Wonders of the Cosmos

1. How did the universe begin? ...Really with a Big Bang?

2. What does it mean that the universe is expanding?

3. How old is the universe?

4. How has the universe evolved?

5. What have we learned from the cosmic microwave background radiation?

7. What's the "dark energy"?

8. What does it mean for the universe to be "flat"?

9. What powered the Big Bang? Inflation?

10. Where do the structures in the universe come from?

Cosmic Microwave Background Polarization

1. How did the universe begin? Really with a Big Bang?

3 main pieces of conclusive evidence suggest that our universe began with an expansion of a very compact and hot concentration of energy (the "Big Bang"):

Since the 1920s astronomers have discovered that all the distant galaxies are going further and further from us and from each other. This means that the galaxies used to be closer and closer to each other as we go back in time... until at some long time ago all the matter in the universe was squeezed together. The universe back then must have been very dense and very hot.

This high temperature explains why there seems to have been nuclear fusion that created helium (by fusing protons and neutrons) even before the first stars formed. Calculations based on the hot beginning of the expanding universe conclude that about 1/4 of the matter must have been converted into helium at the time, and this fraction is exactly what the observations show to be the abundunce of helium before star formation.

If it was so hot everywhere in the beginning, the universe must still be filled with the radiation left over from such a hot beginning. This radiation was first detected in 1964 and has been studied in more and more detail since then.

Learn more about the Big Bang (still accessible to any reader).

2. What does it mean that the universe is expanding?

The "explosion" at the Big Bang does NOT mean that a clump of matter exploded and expanded in some pre-existing space. The space itself was probably created at the Big Bang and has been expanding in volume since then, just like the surface area of an inflating balloon. In this analogy, we must imagine that the 3-dimensional volume of space is represented by the surface of the balloon and it's expanding (stretching) with time, not into some pre-existing space, but along some other dimension orthogonal (perpendicular) to the 3 dimensions of space. The "membrane" or the "fabric" of space is stretching, but that doesn't mean that you or any other matter is also stretching in size (just as a bug or a dust particle on the balloon doesn't get stretched as you inflate the balloon!).

If you were a dust particle stuck on the surface of an inflating balloon, every other dust particles on the surface would appear to be going further and further away from you (even if you or any other particles are just stuck on the suface and not moving around... just "riding" on the expanding surface). The further the dust particle, the faster it would seem to go away from you. This is exactly what the astronomer Hubble discovered in the 1920s: all the distant galaxies appear to be going away from us, the more distant ones the faster. In fact, the receeding speed seems to be exactly proportional to the distance, which makes sense if space is expanding uniformly everywhere.

How fast is the universe expanding?

Since space seems to be expanding uniformly everywhere, we can quantify this expansion rate as the fractional stretching of space per unit time. Cosmologists have measured the current expansion rate to be 73 ppt (parts per trillion) per year , meaning that the distance between two locations in space is expanding by this tiny fraction every year. This is equivalent to 2 cm/s per light-year, meaning that the distance to a location currently one light-year away is expanding by 2 cm (about the width of your thumb) every second. In other words, the parts of space 1 light-year away appears to become further from us by 2 cm per second, and the parts of space 2 light-years away appears to become further at 4 cm per second, and so on. By measuring how fast the distant galaxies appear to go away from us, cosmologists have measured this expansion rate (called "the Hubble parameter" H) to within 5% precision: H = 71 km/s per million parsec (where "parsec" is a distance unit equal to about 3 light-years).

To get a feel for how much the universe is expanding,

At the distance of...speed
nearest star (4.3 ly)10 cm/s
Orion nebula (1500 ly)33 m/s
other side of galaxy (1,000 ly)2 km/s
Andromeda galaxy (2,500,000 ly)50 km/s
Virgo cluster (52,000,000 ly)1133 km/s

How has the universe expanded over time?

To see how the universe has expanded over time, let's consider a very simple model of a spherically expanding universe with a uniform density everywhere. If the initial expansion happens to be such that the total energy of any test mass happens to be 0, its kinetic energy will always balance its gravitational potential energy: , where Mr = (4/3)πr3ρ is the mass inside the radius r. With v=dr/dt ≡ (r dot), we can see how the expansion rate changes with time: , related to how the density ρ(t) changes as the universe expands.

Instead of talking about an arbitary distance scale r, we can define the scale factor a(t) as a ratio describing how much smaller this distance scale used to be compared to the present, as a result of the universe's expansion: a(t) ≡ r(t)/r(t0), where t0 is the present time. For example, a scale factor of 1/2 means that the universe used to be half the present size at that time. The above expansion rate is called "the Hubble parameter": , proportional to the square root of the density. So, as the universe expanded and became less dense, the expansion became slower and slower. The expansion rate is related to how the density varied over time.

For ordinary matter, density decreases as it spreads over increasing volume (ρ ∝ 1/V ∝ a-3). For radiation (photons), the stretching of space makes the wavelengths of the electromagnetic waves longer and longer, making each photon less and less energetic as the universe expands. not only does the number density of photons decrease with volume, but also the energy of the photons also What is the universe made of?

Expansion of the universe is a significant discovery because if you see an inflating balloon it must have begun inflating at some time in the past: it was the first time humans realized from observational evidence that our universe must have begun at a certain time in the past, instead of always existing the way we see it today...

3. How old is the universe?

By studying how the universe expanded over time, we have learned that the Big Bang happened 13.7±0.2 billion years ago. It's amazing that we know the age of the universe to within only 1.5%.

How do we know the age of the universe so precisely?

We can calculate how long it has been since the Big Bang by knowing how the expansion rate of the universe changed over time. Integrating this from the Beginning (when the scale was pretty much zero) to the present (when the scale factor is just 1), the cumulutive time since the Big Bang is: .

4. How has the universe evolved?

Based on calculations in radiation- and matter- dominated eras, I am compiling a tabulated History of Our Universe.

t z dH T kT r (g/cm3)
quantum gravity primordial black holes            
gravity decoupled gravitons 0.5x10-43 s 10 32 10-35 m 1032 K 1019 GeV > 1e94
Inflation began (GUT)   10-35 s 10 28 10-27 m 1028 K 1015 GeV 1095 erg
strong force decoupled   10-34 s     1027 K 1014 GeV  
Inflation ended q,q,e,e,n,n,t,t,m,m,W-,g 10-33 s 10 27 1 1027 K 1015 GeV  
quark era   10-23 s 10 21   1021 K 109 GeV 1.E+55
electroweak transition p,p,n,n,e,e,n,n,t,t,m,m,W- 10 ps = 10-11 s 10 15   1015.5 K 300 GeV 3.E+27
quarks -> hadrons p,n,e,e,n,n,t,t,m,m 1 ms = 10-6 s 10 12.5 .1 ly 1013 K 1 GeV 4.E+17
    0.01 ms 10 12 .3 ly 1012.5 K 272 MeV 3.E+15
antiprotons annihilate muons anihilate 0.1 ms 10 11.5 1 ly 1012 K 86 MeV 4.E+13
    1 ms 10 11 3 ly 1011.5 K 27 MeV 3.E+11
  p~n,e,e,n,n 0.01 s 10 10.5 10 ly 1011 K 8.6 MeV 4.E+09
  62%p,38%n,e,e,n,n 0.1 s 10 10 30 ly 1010.5 K 2.7 MeV 3.E+07
neutrinos decouple 76%p,24%n,e,e,n 1 s 10 9.5 100 ly 1010 K .86 MeV 400,000
ee annihilate 83%p,17%n,e,n 14 s 10 9 300 ly 109.5 K .27 MeV 3,000
D,He form, free n decay 86%p,14%n,e,n 3 min 10 8.5 1000 ly 109 K 86 keV 40
Nucleosynthesis begins p+n => D 3.75 min 10 8.5 1000 ly 109 K 80 keV  
  He 30 min 10 8 3000 ly 108.5 K 28 keV 0.3
CMB spectrum fixed p, e, He 1 month 10 6.5 100000 ly 107 K 500 eV 4x10-7
    3,000 y 100,000 300000 ly 300,000 K 26 eV 3x10-13
matter-radiation equality   75,000 y 3233 4x106 ly 9000 K 5.5 eV 1x10-17
Recombination p+e => H 200,000 y 1705   4650 K 0.4 eV 31 mp/mm3
Decoupling begins   320,000 y 1186   3235 K 0.28 eV 10 mp/mm3
Decoupling   379,000 y 1089 107 ly 2967 K 0.26 eV 8 mp/mm3
Decoupling ends   438,000 y 990   2700 K 0.23 eV 6 mp/mm3
Reionization 1st stars 180,000,000 y 20   57 K 5 meV 1Ms/(30ly)3
Earliest galaxy observed 1st galaxies 850,000,000 y 6.58   20 K 1.72 meV 2613 mp/m3
Solar System   9,100,000,000 y 0.44   3.9 K 0.34 meV 18 mp/m3
matter-Λ equality   9,500,000,000 y 0.39   3.8 K 0.33 meV 16 mp/m3
life on Earth   10,200,000,000 y 0.31   3.6 K 0.31 meV 13 mp/m3
Today   13,700,000,000 y 0 1010 ly 2.725 K 0.25 meV 6 mp/m3

6. What have we learned from the cosmic microwave background radiation?

By studying the cosmic microwave background (CMB) radiation, we learned that:

7. What's the "dark energy"?

We learn that the ordinary matter that makes up everything we see around us (including all the stars and galaxies) sums up to be only 4% of the total energy content of the universe. The rest is about 1/4 "dark matter" and 3/4 "dark energy". The Dark matter is exotic, but at least seems to have similar properties as ordinary matter except The dark energy is even more exotic: it seems to be responsible for repulsive anti-gravity effect that has made the universe expand at a greater and greater rate during the last 1/3 of its history! Unlike radiation, it seems to have a negative pressure. The expanson of the universe seems to be accelerating!

8. What does it mean that the universe is flat?

Most of us learned in school how big an object of a certain size should look like from a certain distance (its angular size). However, if our universe was reall like the surface of a balloon and was curved in, the same object at the same distance would look bigger (larger angular size).

9. What powered the Big Bang?

The question of what powered the Big Bang is so fundamental and partly philosophical. Having learned during the past century that the universe began with the Big Bang, humanity's big question for this century is: What caused this explosive expansion? People's curiosity is reflected in NASA's question "What powered the Big Bang?" The current best observations and theories suggest that the Big Bang began with a brief moment (~10-33 second) of accelerated expansion called "inflation". Inflation is a testable paradigm about the earliest event in the history of the universe. Inflation helps answer profound mysteries like How the structures in the universe originated, Why the universe appears to have no overall curvature, Why it appears so smooth on large scale, Why it seems so large. The best current theory is that the universe began with a explosive exponential expansion ("inflation") within 10-35 second of the Big Bang. Although this theory is mind-boggling, it is actually testable by observations. Inflation would have produced gravity wave, which is something predicted by the relativity theory but never yet detected. Detecting the gravity wave would be a significant achievement. Studying it would allow us to explore the unimaginable energy scale of 1016 GeV, where the grand unified theory is thought to be in effect. Flatness is intrinsic to inFLATion (...sorry).

10. Where do the structures in the universe come from?

Why does the universe have structures (like galaxies, galaxy clusters, superclusters, and so on) instead of being uniform? Without such inhomogeneity, stars would not have formed to make life possible.

This map of about 1/7 of the whole sky contains about 3 million galaxies.
Each small bright spot is a galaxy cluster; these group together to form superclusters.
Superclusters in turn are arranged like filaments surrounding darker voids.

The origin of this inhomogeneity seems to be the zero-point energy fluctuations in the vacuum, governed by the uncertainty principle of quantum mechanics. Quantum mechanical effects normally have little influence on large scales, but this was an exception. It was an exception thanks to "inflation", an exponential expansion of the universe that stretched the quantum fluctuations by many orders of magnitude.

Inflation was driven by the potential energy of what's called a "scalar field". The excitation of a scalar field is responsible for spin-0 particles like the Higgs boson. The scalar field particularly responsible for inflation is called "inflaton", which has a negative pressure. There were quantum fluctuations in the inflaton field. Right after the Big Bang, the total energy density of the universe was dominated by the inflaton potential energy. Thus, fluctuations in the inflaton field gave rise to fluctuations in the energy density.

Potential energy of the scalar field drove rapid inflation of the universe between the cosmic times t = 10-35s and t = 10-33s. During this short period , the causal horizon size (red line) did not have a chance to increase much at all, whereas the fabric of space and any comoving scales within it (blue line) expanded by tens of orders of magnitude. The expanding space stretched each Fourier modes of the quantum fluctuations past the causal horizon at the first purple point. After exiting the horizon (when a(t) = ck/H), the fluctuations no longer evolved quantum mechanically because their scales increased beyond causal connection. The fluctuations became frozen in to become super-horizon metric perturbations (became a classical quantity after leaving the horizon). Much later, the horizon (the Hubble radius) expanded enough (at the second purple point) for the perturbations to begin growing. These density perturbations, through gravitational effects, eventually resulted in the large-scale structures of the universe.

According to the observations of the cosmic microwave background (CMB) radiation, the perturbations seem to be ideally Gaussian (their Fourier modes are uncorrelated). This suggests that the perturbation has a quantum mechanical origin: each Fourier mode evolves independently of others like a quanta governed by the commutation relations. Also according to the CMB observations, the power spectrum seems to be ideally scale-invariant (the fluctuations per decade in wavenumber is constant). Physically this is because the horizon size c/H was nearly constant as the Fourier components exited the horizon during inflation. Soon, the spectral index n [defined as in P(k) ~ kn-1 ] could be measured with a precision of Δn ~ 0.01. The scale-invariance imply fractal-like structures, as might be observed in the large-scale structures of the universe. Finally, the observed distribution of galaxies and isotropy of the CMB suggest that the relative amplitude of the density perturbations should be 10-5 ~ 10-4.

How inflation produced scale-independent fluctuations


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