How big is the Universe? How big is a large, expanding object? Spatial separation NOW, with the positions of both objects specified at the current time

How big is the Universe?

How big is a large, expanding object?

Spatial separation NOW, with the positions of both objects specified at the current time

This distance NOW is larger than the speed of light times the light travel time due to the increase of separations between objects as the Universe expands

Caused by things being farther apart now than they used to be


What is the distance NOW to the most distant thing we can see?

Suppose the Age of the Universe is 10 billion years In that time, light travels 10 billion light-years

But the distance has grown while the light traveled


A Good Rule of thumb

Universe is three times the speed of light times the age of the Universe.

What shape is the Universe?

General Relativity leads to geometry of spacetime

Einstein showed that mass caused space to curve Objects travelling in curved space have paths deflected, as if a

force had acted on them

Since Space is curved- 3 possibilities

Tied intimately to the amount of mass (and thus to the total strength of gravitation) in the Universe


Flat Surface

Zero curvature There is insufficient mass to cause the expansion of the Universe

to stop Has no bounds, and will expand forever An Open Universe

Euclidian Universe


Spherical Surface

Positive curvature More than enough mass to stop the

present expansion of the Universe Not infinite, but it has no end Expansion will eventually stop and

turn into a contraction Closed Universe


Saddle-Shaped Surface

Negative curvature Insufficient mass to cause the expansion of the Universe to stop Universe has no bounds , and will

expand forever Open Universe


Critical Density

Density Parameter (ratio of actual density of Universe to critical density that would just be required to cause the expansion to stop)

Universe is flat (contains just the amount of mass to close it) the density parameter is exactly 1

Universe is open with negative curvature the density parameter lies between 0 and 1

Universe is closed with positive curvature the density parameter

is greater than 1

Critical Density

Density Parameter gotten from various methods

Calculating the number of baryons created in the big bang Counting stars in galaxies Observing the dynamics of galaxies both near and far

With some rather large uncertainties, all methods point to the Universe being open (i.e. the density parameter is less than one)

And we must remember that they have likely not detected all of

the matter in the Universe yet

Critical Density

Here’s what the experts think...

Current theoretical prejudice is Universe is flat Exactly the amount of mass required to stop the expansion BOOMERANG, MAXIMA, and supernova data say expansion

of Universe is accelerating Universe is geometrically "flat”

Determining the value of the density parameter and thus the ultimate fate of the Universe remains one of the major unsolved problems in modern cosmology. The MAP and Planck missions will be able to measure the value definitively.

No Edge, No Center

That all depends on

Dark Matter and

Dark Energy!

What is the fate of the Universe?

Universe is full of "dark matter”–influences the evolution of the Universe gravitationally

–not seen directly by any of our present methods of observation Fritz Zwicky, 50 yrs. ago, realized clusters of galaxies consisted

predominantly of matter in some nonluminous form Search for dark matter has dominated cosmology for half a

century Precise measurements obtained over 20 years ago, when dark

matter first mapped in galaxy halos Only recently has the existence of dark matter over much larger

scales been confirmed

What is Dark Matter?

Astronomers add up masses and luminosities of stars near the Sun, there are about 3 solar masses for every 1 solar luminosity

Total mass of clusters of galaxies and compare that to the total luminosity of the clusters, they find about 300 solar masses for every solar luminosity

–Evidently most of the mass in the Universe is dark.

–If the Universe has the critical density then there are about 1000 solar masses for every solar luminosity, so an even greater fraction of the Universe is dark matter.


But Big Bang nucleosynthesis says density of ordinary matter (anything made from atoms) can be at most 10% of the critical density

–the majority of the Universe does not emit light, –does not scatter light –does not absorb light –is not even made out of atoms

–It can only be "seen" by its gravitational effects This dark matter can be neutrinos, if they have small masses

instead of being massless It can be more exotic particles like WIMPs (Weakly Interacting

Massive Particles), It could be primordial black holes.


First real surprise in outermost parts of galaxies, known as galaxy halos

–negligible luminosity

–occasional orbiting gas clouds

–allow one to measure rotation velocities and distances The rotation velocity is found not to decrease with increasing

distance from the galactic center This implies that the galaxy's cumulative mass must continue to

increase with the radial distance from the center of the galaxy, even though the light levels off

Evidence for Dark Matter

This rise appears to stop at about 50 kiloparsecs–halo seems to be truncated

We infer that the mass--to--luminosity ratio of the galaxy including its disk halo, is about five times larger than estimated for the luminous inner region, or equal to about 50

–This is the first solid, incontrovertible evidence for dark matter

The rotation velocities throughout many spiral galaxies have been measured, and all reveal dominance by dark matter

Galactic Halo Mass

What else could it be?

• MACHOs

(MAssive Compact

Halo Objects)

- baryonic dark

matter

- strong evidence

from gravitational

microlensing

MACHOs

MACHO in our galaxy's halo passes very close to line of sight from Earth to a distant star, the gravity of the otherwise invisible MACHO acts as a lens that bends the starlight

–star splits into multiple images that are separated by a milliarc-second, far too small to observe from the ground

–background star temporarily brightens as the MACHO moves across the line of sight in the course of its orbit around the Milky Way halo

To overcome the low probability of observing a microlensing event, the experiments were designed to monitor several million stars in the Large Magellanic Cloud

–stars observed hundreds of times over the course of a year

–revealed several events that had microlensing signatures

Microlensing

Microlensing

QuickTime™ and a decompressor

are needed to see this picture.

Microlensing

QuickTime™ and a decompressor

are needed to see this picture.

The event duration is time cross the Einstein ring radius–approximately equal to the geometric mean of the Schwarzschild radius of the MACHO and the distance to the MACHO

–for a MACHO half-way to the Large Magellanic Cloud, that distance is 55 kiloparsecs

The Einstein ring radius is about equal to 1 astronomical unit, or the Earth-Sun distance

–MACHOs must be smaller than the lens, so roughly the radius of a red giant star.

Event durations suggest typical mass around 0.1 solar masses; –at least a factor of 3 uncertainty in either direction.

Measuring Mass through Microlensing

The duration of the microlensing event directly measures the mass of the MACHO

Mass-to-light ratio can also be evaluated by studying galaxy pairs, groups, and clusters

–measure velocities and length scales

–determine total mass required to provide the necessary self-gravity to stop the system from flying apart

–inferred ratio of mass to luminosity is about 100M/L for galaxy pairs, which typically have separations of about 100 kiloparsecs

The mass-to-luminosity ratio increases to 300 for groups and clusters of galaxies over a length scale of about 1

megaparsec –over this scale, 95 percent of the measured mass is dark

Measuring Mass

ROSAT image –hot gas seen in X-rays would have dispersed if it were held in place ONLY by gravity of mass that is producing light in this image (the so-called "luminous mass")

The nature of this dark matter, and the associated "missing mass problem", is one of the fundamental cosmological issues

of modern astrophysics.


Superclusters: largest scale of mass density –aggregate of several clusters of galaxies, extending over about 10 megaparsecs

–our local supercluster is an extended distribution of galaxies centered on the Virgo cluster, some 10 to 20 megaparsecs distant

The mass between us and Virgo tends to decelerate the recession of our galaxy relative to Virgo, as expected according to Hubble's law, by about 10 percent.

–deviation from the uniform Hubble expansion can be mapped out for the galaxies throughout this region, and provides a measure of the mean density within the Virgo supercluster.

Over the extent of our local supercluster, about 20 megaparsecs–ratio of mass to luminosity equal to approximately 300.

More Ways to Measure Mass

Scientific discussions of dark matter typically consider two extremes

Hot Dark Matter Cold Dark Matter

Hot vs Cold

Composed of particles that have zero or near-zero mass (the neutrinos are a prime example)

The Special Theory of Relativity requires that massless particles move at the speed of light and that nearly massless particles move at nearly the speed of light

–must move at very high velocities

–form (by the kinetic theory of gases) very hot gases

Hot Dark Matter

Objects sufficiently massive that they move at sub-relativistic velocities

Form much colder (that is, slower moving) gases.

The difference between cold dark matter and hot dark matter is significant in the formation of structure

–high velocities of hot dark matter cause it to wipe out structure on small scales.

Cold Dark Matter

All theories and observations currently point to 90 – 99% of the mass of the Universe being in the form of dark matter

What type of particles can make up this material?

Current Beliefs on Dark Matter

The known neutrinoes have problems as candidates for dark matter because they are relativistic (hot dark matter)

–they erase fluctuations on small scales

–relativistic neutrinos could form large structures like superclusters, but would have trouble forming smaller structures like galaxies

These arguments might be at least partially invalidated if one of the types of neutrinos (the tau neutrino is the obvious candidate) is considerably more massive than the

electron or muon neutrino.


On smaller scales (galaxies and clusters of galaxies), dynamical estimates of mass indicate that 90% of the total mass is not seen

–implies that the mass density of the Universe is 10% of the closure density

–sub-luminous mass could be normal (baryonic) and be locked up in stellar remnants (white dwarfs, neutron stars, black holes) or just in very dim stars called "Brown Dwarfs”

–recent evidence for possible observation of one of these very dim Brown Dwarfs

The big bang nucleosynthesis puts the 10% limit on this idea–missing mass is more than 90%, it cannot be (entirely) baryonic


Large scale structure (e.g. the distribution of galaxies) very hard to understand

–smooth microwave background as measured by the COBE satellite To accommodate this, go to a mixed dark matter model in which

you have some hot dark matter (for the large scale) and some cold dark matter to act as a seed for galaxy formation

–None fit the data using the critical density Best models to date suggest mixed dark matter and an overall

cosmological mass density of 20-30% of closure –to retain inflation, with its inescapable prediction that the Universe must be flat, requires re-invoking Einstein's cosmological constant - meaning the Universe has vacuum energy (negative pressure) and is currently accelerating.

This makes our cosmology complicated, but much recent data is

pointing this way.


Neutrinos have mass

Supernova 1987a neutrino time of flight studies Solar Neutrino experiment

–not a mass that can cosmologically dominate. We cannot currently test for various supersymmetric particles

which would only be created at very high energy (e.g. the early Universe)

–many viable potential particles that are consistent with the Standard Model of particle physics, that would remain unnoticed in any

accelerator experiments.


Einstein's Law of General Relativity concluded the Universe must collapse under the relentless pull of gravity

–assumed the Universe to be static and unchanging

–added something he called the "cosmological constant" whose gravity is repulsive, though he had no idea if it was real

Shortly afterwards, astronomer Edwin Hubble says: Universe is expanding!

–assumed that the Universe slowing down under gravity and might even come to a halt

–leads Einstein later to say that his cosmological constant was the biggest blunder of his career

–now appears Einstein was on the right track after all!

Dark Energy

The source of the repulsive gravity may be something akin to Einstein's cosmological constant -- referred to as the energy of the "quantum vacuum," a subatomic netherworld pervading space -- or it may be something entirely new and unexpected.

What is “Dark Energy”?

We now have observations which suggest the expansion of the Universe is accelerating rather than slowing down. Whatever is driving this acceleration is unknown at present and is referred to as “dark energy”.

Evidence for an accelerating expansion comes from observations of the brightness of distant supernovae. We observe the redshift of a supernova which tells us by what factor the Universe has expanded since the supernova exploded. This factor is (1+z), where z is the redshift. But in order to determine the expected brightness of the supernova, we need to know its distance now. If the expansion of the Universe is accelerating, then the expansion was slower in the past, and thus the time required to expand by a given factor is longer, and the distance NOW is larger.

Universal Expansion

Yes, This IS Confusing...

If the expansion is decelerating, it was faster in the past and the distance NOW is smaller. Thus, for an accelerating expansion the supernovae at high redshifts will appear to be fainter than they would for a decelerating expansion because their current distances are larger.

Just believe me…we can tell by observations.

The Hubble discovery reinforces the startling idea that the Universe only recently began speeding up; it offers tantalizing observational evidence that gravity began slowing down the expansion of the Universe after the Big Bang, and only later did the repulsive force of dark energy win out over gravity's grip. The record-breaking supernova appears relatively bright, a consequence of the Universe slowing down in the past (when the supernova exploded) and accelerating only recently

Expansion is Accelerating!

HST Observation Image

This supernova appears to be one of a special class of explosions that allows astronomers to understand how the Universe's expansion has changed over time, much as the way a parent follows a child's growth spurts by marking a doorway. It shows us the Universe is behaving like a driver who slows down approaching a red stoplight and then hits the accelerator when the light turns green.

Long ago, when the light left this distant supernova, the Universe appears to have been slowing down due to the mutual tug of all the mass in the Universe. Billions of years later, when the light left more recent supernovae, the Universe had begun accelerating, stretching the expanse between galaxies and making objects in them appear dimmer.

What We See

Understanding Dark Energy will provide crucial clues in the quest to unify the forces and particles in the Universe.


Documents

How big is the Universe? How big is a large, expanding object? Spatial separation NOW, with the positions of both objects specified at the current time