An age of the Universe around 20 billion years

[yheyman]

Is it coincidental that the Hubble Sphere, in light years, is approximately the age of the universe computed as 1/Ho (13.7 billion years)?

If the recession speed exceeds the speed of light, the photon would never reach the observer, this is why there exists a horizon of the visible Universe (the Hubble sphere), beyond which light would never reach us. Historically the age of the Universe was computed from the loockback time between a redshift zero and infinity, which yields 1/Ho. Note that this measure gives the lookback time to the Hubble sphere because the redshift must converge towards infinity at the horizon of the visible Universe. Here is a reference showing the calculations with a De Sitter Universe (http://www.jrank.org/space/pages/2440/look-back-time.html). Another reference where the age of the Universe is computed with the look-back time between a redshift of zero and infinity: http://www.mpifr-bonn.mpg.de/staff/hvoss/DiplWeb/DiplWebap1.html . See A.36 et A.37.

Using another approach we can show that an apparently steady Hubble coefficient in the light travel distance framework is equivalent to a time-varying Hubble coefficient in the Euclidean framework of order two (i.e. Universe expanding at a steady acceleration pace). This approach gives an age of the Universe of about 20-25 billion years. This figure is compatible with the age of the Universe obtained from the datation of old stars. According to Chaboyer (1995) who analysed metal-rich and metal-poor globular clusters, the absolute age of the oldest globular clusters are found to lie in the range 11-21 Gyr. Bolte et al. (1995) estimated the age of the M92 globular cluster to be 15.8 Gyr. Th/Eu dating yields stellar ages of up to 18.9 Gyr (Truran et al., 2001). A paper describing this appoach is available online: http://fr.calameo.com/books/00014533338c183febd92

 

[bcrowell]

Is it coincidental that the Hubble Sphere, in light years, is approximately the age of the universe computed as 1/Ho (13.7 billion years)?

It's not a coincidence, it's just a trivial consequence of the definition of the Hubble constant. The Hubble constant is defined by fitting a slope Ho to a graph of v versus r, where r is the proper distance ( https://www.physicsforums.com/showthread.php?t=506990 ). That means we define H_o by using v=H_or, so if you plug in v=c you trivially get r=1/H_o.

If the recession speed exceeds the speed of light, the photon would never reach the observer, this is why there exists a horizon of the visible Universe (the Hubble sphere), beyond which light would never reach us.

No, this is incorrect: https://www.physicsforums.com/showthread.php?t=506987 The Hubble sphere that you're referring to is smaller than the observable universe.

 

[yheyman]

My argument why the redshift converge to infinity at the Hubble sphere is the following: The main hypothesis for the development of a model for the motion of the photon in an expanding space, is that the speed of light is frame-independent. Considering redshifts, this means that the relative movement of a light source does not change the speed of light emitted; however, it does add or subtract energy. This change in energy level changes the frequency of the source of light, and not the speed. When the recession speed reaches the speed of light, all energy transmitted to the observer is being removed, and the corresponding wavelength tends to infinity according to Planck law. The cosmic microwave background is a good example. It is very close to the Hubble sphere and its redshift is about 1000.

 

[bcrowell]

My argument why the redshift converge to infinity at the Hubble sphere is the following: The main hypothesis for the development of a model for the motion of the photon in an expanding space, is that the speed of light is frame-independent. Considering redshifts, this means that the relative movement of a light source does not change the speed of light emitted; however, it does add or subtract energy. This change in energy level changes the frequency of the source of light, and not the speed. When the recession speed reaches the speed of light, all energy transmitted to the observer is being removed, and the corresponding wavelength tends to infinity according to Planck law.

Your description would be correct according to special relativity, but special relativity isn't valid for cosmology.

Do you have background in general relativity at a mathematical level? If so, then you should be able to follow the calculation given in the FAQ entry linked to from #2, but please feel free to ask questions if there are steps you don't understand.

If not, then here is an article that attempts to explain the ideas without assuming any mathematical background in GR: http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf