What is the Question If Dark Energy is the Answer?

       In the good ol’ days, people thought the universe to be just up to the Milky Way. It was in 1922, that Edwin Hubble found that the universe extends beyond the Milky Way. Using the world's largest telescope - Hooker Telescope, he identified the Cephid Variables, a class of very luminous variable stars, in several spiral nebulae. There is a strong direct relationship between a Cephid Variable's luminosity and pulsation period. His observations proved conclusively that these nebulae were much too distant to be part of the Milky Way and were, in fact, entire galaxies outside our own.

On the other hand, Vesto Slipher observed the spectra of many spirals to be red-shifted. Thus it was concluded that they are going away from us.

Searching for a standard candle

In principle, the expansion history of the cosmos can be determined quite easily, using as a “standard candle” any distinguishable class of astronomical objects of known intrinsic brightness that can be identified over a wide distance range.Astronomers Saul Perlmutter and Brian Schmidt led international teams to study type Ia supernovae. The uniformity of the type Ia supernovae became striking when their spectra were studied in detail as they brightened and then faded.

Fig 1: Light Curves

Absolute magnitude, an inverse logarithmic measure of intrinsic brightness, is plotted against time (in the star’s rest frame) before and after peak brightness. The great majority (not all of them shown) fall neatly onto the yellow band. The figure emphasizes the relatively rare outliers whose peak brightness or duration differs noticeably from the norm. The nesting of the light curves suggests that one can deduce the intrinsic brightness of an outlier from its time scale. The brightest supernovae wax and wane more slowly than the faintest. Simply by stretching the time scales of individual light curves to fit the norm, and then scaling the brightness by an amount determined by the required time stretch, one gets all the type Ia light curves to match.

Thus, the type Ia Supernovae were chosen as excellent candidates for the ‘standard candle’

Hubble’s Law

Combining his own measurements of galaxy distances with Vesto Slipher's measurements of the red shifts associated with the galaxies, Hubble discovered a rough proportionality of the objects' distances with their red shifts.

Hubble Law states that:

(1) all objects observed in deep space are found to have a Doppler shift observable relative velocity to Earth, and to each other;

(2) that this Doppler-shift-measured velocity, of various galaxies receding from the Earth, is proportional to their distance from the Earth and all other interstellar bodies.

Although widely attributed to Edwin Hubble, the law was first derived from the General Relativity equations by Georges Lemaître in a 1927.

Thus we can easily conclude that the universe is expanding. The velocity of a body going away is directly proportional to its distance from us.

v ∝ x               ⇒     Universe is Accelerating

Oops! There’s a problem- Too much mass. Therefore, so much gravity is pulling things back. The universe should Decelerate rather than Accelerate!

HOW’S THIS POSSIBLE ? ? ? ? ? ? ? ? ? ? ?

Now to answer this HOW, came three models of the universe.
a)     Einstein applied the general theory of relativity to model the structure of the universe as a whole. He assumed that the universe was static, even though his first equations showed that in fact the cosmos was moving apart from some source. He thus, included the cosmological constant (an arbitrary constant which gives the energy density of empty space) as a term in his field equations for general relativity.
b)    De Sitter modelled the universe as spatially flat and neglects ordinary matter, so the dynamics of the universe are dominated by the cosmological constant, thus expanding forever.
c)     Friedman-Lemaitre gave three different models of the universe, all homogenous, expanding and containing matter.

Property	Model 1	Model 2	Model 3
Geometry	Surface of a sphere	Euclidean or flat	Surface of a saddle
Average Density	> Critical density	= Critical Density	< Critical Density
Size	Finite	Infinite	Infinite
Fate	Expand, then contract	Expand forever, with và0	Expand forever

Suppose we consider 3 points in space.

It has been observed that the sum of the angles inscribed by these three points is equal to 180^o. Thus it can be concluded that it is a flat space.

How Does The Universe Expand?

            Balloon Analogy

           

        Contrary to popular belief, it is not as if objects are moving farther apart at the edges of the universe. Rather the universe as a whole is expanding similar to a balloon being inflated.

UNIVERSE AS AN EXPANDING RUBBER SHEET

            Now consider 2 points A & B w.r.t to origin at O. As the rubber sheet (our Universe) expands, A & B go farther away from O. If A covers S₁ distance and B covers S₂ distance, we can say that S₁ is greater than S₂. So we see that Hubble’s Law is valid since distance of A from O is greater than that of B.

DARK ENERGY

The expansion of the universe has not been slowing down due to gravity, as everyone thought, it has been accelerating. No one expected this. No one knew how to explain it. But something was causing it. Eventually theorists came up with three sorts of explanations. Maybe it was a result of a long-discarded version of Einstein's theory of Gravity, one that contained what was called the "cosmological constant". Maybe there was some strange kind of energy-fluid that filled space. Maybe there is something wrong with Einstein's theory of gravity and a new theory could include some kind of field that would create this cosmic acceleration. Theorists still don't know what the correct explaiation is, but they have given the solution a name. It is called dark energy.

One explanation for dark energy is that it is a new kind of dynamical energy fluid or field, something that fills all of space but something whose effect on the expansion of the Universe is the opposite of that of matter and normal energy. But, if dark energy is the answer, we still don't know what it is like, what it interacts with, or why it exists.

So the mystery continues . . . .

References:
en.wikipedia.org/wiki/Dark_energy
http://science.nasa.gov/astrophysics/focus-areas/what-is-dark-energy/
hubblesite.org/hubble_discoveries/dark_energy/
imagine.gsfc.nasa.gov/docs/science/mysteries_l1/dark_energy.html