with Matter and Radiation By: Michael Solway

Transcription

1 Interactions of Dark Energy with Matter and Radiation By: Michael Solway Advisor: Professor Mike Berger

2 What is Dark Energy?

3 Dark energy is the energy needed to explain the observed accelerated expansion of fthe universe. It must have a negative pressure to counteract gravity and produce expansion. In theory, it is homogeneously spread with a small density throughout the universe, making up about 70% of the total energy. e It does not interact strongly through any fundamental forces except gravity. And since it has a small density, we have not detected it yet; And since it has a small density, we have not detected it yet; hence the name dark energy.

4 Type Ia Supernovae The evidence for the existence of dark energy comes from type Ia supernovae. They are the brightest and the closest to standard candles objects that we know in the universe, which makes measuring their characteristics easy. The comparison of their redshifts z to their distances away from Earth, which are obtained through the standard candle model, show signs of an accelerated expansion. Redshift: 1 + z = λ observed / λ emitted

5 Cosmic Microwave Background Radiation The cosmic microwave background radiation is the radiation of the last scattered photons before the universe grew to a size when the photons were very unlikely to scatter again. It fills up the entire universe and is very isotropic to roughly one part in 100,000. Measurement of the CMB suggest that the universe at present is flat. This can only be so with a critical energy density. Matter makes up only 30% and free radiation about 10-7 % of that density. Dark energy is a very good candidate for the remaining 70%.

6 Leading Theories to Explain Dark Energy Adding a cosmological constant to Einstein s s equations from general relativity. this theory fits the supernova data well all other theories are compared to this one. Quintessence a field that varies with time and space in the universe scalar fields

7 Evolution of the Universe The evolution of the universe is described by Einstein ss equations. For a locally isotropic and homogeneous universe, they are simplified to the Friedmann equations: These are derived for a perfect fluid with energy density ρ and pressure p. G is the gravitational constant. Λ is the cosmological constant. k is a parameter that describes the shape of the universe. a is a dimensionless parameter called the scale factor. It depends on time and is a measure of the size of the universe. H is called the Hubble parameter, and measures the rate of expansion.

8 At present, the scale factor a is set to 1 and the Hubble parameter is called the Hubble constant H 0. The scale factor relates to redshift by: 1 + z = 1 / a Ad density parameter is defined dfrom the first tfriedmann equation: If Ω for the total energy in the universe is 1, then the universe is flat. If it is less than 1, then the universe is open with negative curvature. And if it is greater than 1, then the universe is closed with positive curvature.

9 Perfect Fluids All the different types of energies in the universe: dark energy, matter, and radiation are modeled as perfect fluids. matter includes ordinary and dark matter radiation is matter at very high relativistic speeds The ratio of a perfect fluid s pressure to its energy density is defined to be the equation of state w: w = p/ρ for dark energy: w Λ -1 ( < w Λ < -.8) for matter: w m = 0 for radiation w R = 1/3 The equation of state is related to the scale factor by:

10 Continuity Equations Without Interactions Continuity Equation: Without interactions, the continuity equations for dark energy, matter, and radiation are:

11 Dark Energy, Matter, and Radiation Interaction Q = R + S

12 Old Variables Ω Λ + Ω m + Ω R = 1 a flat universe is assumed New Variables

13 Effective Equations of State

14 Differential Equations x = ln(a)

15 Defining the Length Scale for Dark Energy LΛ

16 Simplified w eff s

17 Holographic Principle Condition

18 Simplified Differential Equations

19 Initial Conditions x = 0 when a = 1 since x = ln(a) so these conditions are assigned at present time

20 γ = 0 δ = 0

21 γ = 1 δ = 0

22 γ = -1 δ = 0

23 γ = 0 δ = 1

24 γ = 0 δ = -1

25 γ =.5 δ = 10-10

26 γ =.5 δ = -.45

27 Initial Conditions

28 γ = 0 δ = 0

29 γ = 1 δ = 0

30 γ = -1 δ = 0

31 γ = 0 δ = 1

32 γ = 0 δ = -1

33 γ =.5 δ =

34 γ = 2 δ = -.4

35 Acknowledgments Thanks to Professor Mike Berger for helping me with this research.