cosmology - On Distant Lanterns and Relative Speed

It is said, that by measuring distant sources, we can gather information about the past state of the universe. The further we measure, the faster things appear to recede, which brings me to my question, which has puzzled me literally for years.

If distant sources tell something about the past, would that not mean the universe is slowing down today? If not, how come?

Answer

If distant sources tell something about the past, would that not mean the universe is slowing down today? If not, how come?

If in the past they are accelerating they should accelerate now too. Since we cannot expect that galaxies will slow down and come towards us at some point.

I want to talk about two things.

I-Redshift Observation

The EM spectrum of the galaxies shows us that, galaxies are receding from us And in cosmology, redshift observation is independent of time. For instance, we are observing a galaxy that is 100Mpc away. Which means we are observing 30 million years ago in time and we see that the galaxy is redshifted. Since in time it's not possible to expect that the galaxy will slow down and coming back to us, I think we can safely assume that it will be redshifted forever. Because from the observational data it seems that the further they are their velocity is higher. By observing the spectrum we can determine the speed of the galaxies or light sources. And it seems that they are accelerating.

II- The Deceleration Parameter

We can measure the density of the matter, and dark energy by modeling our universe. By using Friedmann Equations and by calculating density parameters we can understand the evolution of the universe. Now I want to talk about the deceleration parameter.

The deceleration parameter can be written as,

$$q_0=1/2\Omega_{m,0}-\Omega_{\Lambda}+\Omega_{r,0}$$

If $q_0>0$ it means that the universe is decelerating and if $q_0<0$ the universe is accelerating. By setting the current values of $\Omega_{m,0}=0.30$, $\Omega_{\Lambda}=0.70$ and $\Omega_{r,0}\approx0$

$$q_0\approx-0.55$$

And our observations and data best fit shows us that $q$ is negative and close to $-0.55$

So by looking at the CMBR data and observing the supernovas, we can see that the universe is accelerating.

The universe is accelerating because the dark energy density will become dominant over time. Since the matter density drops like $a^{-3}$ however the dark energy is independent of $a$ (where $a$ is scale factor). And this is currently what is happening.