Accelerated Expansion of the Universe

Before 19th century, the idea of static universe filled with ordinary, visible matter and radiation was widely accepted among the astronomers. Even when the first relativistic model of the universe was developed by Einstein in 1917, he added an extra term to the field equations in order to stabilize universe and make it static. This term was called cosmological constant. Cosmological constant is the energy density of the vacuum that acts against gravitational attracting force. But when astronomical observations revealed the expansion of the universe, and astronomers hypothesized that our universe had begun by a Big Bang, Einstein came to this idea that there was not any need to the cosmological constant in his equations, because the expansion of the universe could be aftermath of the Big Bang, preventing gravitational attracting force to collapse our universe.

The expansion of our universe was expected to be decelerating, but today’s observations show that the expansion of our universe is accelerating, and in order to explain this accelerated expansion of the universe, cosmologists hypothesized the term ‘dark energy’ that is a fluid with negative pressure filled our universe, and it works against gravity and accelerates the expansion of today’s universe. There are different models of dark energy; the first one is again cosmological constant, because it exerts repulsive force; and also there are dynamic and evolving models of dark energy, e.g. scalar field.

On the other hand astronomers have found evidence that more than 85 percent of mass in our universe is invisible; they call it ‘dark matter’.

In addition to these two strange components, dark matter and dark energy, cosmologists have added a bizarre phenomenon to our universe in order to solve issues with Big Bang model of universe; this phenomenon is called inflation or exponential expansion of universe just after the Big Bang.
So according to the modern cosmology, in addition to the visible (ordinary) matter and radiation, our universe contains two other mysterious components, dark matter and dark energy; and our universe is not a static universe, it is dynamic, evolutionary universe; and it has gone into different phases through its expansion over time. Just after the Big Bang, when it was in planck scale (the smallest scale in the universe), universe expanded exponentially to an astronomical scale, that is called inflationary era. Inflation happened in a very brief period of time and when it was ended the age of our universe was about 10-33 to 10-32 seconds. After inflation, radiation appeared in the universe; then dark matter and ordinary  matter dominated our universe. So the rapid expansion of the universe due to the inflation, was slowed down by the positive pressure of these fluids ( radiation, dark matter, and ordinary matter). But again through the appearance of dark energy, the expansion of the universe began to speed up and today’s expansion of the universe is accelerating.

So the Big Bang model of the universe (with dark matter, dark energy, and inflation) is based on general theory of relativity and astronomical observations. The big issues with this model is the Big Bang itself, a singular point that gives birth to a Planck scale universe, and inflation where general theory of relativity meets quantum mechanics.


According to the inflationary cosmology, universe experiences an accelerated, exponential expansion in its early stages, at about  t∼ 10−35 s just after the Big Bang . This idea is introduced to solve the key problems of the ordinary Big Bang theory. The most important problems with the Big Bang theory without inflation are as follows:

Flatness problem:

Observations shows that total energy density of the universe today, is close to its today’s critical value  (or total density parameter today Ω0∼ 1); this means that our universe is flat. But according to the first Friedmann equation, any deviation of the mass/energy density from its critical value at a given time, causes deviations in curvature of the universe:  

This deviation increases with time for a universe started with a Big Bang and filled with matter or radiation. So the mass/energy density of the early universe must be very closer to its critical value, than it is today.

Inflation (or exponential expansion ) of the early universe, resolve this issue by driving mass/energy density to be extremely close to its critical value at the end of the inflation, while the universe grows rapidly from Planck scales to astronomical scales:

Where ti and tf are the times when inflation starts and ends, respectively; a(ti ) and a(tf ) are scale factors of the universe at the beginning and ending of the inflation. Hi is the Hubble parameter at the beginning of the inflation which is constant during the inflation. N is called number of e-foldings which is a large number.
An important point here is that inflation theory resolves the issue of positive deviations of mass/energy density; for negative deviations, dark matter is assumed to save the flat universe.

Horizon problem:

The universe is isotropic and homogeneous in large scale; it looks the same on opposite sides of the sky (opposite horizons); so there should have been communications between points with distances larger than particle horizon, in the past. Inflation of the early universe resolves this problem, too: The rapid exponential expansion of the universe from planck scales to the astronomical scales means that regions of the observable universe which are separated in the sky today, were much closer together before the inflation and they were in contact by light signals.
•Inflation theory resolves other problems too: It explains why we cannot observe any magnetic monopole in the sky; it explains the existence of galaxies and other structures and so the living beings in the universe, by producing small density fluctuations that can later in the history of the universe provide the seeds to cause matter to begin to clump together to form the galaxies and other observed structures.

Dark Energy

Dark energy is a hypothesized term given to a mysterious force that accelerates the expansion of the universe; it works like anti-gravity. While gravity is an attractive force which draws mass together in a very local level, dark energy is a repulsive force.

Before 1990s most astronomers believed that expansion of the universe which started by the Big Bang, was decelerating and in the future it may turn into contraction; but during 1990s the Hubble Space Telescope and ground-based telescopes allowed astronomers to see almost the edges of the universe; they detected many supernova explosions; they saw that the light coming from these stars had the same characteristics as the light coming from local supernovas, as they reached their maximum brightness and faded away; so there is no differences between distant supernovas and local ones; the only difference is their brightness that is a good hint to determine their distances; if you know how a supernova works you can determine its intrinsic brightness and by comparing it with its appearance brightness you can determine how far away it is. By doing so and measuring the red-shifts of supernovae in different distances astronomers found that how our universe was expanding in different times of its history; they concluded that universe has gone into different phases of expansion through its history. After the big bang our universe was slowing down that is expected because of gravity force; but then it begins to speed up and today’s expansion rate of universe is more than its value at any point in the past. What caused the universe to shift from expected decelerating phase to an unexpected accelerating phase? In order to explain this phenomenon cosmologists hypothesized dark energy that is acting against gravitational attraction and speeding up the expansion of the universe. But what is dark energy? Cosmologists have different ideas about it with different names: Cosmological Constant, Vacuum Energy, Vacuum Pressure, and  Scalar Field, for examples.

Negative Pressure

We live in a flat FRW (Fridmann-Robertson-Walker) universe, where the mass/energy density of its components (fluids) are constrained by first Friedmann’ equation:

In this equation ρi represents different fluids, and the linear combination of mass/energy densities in this equation is valid if the species (or fluids) evolve independently. The evolution of mass/energy density of each fluid for a adiabatically expanding universe is:

So the evolution of universe will be given by:

The linear combinations above are valid if different species evolve independently.

The acceleration equation (second Friedmann’s equation) of universe can be found from equations above, that is:

If the expansion of the universe is accelerating the second derivative of the scale factor over time, must be larger than zero. So the dominated fluid must have negative pressure to comply this relation:

                    ρi + 3pi < 0 ⇒ 1 + 3wi < 0 ⇒ wi <−1/3

Matter is pressure-less (wm= 0) and radiation with wr =1/3 has a positive pressure, so none of them could satisfy the relation above. So there is a need for another fluid with negative pressure to explain the inflation of the early universe and accelerating expansion of the today’s universe that is proved by the observations. This fluid is called dark energy. Cosmological constant (or vacuum energy density), is the first and simplest model of dark energy; but there are another models of dark energy, called quintessential models. Unlike the cosmological constant which has the same value everywhere in space for all the time, quintessence is a dynamical, evolving component of universe, with possibility to be spatially inhomogeneous.
 The vacuum energy is overabundant, causing the expansion of the universe to accelerate; it is completely defined by one number, its magnitude. The value of energy density of vacuum, based on the result of different theories, is 1050 − 10120 times larger than the magnitude allowed by cosmology.
There are different models of quintessential approach to negative pressure (dark energy and inflation), for instance  scalar field. There are also, alternatives to early inflation of universe. For instance varying speed of light scenario that assumes the speed of light in the very early universe was much greater than it is today; or the cyclic theory which assumes that the big bang is not the beginning of space and time.

%d bloggers like this: