Big UniverseReally, really big!

From Kant to Curtis: Are there other Galaxies? or just ours?

• Immanuel Kant, Swedenborg, Thomas Wright in 18th century - island universes

• Messier famous for his catalog called fuzzy unclear nebulae ‘nuisances’

• Earl of Rosse 1855, M51 is a spiral shape

• And yet at the beginning of the 20th century scientific consensus was nebulae were within our Milky Way

• 1914 Slipher velocity - 300 km/s velocity for Andromeda galaxy

• 1920: Curtis (other galaxies) - Shapley (no) debate, Curtis wins

Age of Universe13.8 billion years

Multiple methods, including Cosmic microwave background

radiation (CMB) (2.73 Kelvins from epoch 380,000

years)

Temperature fluctuations (very tiny)

Size = Age?

Is the size = age * c ?

13.8 billion light-years ?

No! But proportional

Speed of light, c300,000 kilometers per second

Sun 500 light-seconds

31.6 million seconds per year

Proxima Centauri 4.25 light-years Andromeda galaxy 2.5 million ly

Redshift, zDue to cosmological expansion

Not same as Doppler shift Depends on cosmological details

z ~ 0 nearest galaxies v ~ cz nearby

z = 1, wavelength doubled z = 11 oldest galaxy

z = 1100 CMB

Scale factor for sizeDefine a = 1 as present

a = 1/(1+z)

Relative volume ~ a^3 Density matter ~ 1/a^3

Horizon

Hubble's LawUniform expansion

v = H*d

H0 ~ 21 km/sec/ million ly (68 km/sec/Mpc)

Hubble sphere, radius

Rh = c/H 14.4 billion ly

Smaller than our 'proper' horizon

Light cone

Stuff we can now see from past

As we look farther in distance, we necessarily look back in time (higher redshift)

Proper distanceDistance accounting for the expansion of the universe

(Where that other galaxy would be now) During light travel time

R ~ 46 billion ly ~ 3.2 Rh Is our particle horizon

Local universe (Observable)

Volume ~ 34 Hubble spheres

Using 3.23^3

Event horizonThere is a limited region that is

Possible for us to ever see in future

It is shrinking in relative terms Since the expansion is accelerating

A trillion years from now we will only see Our own (super) galaxy

Implied UniverseCurvature parameter K

K = 0 flat

K > 0 closed

K < 0 open

|K| < 1/2 of 1%

Homogeneous, isotropic, non-rotating On largest scales > 500 million ly

Reasonable to assume that what is beyond Our observable universe is more of the same

Minimum UniverseSince K small, even if spherical

At least 216 Hubble spheres Volume > 6 x Observable 'proper' volume

InflationWhy is U isotropic?

CMB same everywhere

But regions were too far apart to have been in communication,

Even those only 2 degrees apart in the sky

InflationScalar field that decayed at ~ 10^-33 or 10^-32 sec. Or later.

Had property of negative pressure (like dark energy) Dumped energy into radiation, particles

Expanded the universe by at least ~ 100 trillion trillion (each dimension) Made it flat, isotropic, homogeneous

Scale from one billionth of a proton to size of a grapefruit

Inflation

Inflation is not about making the universe bigger so much as it is about making the starting kernel for our

universe much smaller!

It drives everything to be homogenous, isotropic, and for the space to be flat and for the mass-energy

density to be = 1 in units of critical density

(Critical density is the boundary between eventual collapse and continual expansion for a matter-only

universe)

At least a factor of 10^26, each dimension (nearly a trillion trillion trillion)

Inflationary Universe Alan Guth, 1979

Could be enormously larger Factor > 100 trillion trillion

Corresponds to 60 e-folds Expansion in each dimension Factor of e (2.71828) over and

over for 60 timesDocument inflation

Example Inflation Model• Depends on detailed inflation model

• Slow roll models

• e.g. SMASH model of Ballesteros et al. fits cosmic microwave background observations around 60 to 80 e-folds

• If 70 e-folds, universe is larger by 22,000 times in each of the 3 dimensions

• Volume larger by 10 trillion relative to our observable (particle horizon)

SMASH ModelFigure 1 from “Unifying inflation

with the axion, dark matter, baryogenesis and the seesaw

mechanism” G. Ballesteros et al. 2016 arxiv:1608.05414v1.

The colored regions are the Planck and other experiment

measurements. ns is the spectral index for density fluctuations and r is the tensor to scalar power ratio.

The nearly vertical lines labelled 50, 60, 70, 80 refer to the number of e-folds during inflation. Around

50 to 100 e-folds seem to be indicated by the data, with the

best fit around 70.

Eternal InflationMany inflation models (e.g.

'chaotic) suggest Eternal Inflation Eternal is forward in time (only?)

Many ‘pocket universes' are created: Multiverse

Each universe has its own physics

Multiverse as a whole is heading inexorably toward Infinity

Steinhardt, Viliken, Linde (‘chaotic inflation’)

Mickey Mouse

Summary: How Big?• Observable 34 Hubble spheres of 14 billion light-

year radius - Very Big

• Implied has 216 Hubble spheres - Super Big

• Inflationary models indicate could be trillions of times larger - Enormously Big

• All that is for one universe

• Then there's the Multiverse - Unfathomably Big

Learn More• darkmatterdarkenergy.com

• https://darkmatterdarkenergy.com/2015/12/06/eternal-inflation-and-the-multiverse/ - references to Guth and Linde review articles

• https://darkmatterdarkenergy.com/2016/10/31/axions-inflation-and-baryogenesis-its-a-smash-pi/

• 72beautifulgalaxies.com

• Dark Matter, Dark Energy, Dark Gravity (Amazon)

• 72 Beautiful Galaxies (iTunes, Amazon)