Ch. 24 - The Early Universe

From t=0 to the CBR Era

The CBRUniverse hotter & denser in the past

For T high enough - ionized & opaque – blackbody

and

Currently T=2.726 K

z(opaque transparent)~1100 K

So T(opaque transparent)~3000 K

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Radiation & Matter Eras•# photons and nucleons roughly constant since decoupling (“recombination”) era with ratio of 109photons/nucleon, SO

•#density photons/nucleons also constant at 109photons/nucleon, BUT

•Energy of photons increases with decreasing R(t) HENCE,

•AT SOME TIME IN THE PAST, THE ENERGY DENSITY OF RADIATION EXCEEDED THAT OF MATTER

To see this, we write the energy density of radiation:

We can convert this to equivalent mass density:

Or, as a function of the scale factor:

Now do the same for the mass density:

These were equal when :

setting

In terms of the redshift z:

Note: some of the energy density of the universe will be in the form of neutrinos, which have already decoupled from baryonic matter and radiation. So the second relation above is more realistic.

So:

Note that this gives us a value close to those in Hinshaw et al. (2013, ApJS 208, 19) of 3184 to 3312 in their Table 4.

Particle Production in the Radiation Era

Examples: Tth~6x109 K for e-e+

Tth~1.5x1013K for p+p-

etc.

(Note, some people use 3/2 kT for the (mean) photon energy and/or 2mc2 for the combined energy of the particle-antiparticle pair.)

Where Does the Matter Come From?According to the Heisenberg Uncertainty Principle,

Particles are allowed to spontaneously appear & disappear as long as they do not remain longer than a small interval of time. For electrons:

~6x10-21sec

“Virtual Pairs” detected indirectly in 1947 Lamb Shift (also Casimir Effect)

The universe is filled with a sea of virtual particles just waiting to be made real!

e-

e+

Converting virtual pairs into real pairs: ADD ENERGYExample: γ-rays 2 views of the process:

In the Big Bang, gravity (or some other source) could provide the energy AND space expanded fast enough to prevent pairs from annihilating.

Net Effect:

Note: in thermal equilibrium, if T>Tth the reactions go at equal rates in both directions, so the number densities of photons and particles tend to be about equal (with corrections for spin states & exclusion principle). Also, at these T’s. velocities are relativistic, and matter behaves like radiation.

Early Particle Production through Big Bang Nucleosynthesis

•Initially, at the very “highest” temperatures, the universe was filled with radiation and those particle-antiparticle pairs whose Tth < T.

•As T dropped, particle-antiparticle pairs whose Tth~T “froze out”, but because there is no E-threshold for particle annihilation, they usually did, leaving photons.

•Eventually, the universe consisted of neutrons, protons, electrons, various neutrinos (and their antiparticles) and photons. Due to spontaneous symmetry breaking, there was an excess of matter over antimatter by 1 part in 109, so when annihilation was complete, photons outnumbered baryons by 109 to 1. (The WMAP results are

baryon/photon = 6.08-6.19x10-10 - not in Hinshaw 2013 but see table 17 of

Bennett et al. 2013, ApJS, 208, 20).

First p+,n (Tth~1013 K) freeze out

Then e- (Tth~1010 K) freeze out

As T drops, so does n/p+due to slightly larger mass of n

4He could exist, if it could be made via n+p⇒2H

But 2H easily destroyed - “deuterium bottleneck”

When t=3 min 2 sec, 2H forms, then quickly goes to 4He

All the while, n is decaying due to its half-life of ~ 10 min

When n/p+~1/7, 4He-production complete, giving initial 4He/1H ratio

Half a million years later, photons decouple from the matter…..

The First 3 Minutes (after the first few seconds)

Earlier History Depends on Forces of NatureUnification of the 4 (or 5) Forces of Nature:

Electricity & Magnetism (Electromagnetism)

Weak Nuclear Force

Strong Nuclear Force

Gravity

Electric & Magnetic ⇒Electromagnetic - E ~ 0 eV Maxwell 1865

Electromagnetic & Weak Electroweak - E ~ 100 GeV Weinberg, Salam, Glashow 1968

Electroweak & Strong goal of Grand Unified Theories (GUTs) ⇒ 1014 GeV?

EM+W+S+Gravity ⇒ goal of Theory of Everything (TOE or “Super-GUTs) ⇒ 1019 GeV?

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The Planck Era - the First 10-43 secFrom the Heisenberg Uncertainty Principle

For “relativistic” particles, mv ~ mc

So a particle of mass m is essentially localized over a spatial length

This can be thought of as the “size of a particle of mass m”

At what point do we seriously have to think about gravity???

The size of the event horizon of a black hole is:

If the size of a particle is comparable to its Schwarzschild Radius, then we MUST treat GRAVITY with QM:

To do so, we need a Theory of Quantum Gravity (i.e.TOE, essentially)

WE DO NOT HAVE THIS YET!

Without it, we cannot address what happened before tP

“Here there be dragons….”

Inflation (Alan Guth)How to deal with the flatness problem, horizon problem, and the lack of magnetic monopoles, etc.? The popular solution is “inflation”.

Suppose the early universe was a de Sitter type one with exponential expansion. Then:

•Distant regions could have been causally connected

•Rapid expansion would flatten space (like inflating a balloon)

•Surviving magnetic monopoles would have been spread very thinly.

Is such a scenario possible?

InterludeAlan Guth first approached inflation due to the problems with the production of monoloples during a phase transition in the early universe (Guth & Tye 1980, PhRvL, 44, 631). Such phase transitions had already been discussed by others (i.e. Linde 1979, Rept.Prog.Physics, 42, 389)

Guth published his paper on an inflationary model of expansion in January 1981 (Guth 1981, PhRvD, 23, 347)

A similar paper in many respects was published months earlier (October 1980) by Demosthenes Kazanas (1980, ApJ, 241, L59).

But Guth usually gets the credit (better campaigner, maybe).

Vacuum EnergyA positive vacuum energy acts physically like a “negative pressure” that promotes expansion (positive pressure supplements gravity). Essentially a positive Λ-term.

As the universe expanded, around t~10-34 sec, it may have found itself in a supercooled “false vacuum” of positive energy, trying to decay into a lower (zero) energy state. This false vacuum would provide a constant energy density (~1095 erg cm-3?) regardless of the value of R.

When we derived the acceleration of the “Newtonian” universe we got:

In the relativistic version, we would get:

Where P is the pressure term associated with the false vacuum and U is its energy density.

For a constant energy density (i.e. a cosmological constant), Pfv=-Ufv, so Ufv+3Pfv=-2Ufv and

whose solution is

which is an exponentially expanding universe. It is thought that the expansion caused the size of the universe to increase by a factor of about 1050-10100! This reduces the “horizon problem” by a similar factor, and the space density of magnetic monopoles even further!

Furthermore, expanding R by a factor of 1050 or more makes Ω

go to 1! In essence, no matter what k really is it acts as if k=0. This solves the flatness problem.

The Ultimate Free Lunch

•While the false vacuum powers the inflation, it is also decaying into a true vacuum, with the energy being converted to particles/radiation. The origin of matter!

•Note: Any Λ today may represent the tiny part of the false vacuum energy that was left after the decay.

•Also, if the decay was too fast, it would not allow inflation to work effectively.

Constraints on Particle Physics

Schramm & Turner (1998, RevModPhys, 70, 303)

Experimentally, as of 1998, Nν = 2.989 ± 0.024 (2σ) Schramm & Turner (1998)

2012: 2.9840 ± 0.0082 but see more recent papers....

Other Matters

Original inflation model by Alan Guth “stalls” and cannot produce what we see today.

New inflationary models (Andrei Linde & others). Some are “chaotic” or “frothy” models where there are multiple seeds of inflation. These may not necessarily be connected nor have the same laws of nature. Or they might be connected in some strange ways by wormholes. We just do not know.

Other Peculiarities of the Cosmos (one example):

The Strength of the Strong Force (Freeman Dyson):

If it were 5% weaker - there would be no nucleosynthesis

If it were 2% stronger - there would be too much nucleosynthesis

“God tinkered with the physics” (Fred Hoyle)

“Inflation makes it so” (a generalization of #1)

(Weak) Anthropic Principle - it’s a selection effect - works well if chaotic inflation is correct - we just inhabit one of the infinite number of universes where the physical constants have the right values. (But see Smolin 2004, astro-ph/040721 about why AP is unscientific, lacking the Popper-ian quality of falsifiability)

Cosmic Inventory “Table of Everything”

Bennett et al. 2013, ApJS, 208, 20)

The History of

Everything