# Dark Energy / Accelerating universe: naive question

Folks, I have a naive question regarding the subject of dark energy and an accelerating universe:

From what I understand/read, it seems that the further we look out into deep space, the faster the objects are moving away from us - in all directions.

Is this basically what is meant by "accelerating universe"?

Because it seems that this situation is exactly what we should expect to see (according to Big Bang theory). The further out we peer into space, the further back in time we are "seeing", so wouldn't we expect to see higher rates of acceleration/expansion the further back in time we peer?

• Please clarify if this is your question: you are saying that if expansion is accelerating, it means that it was slower in the past, and faster at present. So distant galaxies should be expanding actually slower (at least from each other) that current nearby galaxies are expanding from us at this time. Is that your question? – diffeomorphism Jun 1 '14 at 6:39
• Check also this question/answer: physics.stackexchange.com/q/68493 – Anne O'Nyme Jun 1 '14 at 7:07
• @diffeomorphism: no, I'm saying the opposite. (I've yet to read the answers submitted below, so forgive my ignorance if this makes no sense: ) Distant galaxies should be expected to accelerate faster than nearer ones. – Oke Uwechue Jun 1 '14 at 19:22

We indeed expect that the universe expands on the basis of the Big Bang theory. Hence by looking at higher redshift, i.e. further in time, you should expect objects to recede faster. This is reflected in the linear relationshift that first measured by Hubble $$v=H_0D,$$ where $v$ is the recession speed, $D$ the distance to the object and $H_0$ the Hubble constant.

However from the observation of SNIa, that completes the plot for higher redshifts, the linear relationshift deviates! It suggest that the relation between velocity $v$ and the distance $D$ is no longer linear for higher $z$. The expansion is accelerating.

This acceleration depends on the geometry and energy content of the universe.

Take a look at the graph below: in a empty universe, as you noted, the recession velocities to deviate from the linear Hubble relation and it is indicated by a straight line. The measurement from the SN Ia however show that the universe deviates from this relation due to the presence of a repulsive energy component that result in an accelerated expansion of the universe to account for the observed recession velocities. This repulsive energy content is called dark energy and is still highly mysterious.

• Thnx. Nice concise answer. Thnx for the clarification. – Oke Uwechue Jun 1 '14 at 19:30

It's not as naive a question as you may think, and the answer is a lot more complicated than you may think.

When we're calculating how the universe expands we assume it's isotropic and homogeneous (this just means on average it's the same everywhere) and it has a scale factor that is normally written as $a(t)$. The scale factor tells us how much the universe has expanded. We set the scale factor to be 1 at the current time, so a scale factor of 2 means everything is twice as far away and a scale factor of 0.5 means everything is half as far away.

If our scale factor $a(t)$ was constant then the universe would be static i.e. distant galaxies would be stationary with respect to us. When we say the universe is expanding we mean that the scale factor $a(t)$ increases with time. To find out how $a(t)$ changes with time we have to solve Einstein's equations, and this is where things get messy because the solutions are complicated. If you're interested have a look at the Wipedia articles on the FLRW metric and the Friedmann equations. Without going into the details, we expect the scale factor to look something like:

Without dark energy the rate of increase of the scale factor gradually decreases with time because the mutual gravitational attraction of all the matter in the universe slows the expansion. With dark energy the expansion rate is always slightly higher, and at large times the expansion rate starts increasing again.

The original detection of dark energy was based on measuring the recession velocity of supernovae, and discovering that they matched the predictions from the red line not the black one.

A few additional notes: we believe the universe is flat, and this means that (in the absence of dark energy) the expansion rate shown by the black line would continue to slow but would never actually become zero. More precisely it would tend asymptotically to zero as time tends to infinity. An open universe means the expansion rate would tend to a value greater than zero, and a closed universe means the expansion rate would reach zero in finite time then become negative. A closed universe would start contracting again.

Also note that at time zero the scale factor is zero i.e. the distance between everything in the universe would be zero. This point is what we call the Big Bang. The name is misleading because it wasn't an explosion (as so often shown on popular science TV programmes). It's actually a singularity because if the spacing between everything is zero the density must be infinite. A singular point is where our equations break down because we can't do arithmetic with the number $\infty$.

• actually at factor 1 it cannot be 'current time' since other that means spatial distance zero, and there is no 0.5 that is closer than an object that is already at zero distance. I think you meant that at factor 1 we set some 'ruler gauge' distance – diffeomorphism Jun 1 '14 at 6:27
• @diffeomorphism: We define $a$ using $ds^2 = -dt^2 + a(t)d\Sigma^2$ ($\Sigma$ is the comoving distance coordinate). Defining $a(t)$ to be 1 at the current time is just choosing our distance scale so that right now the metric is $ds^2 = -dt^2 + d\Sigma^2$. It just sets the scale of the comoving coordinates. – John Rennie Jun 1 '14 at 6:33
• Thnx for the explanation about scale factors; I learnt a thing or two here. – Oke Uwechue Jun 1 '14 at 19:40

The Big Bang model accommodates many possibilities: steady state, the expansion is constant; accelerating expansion; decelerating expansion. In order for the value of the Hubble constant and the microwave background radiation to be consistent and describe the observable universe with a Big Bang formula, an accelerating expansion is the most economical hypotheis, due to the existence of a positive cosmological constant in the general relativity equations.

where lamda is larger than zero. The Big Bang model works with any lamda, and before dark energy was dreamed of one thought that the expansion in the past was the same as at present and lamda was assumed to be 0. Data indicates that there is continuous acceleration of the expansion, we are expanding now faster than at 380.000 years after the Big Bang. This is shown in the graphic of the history since the BB.

By bracketing the expansion history of the universe between today and when the universe was only approximately 380,000 years old, the astronomers were able to place limits on the nature of the dark energy that is causing the expansion to speed up. The measurement for the far, early universe is derived from fluctuations in the cosmic microwave background, as resolved by NASA's Wilkinson Microwave Anisotropy Probe, WMAP, in 2003.)

Their result is consistent with the simplest interpretation of dark energy: that it is mathematically equivalent to Albert Einstein's hypothesized cosmological constant, introduced a century ago to push on the fabric of space and prevent the universe from collapsing under the pull of gravity.