Size and age of the Universe

What is the size of the universe?

Behind this simple question hides extremely complex concepts, and perhaps even to redefine.
The universe or universum is "everything" in Latin. Issues concerning the "everything" are so many of a metaphysical order than scientist, then it is possible that there is no answer to this simple question. The universe contains by definition, everything that exists, matter with its space-time, so it has no "edge". The existence of an edge implies that beyond this boundary (edge), we would not be in the Universe. The universe is not in a space, it contains material which is in the vicinity of the material that space exists. The absolute space and absolute time independently of the rest, do not exist.
Thus, we do not know if the universe is finite or infinite, single or multiple, eternal or older. Many competing scientific theories awaiting validation or invalidation that would come of the observations. But then again how can one observe something infinite or eternal?
However, the theories on which we can rely is general relativity, quantum mechanics and quantum field theory, as many astronomical observations based on these theories, allow we to write a small part of the history of the universe, the most recent the one taking place before our eyes and that started there is 13.8 billion years.
We are used to read in most of the articles, that the universe is 13.8 billion old years, but we must understand that the author speaks of the observable universe or of the cosmological horizon or of the last scattering surface or of the Hubble radius. These notions of distances, close to each other, can be confused as the context, but they never give an age or size of the universe in its totality, precisely for the reasons already cited.
But the human spirit needs to represent things, so how can we still, get a reassuring picture of the universe as a whole?
At the time of the Big Bang, the primordial plasma deprived the photons of liberty, they were issued and immediately reabsorbed by matter who was at a temperature of several million degrees. But the universe continued to expand and cool down very quickly. Then 380,000 years after the Big Bang, the photons have managed to break the plasma, light escaped and the Universe, so opaque, has become "visible". This moment marks the last scattering surface that is the region of space from which was issued last photons, those who were not reabsorbed by matter. Thus the oldest electromagnetic radiation of the universe is out of this last scattering surface, the cosmic microwave background that is observed today throughout our universe.
Recall that the observable universe is the universe in which we see the stars and galaxies, and there is a current limit to the observation.

Because of the speed of light, which is limited to 300 000 km/s, our cosmological horizon is located on the edge of the observable universe, no signal can be received from the beyond, because of the nature finite speed of light. This cosmological horizon mask so we all objects beyond 13.8 billion light years. In other words the real universe is no longer connected to us because the farthest distance we can see is 13.8 billion light-years.
However, this distance is not the physical limit of the universe, what is the radius of the observable universe which itself occupies a volume finished in time and in space. Volume V = 4/3πR3 is already considerable.
An additional complication is added to the notion of size of the universe.
The universe is a dynamic physical object in motion, driven by gravity but also by what scientists call the cosmic inflation, i.e. the expansion of the space-time. The universe would have started as a great "explosion" that created of matter with the space and everything in it. The "everything" is now in permanent expansion rate ≈67.8 km/s/Mpc.
In this expansion of the universe, is not the galaxies are moving away from each other with respect to a spatial frame of reference, but that's spatial framework that inflates. This causes a number of effects including one that allows two very distant objects to have a recession velocity, relative to the other, much higher than the speed of light. These objects "would never see" and this, does not violate the principle that says that no object can not exceed the speed of light, since it is the space between the objects grows. Space-time is a object which we not know the nature.
In addition, if the light of the most distant objects which we observe, traveled for 13.8 billion years to reach us, it does not tell us what real distance are currently these objects because since this event, took place 13.8 billion years. It is reasonable to imagine that cosmic inflation has significantly moved away these objects carried by expansion. These objects could now be in the tens of billions of light-years from us.
It is therefore possible that the galaxies in our observable universe represents only a tiny fraction of the galaxies in the real Universe. What we can say is that the real world is certainly much greater than 13.8 billion light-years.
In summary, the universe has issued signals that could be received, it is the light of the objects we see today, as well as signals that can be received is the light of the objects we not seen yet, but we'll see because our horizon is 1 year away every year, and finally the universe also issued signals that will never be able reach us because they belong to inaccessible areas moving away faster that the speed of light.
In practice, the most distant signals we receive come from the cosmic microwave background.

Image: the visible universe can be cut into slices observable. Cutting a slice universe located 5 billion light years from us, we see all objects whose light has gone there are 5 Ga. By cutting a slice of universe located to 10 billion-years light, we see all objects whose light has gone there are 10 Ga. By cons in a slice universe located 15 billion light years away, we see nothing but black because all the objects light has gone there are 15 Ga are located behind the horizon and unfortunately for most of them, they will never be visible. The oldest light we see come from 13.8 Ga. In 1.2 Ga we will see those has gone there are 15 Ga. The visible universe grows a year, every year. However the universe continues to expand, and some objects will never be visible as they move away from us faster than the speed of light. Credit: astronoo.com

The real universe

The observable universe is a dynamic theoretical concept, it grows and each observer sees in time, enter the galaxies in his field of vision. However, for us earthlings, many galaxies remain forever beyond our observable universe.
Although the sensitivity of our instruments increases rapidly with technology, light from distant objects decreases. More galaxies that we see, will be far (15, 20, 30 billion light-years) over their light is redshifted so that they will demand an ever increasing sensitivity of instruments to detect. At one point their light will be only a noise, lower than the background noise of the universe, the cosmic microwave background (CMB).
The regions of space beyond our observable universe are the regions that were already outside our Hubble volume when their stars have emerged and began to emit light. The light from these areas will never reach us.
The vast majority of the universe is probably beyond the observable universe. Nobody knows exactly what its size.

The age of the observable universe is estimated at about 13.8 billion years, so the light from an object can not have traveled over 13.8 Ga. But since 13.8 Ga objects that have seen as they were at the time, moved away and are now significantly further (inflation).
But how far are currently the most distant objects, we receive the light?
Depending on the model universe that we adopt and space expansion rate (Hubble constant), we can deduce the distance.
In the framework of the standard model of cosmology the radius of the universe as a whole is about 45 billion light-years.

Video: Possible representation observable universes dynamics in the universe as a whole. The observable universe contains galaxies whose light has had time to reach Earth from the beginning of the cosmological expansion. The observable universe is a spherical volume centered on the observer. Each location in the universe has its own observable universe, which may or may not overlap with that Earth-centered. The universe is dynamic, all objects are in motion.
Video produced by: Rémi Monedi pour Astronoo

Is the observable universe really big?

Measure it in relation to our Galaxy, the Milky Way. A galaxy is a gravitational structure and therefore all objects inside its gravitational area belong to it.
We see that there is here a blur in the notion of size for a galaxy because its boundary ends where that of neighboring galaxies, it is the same for a star system for a cluster of galaxies, for superclusters and thus the entire universe.
Nevertheless give an approximate size of our galaxy, say 130,000 light-years in diameter.
The visible universe is: 13 x 10⁹ / 13 x 10⁴ = 10⁵ that is 100,000 times larger than the Milky Way. The ratio between the diameters of the visible universe and the Milky Way is not very large because 100,000 is a number on a human scale.
One can easily imagine the number 100,000we know that represent 100,000 people, it's a small town, a row of 100,000 people side by side represents only ≈100 km.

Table: equivalences between the distance units.

NB: A stationary traveler moves through time (it ages) and not in space but a traveler who moves, travel through space and time, but if it travel through space at the speed of light, it can not move in time (it does not age). A photon travels at the speed of light and for it time does not flow, the light does not age. The first photons in the Universe are still there.

Image: The first light of the observable universe seen by the Planck mission (March 2013). This picture shows the most distant signals we receive. False colors, red (hot regions) to blue (cold areas) represent the temperature fluctuations of the cosmic microwave background. Image Credit: ESA Planck collaboration.