Mini review of where we’ve come from: CMB, SNe Ia, And Clusters tell us the universe is mostly dark energy and will expand forever. Plus that we need CDM Escape Equation and adiabatic expansion show how why we want to measure H,  m,  , plus how k, R, t, etc are all related. Didn’t derive how t depends on  m,  , etc, did argue by units that 1/H gives approximate age

Defined de-acceleration parameter = as  /2 for  = 0, matter dominated era, but a different physical concept. Showed static universe naturally requires dark energy. This gives a negative pressure for positive matter and k = +1. We can see from dU= -pdV this causes expansion From de-acceleration definition and that q =  m /2-   for measured values of   and  m we can see the universe is accelerating today

Big Bang pretty good BB was invented to explain several things We know we need more (CDM and  ) but There’s more: Inflation is needed ( maybe, you be the judge)

Classical BB was based on laboratory (confirmed) physics. Do next. We can use R(t) and t versus 1+z and T = T 0 (1+z), I never proved in detail: comes from radiation density (  r ) proportional to T 4 and  r goes as  r0 (R(t 0 )/R(t)) 4 Also use  =  o (R(t 0 )/R(t)) 3, for matter

First a review of what BB does explain And how We will put in detail! Logical progression from the escape equation math

The Big Bang “Explains” Why the sky is dark at night (Olber’s paradox). Why the Universe is old. Why the Universe is mainly hydrogen and helium. The existence of the CMB. That the Universe is expanding.

Olber’s Pardox If the Universe were infinite AND UNEVOLVING uniform in density of stars (or galaxies) then we would be “burned to crisp.” From simple geometry: The apparent brightness of objects falls off as one over the distance squared.

Olber’s Pardox, cont. Number of objects per unit volume in a shell at a distance goes as the distance squared. Exactly cancels the one over distance squared dimming of an individual star or galaxy. The sum of all the brightness adds to infinity if the Universe is static, un-evolving, uniform in density, and infinite.

Olber’s Pardox, cont. The BB defeats Olbers Paradox by Expanding universe Star formation had a beginning. Stars to evolve. Expansion is not necessary, however, only that stars live for a finite time is.

The BB says the Universe expands And we observe expansion Our models with the escape equation give expansion The observation of distant objects plus (time it takes light to travel implies a large age) The CMB (universe has been cooling) fits with expansion model and observations Model says the Universe is about 15 billion years old.

BB “Explains” Hydrogen & Helium so called BB Nucleo-synthesis The Big Bang starts the Universe off with a “hot” big bang! The initial universe was then hot and dense in the first 3 minutes (or so) to “burn” (fuse) hydrogen into helium. Expansion prevented heavier elements from being formed in any significant quantities.

Universe in first 3 minutes not too hot to break up He and not too cold or under dense to fuse H into He. Works if we start at 1 second with a “reasonably” high T (about 1 million K). We can estimate this T and density (  ) by extrapolating back from the “brick wall” know T, , 1+z of brick wall when becomes transparent from “simple” atomic physics

1+z = R(t 0 )/R(t) t = AR(t) 2 ; A = constant applies in radiation dominated era about 100,000 years before brick wall becomes transparent. know t, know T at brick wall transparent Extrapolate back to t = 1 second using T =T 0 (1+z) => at 1 second T ~ 1 million K, OK!

We also know the physics of radiation, matter etc. well enough to do this back to 1 second, at least. See the book, page 376, figure 13.7 Key “players” are protons, neutrons, electrons and neutrinos. Neutrons decay into protons, electrons, and neutrinos. the reverse can happen as long as the temperature and density are high enough.

=> density and temperature fall and a “significant” number of free neutrons have decayed, the fusion process halts. Half of all of free neutrons will decay in about 10.6 minutes Net effect is that after about 3 minutes process stops The higher the density, the higher the probability the neutrons and protons will join up and eventually make He.

An intermediate step join of proton to neutron = “deuterium” = D. The “simple” process is then p + n => D D + p => “light” He (with only 1 neutron) written 3 He. 3 He + 3 He => 4 He (ordinary, super stable helium) + stuff The denser the material, the more D is burned into He at faster rate than D is made.

Baryonic matter

=> Higher He/H tracks with lower D/H

The Net Result cont.: => A measure of the ratio of He/H and or D/H is the most direct method we have of determining  b. Therefore a major goal of some people is to go out and measure these quantities while others make sure the theory is correct. => A measure of the ratio of He/H and or D/H is the most direct method we have of determining  b.

How to win a Nobel prize in Physics: Find relic neutrinos from left over n decay n -> p + e + e Good luck, terribly difficult (why hasn’t been done!)

Neutrinos are so penetrating that IF we could detect them we could see back to about the 1st second Very exciting

The BB model then starts out hot and dense to explain He/H and D/H. The Universe expands and cools until the “brick wall” becomes transparent. => What is the brick wall made of and how to we predict transparency? The brick wall is mainly hydrogen gas but before it becomes transparent, the hydrogen is nearly totally ionized. Electrons and protons are free of each other in a ‘weird” state we call a “plasma.”

The CMB more details now: As the Universe expands, Both the hydrogen gas and the photon gas cool. If hot enough, the photons can separate electrons from protons that might have joined together to make ordinary hydrogen gas. And at the same time electrons are very efficient at absorbing or scattering photons. So the photons can’t travel far and we have “brick wall.”

The CMB more details now: Eventually, however, the gases (photons, electrons, and protons) cool so much that the photons don’t have enough energy to free “bound” (to protons) not enough to even to “excite” the atom by being absorbed. (Nature has “conspired” so that electrons can only circle the proton in certain specific orbits and if there isn’t enough energy for an “orbital transfer”, the photon can’t be absorbed be the atom.)

The CMB more details now: So gases cool down to point where hydrogen becomes “atomic” hydrogen and the gas “suddenly” becomes transparent. The photon gas then streams away on its own to reach us today as the CMB.

The BB doesn’t really say why started out hot or expanding but: The model is consistent with this much of the data. Using only laboratory physics We already know some problems: smoothness of CMB, CMB fine structure, SNe Ia, and clusters. But some say we need more => enter Inflation: