# Presentation: 673035

## Hitchhiker’s Guide to the Early Universe

**Hitchhiker’s Guide to the Early Universe**

- Paul Stankus
- Oak Ridge
- RHIC/AGS Users’ Meeting June 20, 05

## Contents

*Contents*
- Evidence for a Big Bang  Experimental  Theoretical  Basic Framework  A Smidgen of GR  Vacuum Energy and Inflation  Thermodynamics  Decoupling and Relics  The QGP Transition

- If I can understand it, so can you!

## The original Hubble Diagram

**Henrietta Leavitt** American
- Distances via variable stars

**Edwin Hubble** American
- Galaxies outside Milky Way

- The original Hubble Diagram
- “A Relation Between Distance and Radial Velocity Among Extra-Galactic Nebulae” E.Hubble (1929)

## Now

**Now**
- Slightly Earlier

- As seen from our position:

- As seen from another position:

- Recessional velocity  distance
- Same pattern seen by all observers!

## ?

**Original Hubble diagram**

- Freedman, et al. Astrophys. J. **553**, 47 (2001)

- 1929: *H*0 ~500 km/sec/Mpc
- 2001: *H*0 = 727 km/sec/Mpc

- Photons

- t

- x

- Us

- Galaxies

**?**

***v*****Recession**** = *****H*****0**** *****d***

- 1/*H*0 ~ 1010 year ~ Age of the Universe?

- 1/*H*0

**W. Freedman **American

- Modern Hubble constant (2001)

## H.P. Robertson American

**H.P. Robertson **American

**A.G. Walker **British

**W. de Sitter **Dutch

**Albert Einstein **German

**A. Friedmann **Russian

**G. LeMaitre **Belgian

- Formalized most general form of isotropic and homogeneous universe in GR “Robertson-Walker metric” (1935-6)

- General Theory of Relativity (1915); Static, closed universe (1917)

- Vacuum-energy-filled universes “de Sitter space” (1917)

- Evolution of homogeneous, non-static (expanding) universes “Friedmann models” (1922, 1927)

## Global Reference Frames

- Convenient Coordinate Systems

- Complete coordinate freedom!  **All physics** is in *g*(*x*0,*x*1,*x*2,*x*3)

**H. Minkowski**        German

- “Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality" (1907)

- x

- t

- t’

- x’

- Photons

- Photons

- E1

- E1

- E2

- E2

- E0

- E0

## Robertson-Walker Metric:

**Homogeneity** = same at all points in space at some ***t ***= constant as seen by observers following *d****x ***= *d****y ***= *d****z ***= 0
**Isotropy** = same in all spatial directions as seen from any point
- (Convenient: want *d****t ***= *d******i.e.*, proper/subjective time, when *d****x ***= *d****y ***= *d****z ***= 0)

## t

****

- A photon’s period grows  *a*(*t*)
- Its coordinate wavelength  is constant; its physical wavelength *a*(*t*)grows  *a*(*t*)
**Red shift!**
-           (*t*2)/(*t*1) = *a*(*t*2)/*a*(*t*1) 1+*z*

*t*1

*t*2

- Us

- Galaxies at rest in the “Hubble flow”

- Photons

**t=now**

****

## a(t)  a Friedmann-Robertson-Walker (FRW) cosmology

- Three basic solutions for *a*(*t*):

- Relativistic gas, “radiation dominated”
- 	*P*/= 1/3    *a*-4    *a(t)**t*1/2
- Non-relativistic gas, “matter dominated”
*P*/= 0    *a*-3    *a(t)**t*2/3
- “Cosmological-constant-dominated” or “vacuum-energy-dominated”
*	**P*/= -1    constant    *a(t)**e**Ht*  “de Sitter space”

## Over-

**Over-**

**B. Riemann** German

- Formalized non-Euclidean geometry (1854)

**G. Ricci-Curbastro **Italian

- Tensor calculus (1888)

## Friedmann Equation 1  (=0 version)

- Energy density (in local rest frame)

- Curvature

- Q: How does  change during expansion?

- Friedmann Equation 1  (=0 version)

## dE = -PdV  therefore dS = 0    Isentropic

- Basic Thermodynamics

- Sudden expansion, fluid fills empty space without loss of energy.
*dE *= 0    *PdV *> 0   therefore  *dS *> 0

- Gradual expansion (equilibrium maintained), fluid loses energy through PdV work.
*dE *= -*PdV  *therefore *dS *= 0    Isentropic

## Friedmann Equation 2  (Isen/Iso-tropic fluid,=0)

- Friedmann Equation 2  (Isen/Iso-tropic fluid,=0)

- However, this cannot describe a static, non-empty FRW Universe.

- Ac/De-celeration of the Universe’s expansion

- Necessity of a Big Bang!

## Re-introduce “cosmological constant” 

- Generalize     (*t*)=Matter(*t*) +/8*P*(*t*)=*P*Matter(*t*) -/8

- Cosmological constant acts like constant energy density, constant negative pressure, with EOS *P*/= -1

## Friedmann 1 and 2:

- Einstein 1917     “Einstein Closed, Static Universe”

-  disregarded after Hubble expansion discovered
- - but -
- “vacuum energy” acts just like 

## The New Standard Cosmology in Four Easy Steps

- Inflation, dominated by “inflaton field” vacuum energy
- Radiation-dominated thermal equilibrium
- Matter-dominated, non-uniformities grow (structure)
- Start of acceleration in *a*(*t*), return to domination by cosmological constant and/or vacuum energy.

*w*=*P*/

- -1/3

- +1/3

- -1

*a*e*Ht*

*a**t*1/2

*a**t*2/3

***t***

- now

- acc dec

## T(t)

***T*****(*****t*****)**

***a*****(*****t*****)**

********(*****t*****)**

***t***

- How do we relate ***T*** to ***a***,******?  i.e. thermodynamics

## Golden Rule 1: Entropy per co-moving volume is conserved

- Golden Rule 2: All chemical potentials are negligible

- Golden Rule 3: All entropy is in relativistic species

- Expansion covers many decades in T, so typically either T>>m (relativistic) or T<<m (frozen out)

- Kolb & Turner, *The Early Universe,* Westview 1990

## Golden Rule 4:

- Kolb & Turner

- QCD Transition

- e+e- Annihilation

- Nucleosynthesis

-  Decoupling

- Mesons freeze out

- Heavy quarks and bosons freeze out

## Golden Rule 5: Equilibrium is boring!

- Weinberg, *Gravitation and Cosmology,* Wiley 1972

- Would you like to live in thermal equilibrium at 2.75oK?

**Relics**  *T>m *but* *>*H* (CMB photons, neutrinos, gravitons,dark matter? free quarks, magnetic monopoles...)
**Remnants** *T<m *but* *≠0 (baryons /B~1010, electrons, dark matter?)

- Example of e+e- annihilation transferring entropy to photons, after neutrinos have already decoupled (relics).

- That which survives:

## The QCD quark-hadron transition is typically ignored by cosmologists as uninteresting

**Weinberg (1972):** Considers Hagedorn-style limiting-temperature model, leads to *a*(*t*)t2/3|ln*t*|1/2; but concludes “...the present contents...depends only on the entropy per baryon....  In order to learn something about the behavior of the universe before the temperature dropped below 1012oK we need to look for fossils [relics]....”

**Kolb & Turner (1990):** “While we will not discuss the quark/hadron transition, the details and the nature (1st order, 2nd order, etc.) of this transition are of some cosmological interest, as local inhomogeneities in the baryon number density could possible affect...primordial nucleosythesis...”

## References

- Freedman & Turner, “Measuring and understanding the universe”, Rev Mod Phys 75, 1433 (2003)
- Kolb & Turner, *The Early Universe*, Westview (1990)
- Dodelson, *Modern Cosmology*, Academic Press (2003)
- Weinberg, *Gravitation and Cosmology*, Wiley (1972)
- Schutz, *A First Course in General Relativity*, Cambridge (1985)
- Misner, Thorne, Wheeler, *Gravitation*, W.H.Freeman (1973)
- Bartelmann & Schneider, “Weak Gravitational Lensing”, Physics Reports 340, 291-472 (2001)