The Origin of our Universe

The Origin of our Universe

!

!

!

Henry S.-H. Tye

戴⾃自海 !

Hong Kong University of Science and Technology

Cornell University

!

!

3 November, 2015

National Taiwan University




Our whole universe came from (absolutely) Nothing

13.8 billions years ago Nothing = 無

NOT!

Vacuum =

真空

四⽅方上下⽈曰宇 ,古往今来⽈曰宙。－ 《庄⼦子》

“The Universe’’ means “all of space-time’’.

The Universe ^宇宙

Newton’s apple tree Gravity

Gravitational force

引⼒力

.

重⼒力

1687

There are about 400 billion stars in our galaxy.

Our sun is a star close to the edge.

Hubble Space Telescope

A galaxy like ours

There are many billions

of galaxies in

our universe.

!

A convenient way to write very big and very small numbers

• Speed of light c = 299,792,458 meters per second

• c ~ 300,000,000 m/s = 3x10 ⁸ m/s

• ^{10 -3 =0.001}

• ^{10 -34 second}

Einstein’s Theory of Special Relativity (1905)

E=Mc ²

Planets move according to

Newton’s gravitational force law

Einstein asked :

!

Since there is nothing in between the earth and the sun except empty space, how does the earth know about the gravitational pull

of the sun ?

There is space !

Theory of General Relativity

(1915)

Space-time is an active player:

warps, curves, expands, shrinks,

…

.

Hubble(1929):

The Universe is Expanding

The further away a galaxy is, the faster it moves away from us.

The expansion of the Universe is similar to the expansion of a balloon: while objects are fixed at their comoving locations,

their relative distances are increasing in all directions.

http://www.astro.ucla.edu/~wright

Hubble(1929):

The Universe is Expanding

The further away a galaxy is, the faster it moves away from us.

The expansion of the Universe is similar to the expansion of a balloon: while objects are fixed at their comoving locations,

their relative distances are increasing in all directions.

http://www.astro.ucla.edu/~wright

What is in Our Universe today ?

Are all we see in the sky all there are ?

Atoms, molecules, electrons, photons, ....

Matter in Our Universe

85%

Ordinary matter = atoms and molecules

15%

Other matter ?

Contents in Our Universe

4%

23%

73%

Dark energy Dark matter

Ordinary matter

very mysterious

mysterious

* * *

*

* *

matter * density goes down, but not the dark energy (blueness) density.

While the objects move away from each other,

What is the difference between dark matter and dark energy ?

How is it possible that the volume grows while the

energy density stays constant ?

As universe expands :

Our future universe will be space filled with only dark energy.

Today

Past Future

Blue : dark energy Red : dark matter

Yellow : ordinary matter

[Lesson 5]

It is possible because General Relativity tells us that dark energy has negative pressure.

It also tells us that the expansion becomes “exponential”.

The dark energy is the vacuum energy, most likely the cosmological constant that Einstein introduced and abandoned almost a century ago.

So the expansion of the universe is accelerating.

This is what Perlmutter, Schmidt and Riess and their teams observed in 1998.

They shared the Nobel prize in 2011.

Big Bang Theory

Going back in time,

the universe was smaller and hotter.

Today, it should have a temperature of about

3K= -270 ⁰ C.

Our universe is expanding and cooling today

Note : 0K= -273 ⁰ C is absolute zero.

Prediction :

⼤大爆炸理论

A little quantum physics

• Wave-particle duality : waves behave like particles and particles behaves like waves.

• Example : Light or microwaves are collections of photons.

• An electron behaves like a wave, so it

fluctuates, say, over a barrier, or around a

proton to form a hydrogen atom.

Planck’s Black Body Radiation Spectrum

microwave

In 1964, Penzias and Wilson measured the intensity of microwave at 7.35cm.

They received the Nobel prize in 1978.

Today, the universe should have a temperature of about 3K = -270

⁰

C.

This means we are living in a “thermal” bath of cosmic

microwave radiation.

T=2.7260 ⁰ K Mather etc. 1992 Nobel prize in

2006.

The age of our universe is 13.798 billion years.

7.35cm

COBE

In early Universe

It is believed that the dark energy is much bigger.

H ² = Λ + k

a ² + ρ ^m

a ³ + ρ ^r a ⁴

→ H ² = ( ˙a

a ) ² ≃ Λ

→ a(t) ≃ e ^{H t}

Λ → ρ

After a while,

Thursday, 8 December, 11

Going back in time, the size of our universe becomes smaller and smaller, eventually becomes a point.

!

We learned that the universe would have been a point about 13.8 billions years ago.

!

Squeezing everything into a point is not possible, but a very small region is possible.

!

When squeezed to a very small region, the universe was very hot, and the description becomes very simple.

!

The history of our universe can be traced all the way back to 10

^-37

second old.

The inflationary universe _{暴涨宇宙论}

• Start with a single point of size 10 ^-30 m, with total energy much less than that of a single electron.

• This point is filled with a much much larger dark energy density than today’s.

• This point grows “exponentially” in the inflationary phase, with the dark energy density staying more or less constant.

• At the end of inflation, at about 10 ^-35 second, almost all of the dark energy converts to radiation and particles. This

leads to the hot big bang.

How did the hot big bang start ?

•

1, 2, 3, 4, 5, 6, . . . .

•

1, 2, 4, 8, 16, 32, 64, . . . .

• All matter comes from inflation (converted from dark energy).

• Space is created by inflation.

^{無極⽣生太極}

Everything comes from nothing

!

無中生有

Ultimate free lunch

The Inflationary Universe Scenario says :

Everything (all matter as well as space) comes from nothing !

What About Energy Conservation ?

Energy is conserved only if the total energy of

our whole universe is exactly zero today.

•

Recall the electric field E. Energy is stored in the electric field : energy ~ +E

²

/2. The 2 (oppositely charged) plates are attracted towards each other.

•

For gravitational field g, the 2 (same) massive plates are attracted toward each other, so energy is taken away from g: energy ~ - g

²

/2.

•

So gravitational field g yields negative energy.

•

Matter + gravitational field energy = matter - g

²

/2 = 0

27 28

• Recall electric field E. Energy is stored in the electric field. Energy density ~ E ² /2.

• For gravitational fields g, the energy stored is negative. So

E

Capacitor

Energy ~ 0

Energy = matter + its gravitational field energy mc ² - g ² /2 ~ 0

+ -

+ +

-

Energy can be conserved ! -

Negative energy stored in the gravitational field.

+ _

E ² /2 -g ² /2 -g ² /2

M M

So the total energy of our universe is exactly ZERO.

Dark energy comes from the inflaton potential

V( )!

! Slow!Roll Region

Reheating Oscillations,

Damped Quantum Fluctuations

The quantum fluctuation resulted in density and temperature fluctuations.

Thursday, 8 December, 11

What started the hot big bang ?

Alan Guth

•

The magnetic monopole problem

•

The flatness problem

•

The horizon (or homogeneity) problem

•

All matter comes from inflation (converted from dark energy).

•

Space was created by inflation.

Ultimate free lunch ^{無極⽣生太極} ?

The Inflationary Universe Scenario says :

It solves

The inflationary universe _{暴涨宇宙论}

• Start with a single point of size 10 ^-30 m, with total energy much less than that of a single electron.

• This point could have been a single quantum fluctuation out of absolute Nothing.

• This point grows exponentially in the inflationary phase, to 10 ^-35 second.

• At the end of inflation, almost all of the dark energy

converts to radiation and matter, starting the hot big bang.

• The size of an apple then expanded to our observable universe today.

• Our observable universe is only a tiny fraction (of size

10 ^-20 ) of the whole universe from the original point.

The general theoretical picture of the

inflationary universe was completed by 1983.

•

Many cosmologists embrace it. Many hate it. Overtime, more and more accept it.

•

E.g., Steve Hawking considers the evidence for inflation to be overwhelming.

•

Some very vocal objections to it, e.g., Roger Penrose believes inflation is totally unlikely.

•

One of the founding leaders of inflation, Paul Steinhardt, became its sharpest critic in recent years.

⾛走⽕火⼊入魔

Quantum fluctuations during inflation led to fluctuations in density and temperature.

This fluctuation will eventually lead to star and galaxy formation.

The temperature fluctuations was first observed by the COBE satellite in 1992.

The general theoretical picture was essentially completed by 1983.

2.7260 ⁰ K to 2.7261 ⁰ K

1993

2005 2013

Planck Collaboration: The Planck mission

Fig. 14. The SMICA CMB map (with 3 % of the sky replaced by a constrained Gaussian realization).

Fig. 15. Spatial distribution of the noise RMS on a color scale of 25 µK for the SMICA CMB map. It has been estimated from the noise map obtained by running SMICA through the half-ring maps and taking the half-di↵erence. The average noise RMS is 17 µK. SMICA does not produce CMB values in the blanked pixels. They are replaced by a con- strained Gaussian realization.

for bandpowers at ` < 50, using the cleanest 87 % of the sky. We supplement this ‘low-`’ temperature likelihood with the pixel- based polarization likelihood at large-scales (` < 23) from the WMAP 9-year data release (Bennett et al. 2012). These need to be corrected for the dust contamination, for which we use the WMAP procedure. However, we have checked that switching to a correction based on the 353 GHz Planck polarization data, the parameters extracted from the likelihood are changed by less than 1 .

At smaller scales, 50 < ` < 2500, we compute the power spectra of the multi-frequency Planck temperature maps, and their associated covariance matrices, using the 100, 143, and

Fig. 16. Angular spectra for the SMICA CMB products, evaluated over the confidence mask, and after removing the beam window function:

spectrum of the CMB map (dark blue), spectrum of the noise in that map from the half-rings (magenta), their di↵erence (grey) and a binned version of it (red).

217 GHz channels, and cross-spectra between these channels¹¹. Given the limited frequency range used in this part of the analy- sis, the Galaxy is more conservatively masked to avoid contam- ination by Galactic dust, retaining 58 % of the sky at 100 GHz, and 37 % at 143 and 217 GHz.

11 interband calibration uncertainties have been estimated by compar- ing directly the cross spectra and found to be within 2.4 and 3.4⇥10 ³ respectively for 100 and 217 GHz with respect to 143 GHz

25

COBE 1992

Planck 2013

George Smoot,

Nobel 2006

Planck Collaboration: The Planck mission

2 10 50

0 1000 2000 3000 4000 5000 6000

D [µ K 2 ]

90 18

500 1000 1500 2000 2500

Multipole moment,

1 0.2 0.1 0.07

Angular scale

Fig. 19. The temperature angular power spectrum of the primary CMB from Planck, showing a precise measurement of seven acoustic peaks, that are well fit by a simple six-parameter ⇤CDM theoretical model (the model plotted is the one labelled [Planck+WP+highL] in Planck Collaboration XVI (2013)). The shaded area around the best-fit curve represents cosmic variance, including the sky cut used. The error bars on individual points also include cosmic variance. The horizontal axis is logarithmic up to ` = 50, and linear beyond. The vertical scale is `(` + 1)Cl/2⇡. The measured spectrum shown here is exactly the same as the one shown in Fig. 1 of Planck Collaboration XVI (2013), but it has been rebinned to show better the low-` region.

2 10 50

0 1000 2000 3000 4000 5000 6000

D[µK2 ]

90 18

500 1000 1500 2000

Multipole moment,

1 0.2 0.1

Angular scale

Fig. 20. The temperature angular power spectrum of the CMB, esti- mated from the SMICA Planck map. The model plotted is the one la- belled [Planck+WP+highL] in Planck Collaboration XVI (2013). The shaded area around the best-fit curve represents cosmic variance, in- cluding the sky cut used. The error bars on individual points do not in- clude cosmic variance. The horizontal axis is logarithmic up to ` = 50, and linear beyond. The vertical scale is `(` + 1)Cl/2⇡. The binning scheme is the same as in Fig. 19.

8.1.1. Main catalogue

The Planck Catalogue of Compact Sources (PCCS, Planck Collaboration XXVIII (2013)) is a list of compact sources de-

tected by Planck over the entire sky, and which therefore con- tains both Galactic and extragalactic objects. No polarization in- formation is provided for the sources at this time. The PCCS di↵ers from the ERCSC in its extraction philosophy: more e↵ort has been made on the completeness of the catalogue, without re- ducing notably the reliability of the detected sources, whereas the ERCSC was built in the spirit of releasing a reliable catalog suitable for quick follow-up (in particular with the short-lived Herschel telescope). The greater amount of data, di↵erent selec- tion process and the improvements in the calibration and map- making processing (references) help the PCCS to improve the performance (in depth and numbers) with respect to the previ- ous ERCSC.

The sources were extracted from the 2013 Planck frequency maps (Sect. 6), which include data acquired over more than two sky coverages. This implies that the flux densities of most of the sources are an average of three or more di↵erent observa- tions over a period of 15.5 months. The Mexican Hat Wavelet algorithm (L´opez-Caniego et al. 2006) has been selected as the baseline method for the production of the PCCS. However, one additional methods, MTXF (Gonz´alez-Nuevo et al. 2006) was implemented in order to support the validation and characteriza- tion of the PCCS.

The source selection for the PCCS is made on the basis of Signal-to-Noise Ratio (SNR). However, the properties of the background in the Planck maps vary substantially depending on frequency and part of the sky. Up to 217 GHz, the CMB is the

27

PLANCK 2013

Inflationary Universe also predicts :

Inflation predicts quantum fluctuation that creates a density fluctuation which seeds the galaxy formation. This leads to a temperature fluctuation that can be measured and tested.

36

String Theory Brane World

Multiverse ~ multiple universes We live in a 3-brane, with 3 spatial dimensions

Extra dimensions

Brane Inflation

In string theory:

!

Strings Cosmic strings

• Due to warped geometry, cosmic strings can have different tensions and spectra.

• Small tension cosmic strings decay slowly, so they can cluster, just like dark matter.

• They can micro-lens stars, which may be

detected in the coming years.

A typical microlensing signal of a star by a moving cosmic string

Tim e Flux

Figure 8: A Schematic Pattern. Digital microlensing doubles the flux over the time period that source, loop and observer are aligned within the deficit angle created by the string (red line). The repetition interval for lensing a particular source is the loop oscillation timescale (green line) and ∼ 10

³

repetitions in total occur (yellow line). The timescale for a new source to be lensed by the original loop (or the original source by a new loop) is much longer (black line).

microlensing). Detection efficiency for digital lensing depends upon the string ten- sion, the magnitude and angular size of the background stars and the time sampling of the observations. Estimates can be made for any experiment which repeatedly measures the flux of stellar sources.

The first string microlensing search [143] was recently completed using photo- metric data from space-based missions CoRoT

¹

[144] and RXTE

²

[145]. The method- ology was potentially capable of detecting strings with tensions 10

⁻¹⁶

< Gµ < 10

⁻¹¹

though the expected number of detections was limited by the available lines of sight studied in the course of the missions. In principle, any photometry experiment that makes repeated flux measurements of an intrinsically stable astronomical source has the power to limit a combination of the number density of loops and string tension.

Previous estimates for the rate of detections for GAIA [130] and LSST [146] were encouraging. Now, detailed calculations for WFIRST are available.

8.2 WFIRST Microlensing Rates [2]

The Wide-Field Infrared Survey Telescope

³

(WFIRST) is a NASA space observatory

1

The 2006 mission was developed and operated by the CNES, with the contribution of Austria, Belgium, Brazil, ESA (RSSD and Science Program), Germany, and Spain.

2

The 1995 mission was developed and operated by NASA.

3

http://wfirst.gsfc.nasa.gov/

– 36 –

Many ways to study the universe

and many ground based telescopes and other detectors as well

as satellites

B-mode

E-mode Fluctuation of

space-time

Polarization of photons

The red and blue shading shows the degree of clockwise and anti- clockwise twisting of this B-mode pattern.

South Pole

Why the B-mode polarization is important ?

• Inflation predicts the existence B-mode polarization with a well determined spectrum.

• “Alternative to inflation” models predict none.

• It comes from the quantum fluctuation of space-time.

So this will confirm that space-time is also quantized.

Other experiments, PLANCK, ACT, PolarBeaR, SPT, SPIDER, QUEIT, Clover, EBEX, QUaD..., will have a lot of data coming soon, so we should

wait for confirmation and more detail.

THANKS

It has been very exciting in cosmology in the past century. More exciting discoveries are

expected in the coming years.