The Consequences of a The Consequences of a Dynamical Dark Energy Dynamical Dark Energy

Density on the Evolution of Density on the Evolution of the Universethe Universe

By Christopher Limbach, By Christopher Limbach, Alexander Luce, and Amanda Alexander Luce, and Amanda

StitelerStitelerBackground image: Andrey Kravtsov., University of Chicago, 2003.

Presentation Overview

• Amanda Stiteler– Introduction– Theory

• Chris Limbach– Assumptions– Verification of Methods

• Alex Luce– Results– Conclusion

Image by Martin Altmann, Observatory Hoher List, 1997.

The Big Bang in BriefThe Big Bang in Brief

Einstein’s Cosmological ModelEinstein’s Cosmological Model

Rij = Ricci tensor

R = curvature scalargij = space-time metric tensor

G = Newton’s gravitational constantTij = stress-energy tensor

Λ = cosmological constant

ijijijij GTgRgR 82

1

The Friedmann EquationThe Friedmann Equation

a = dimensionless scale factorρR = relativistic matter density

ρM = non-relativistic matter density

ρΛ = dark energy density

k = curvature of the universec = speed of lightl0 = present distance between two galaxies

22

0

22

3

81

al

kcG

dt

da

a MR

QuintessenceQuintessence• Equation relating the scalar field, , and its

potential, :

• Energy density of the scalar field:

• Evolution of the scalar field:

22

2

32 pp m

m

02

3 )1(2 pma

a

V

V

Free Parameters Free Parameters andand

• Parameters which characterize potential

• Chosen such that V(φ) mimics nearly constant Λ at present

V

Purpose of this ProjectPurpose of this Project

• Compare the evolution of a universe Compare the evolution of a universe with constant dark energy density to with constant dark energy density to one with variable dark energy densityone with variable dark energy density

• Determine restrictions of the Determine restrictions of the constants constants κκ and and αα

Image by NASA., 2006.

AssumptionsAssumptions• Homogeneous, Isotropic Universe

• (from WMAP)

• Total Density = Critical Density

• Initial Conditions for ΩR, ΩM, ΩΛ from WMAP

• No Spatial Curvature

Mpc

kmH

1

sec680

critMR

critcrit

MM

crit

RR

,,

MethodMethod

• 4th Order Runge-Kutta• Equations Solved:

RMadt

da

3

8

dt

d

a

a

dt

d3

2)1(

Numeric SolutionsNumeric Solutions

Time Relative to Present [Gyrs]

Scale Factor

a

1

0

0.01

“Time of Big Bang”

t

Verification Verification

h= 0.02

h = 0.01

h = 0.005

Time From Present [Gyrs]

Scale Factor

1

Solutionerror δh

t

a

h= time step

Simulation ResultsSimulation Results

Constant Dark Energy vs. Time Dependent Dark Energy?

Restrictions on Free Parameters of Model

Dark Energy: Dark Energy: ConstantConstant

• Radiation Plays Large role at early times

• Matter Increases as radiation dies off

• Dominated by Dark Energy at later times

Dark Energy: Dark Energy: Time DependentTime Dependent

• Dominated by Dark Energy at early times

• Again dominated by Dark Energy at later times

• Kappa and Alpha were chosen to agree w/ observations

• Amount of radiation is relatively lower

Dark Energy: Constant vs. Time Dependent

Free Parameters Constrained Free Parameters Constrained by Age of Universeby Age of Universe

Scale FactorScale Factor

• Represents relative expansion of universe

• Independent of Free Parameters which characterize expansion

Power Law Model of Time Power Law Model of Time Dependent dark energy: Dependent dark energy:

PossiblePossible• Free Parameters do

not influence Dynamical behaviour

• WMAP findings: Universe is >13.7 billion years old

AcknowledgmentsAcknowledgments

• Dimitrios Psaltis• Chi Kwan Chan• Drew Milsom

Sources CitedSources CitedKravtsov, Andrey. “Computer-generated image of the distribution of dark matter.” Image

from “Cosmologists to plot strategy for dark energy research campaign at Chicago workshop Sept. 17-20.” 3 Sept 2003. 29 April 2007. <http://www-news.uchicago.edu/ releases/03/030903.darkmatter.shtml>.

Limbach, Christopher, Alexander Luce, and Amanda Stiteler. “The Consequences of a Dynamical Dark Energy Density on the Evolution of the Universe.” 5 Dec 2006. 29 April 2007. <http://www.physics.arizona.edu/~dpsaltis/Phys205/limbach_luce_stiteler.pdf >.

NASA. “WMAP picture of the infant universe.” Image from “Ringside Seat to the Universe’s First Split Second.” 20 March 2006. 30 April 2007. <http://imagine.gsfc.nasa.gov/docs/ features/news/20mar06.html>.

National Taiwan Science Education Center. “The origin and the evolution of the Universe.” Image from “The Emergence of the Cosmos.” 29 April 2007. <http://www.ntsec.gov.tw/ space/EN/show.asp?XH36>.

WMAP. “Geometry of the Universe.” “Image from “Sachs-Wolfe Effect.” 2 May 2007. <http://zebu.uoregon.edu/2004/a321/lec15.html>.

Free Parameters Constrained by Free Parameters Constrained by Age of UniverseAge of Universe

Energy DensityEnergy Density