d*****ln***** a = -3(********+p) = -3******** (1+w)**

**Equation of state ratio **
**w = p/******
**Klein-Gordon equation ****(Lagrange equation of motion) **

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## Equation of State

**Reconstruction from EOS:**** **
******(a) = *************** *********c**** exp{ 3 ********d*****ln***** a [1+****w(z)****] }**
********(a) = ********d*****ln***** a H****-1**** sqrt{ ********(a) [1+****w(z)****] }**
**V(a) = (1/2) ********(a) [1-****w(z)****] **
**K(a) = (1/2)*********** *****2**** = (1/2) ********(a) [1+****w(z)****] **

**.**

## Equation of State

**Limits of (canonical) Equations of State:**** **
**w = (K-V) / (K+V)**
**Potential energy dominates (slow roll) **
**V >> K ******** w = -1**
**Kinetic energy dominates (fast roll)**
**K >> V ******** w = +1**
**Oscillation about potential minimum ****	****	****(or coherent field, e.g. axion)**
******V******** = ********K******** ******** w = 0**

## Equation of State

**Examples of (canonical) Equations of State:**** **
**d********/d*****ln***** a = -3(********+p) = -3******** (1+w)**
**	******** ****= ****(Energy per particle)(Number of particles) / Volume**** ****	****   = E N a****-3**** **
**Constant w implies**** ******** ~ a****-3(1+w)**
**Matter:**** E~m~a****0****, N~a****0**** ******** ****w=0**
**Radiation:**** E~1/********~a****-1****, N~a****0**** ******** ****w=1/3**
**Curvature energy: ****E~1/R****2****~a****-2****, N~a****0**** ******** ****w=-1/3**
**Cosmological constant:**** E~V, N ~a****0**** ******** ****w=-1**
**Anisotropic shear: w=+1 ****	****	****	****	****	****Cosmic String network: w=-1/3  ;  Domain walls: w=-2/3**

## Dark Energy Models

**Scalar fields can roll: **
**fast -- “kination” ****[Tracking models] **
**slow -- acceleration ****[Quintessence]**
**steadily -- acceleration deceleration ****	****	****[Linear potential] **
**oscillate -- potential minimum, pseudoscalar, PNGB ****[V~ ***********n*****]**

## Power law potential

**“****Normal” potentials don’t work: **
**V(**********) ~ ***********n  ***
**have minima (n even), and field just oscillates, leading to EOS**
**w = (n-2)/(n+2)**
**	****	****n****	****0****	****2****	****4****	****∞****	****	****	****	****	****w****	****-1****	****0****	****1/3****	****1    **

## Oscillations

**Oscillating field**
**w = (n-2)/(n+2)**
**Take osc. time << H****-1**** and ******** constant over osc.**
**  ****	***************2********** = *********dt ***********2****** / *********dt = ********d*********** *********** / ********d*********** *****/*********** ***
***	******	*****= 2******** ********d********** [1-V/V****max****]****1/2**** / [1-V/V****max****]****-1/2**
**If ****V = V****max****(********** /**********max****)****n**** then **
**	********w******** = -1 + 2**** ********0****1****dx (1-x****n****)****1/2**** / ********0****1****dx (1-x****n****)****-1/2**** **
**	****      ****= -1 +2n/(n+2)**

**.**

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**.**

- Turner 1983

## Linear Potential

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

**curves of ******

## Tracking fields

**Criterion ******** = VV********/(V********)****2**** > 1****, ****d *****ln***** (********-1)/dt <<H****.  **
**However, generally only achieves ****w****0 ****> -0.7****. **
**Successful model requires fast-slow roll.**** **

**Can start from wide variety of initial conditions, then join attractor trajectory of tracking behavior. **

## Dark Energy Models

**Inverse power law ****V(**********) ~ ***********-******n  ***
**“****SUGRA” ****V(**********) ~ ***********-******n *****exp(***************2*****)**
**Running exponential ****V(**********) ~ exp[- *********(***********)**********]**
**PNGB or “axion” ****V(**********) ~ 1+cos(**********/f)**** **
**Albrecht-Skordis ****V(**********) ~ [1+c****1********** +c****2**********2****] exp(-**************)**
**“****Tachyon” ****V(**********) ~ [cosh(**************)-1]****n**
**Stochastic ****V(**********) ~ [1+sin(**********/f****)] exp(-**************)**
**...**** **

## Equation of State

**Reconstruction from EOS:**** **
**	********(a) = *************** *********c**** exp{ 3 ********d*****ln***** a [1+****w(z)****] }**
***	***********(a) = ********d*****ln***** a H****-1**** sqrt{ ********(a) [1+****w(z)****] }**
**	****V(a) = (1/2) ********(a) [1-****w(z)****] **
**	****K(a) = (1/2)*****   *****2**** = (1/2) ********(a) [1+****w(z)****] **

## 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*****!**

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

## Dynamics of Quintessence

**Equation of motion of scalar field**
** ****driven by steepness of potential**
** ****slowed by Hubble friction**
**Broad categorization -- which term dominates: **
** ****field rolls but decelerates as dominates energy **
** ****field starts frozen by Hubble drag and then rolls **
**	****	****Freezers vs. Thawers**

## Limits of Quintessence

***Driven***** by steepness of scalar potential, *****Dragged***** by Hubble expansion. **
**Analysis shows distinct, narrow regions of ****w-w******

**Entire “thawing” region looks like ****<w> = -1±0.05****.  ****Need w******** experiments with ******** (w********) ≈ 2(1+w)****.**

**Caldwell & Linder 2005 Phys.Rev.Letters 95, 141301**

## Fundamental Physics

**Map the expansion history of the universe**

**The subtle slowing and growth of scales with time – ****a(t)**** – map out the cosmic history like tree rings map out the Earth’s climate history. **

- STScI