Short post number two! Surprise!
Have you ever wondered what is the cosmic energy of the Universe? Well, giving up certain General Relativity issues related to the notion of energy in local sense, there is indeed a global notion of energy for the Universe as a whole. I am not considering the Multiverse as an option today. Let me begin with the High School notion of mass and density, particularized for the Universe:
We are considering a closed spherical Universe with 3-d geometry, and then its volume reads
What is the radius of the Universe? Well, we could take it as the Hubble radius of the observable Universe, i.e.,
where . The density of the Universe can be written as the cosmological value of the vacuum/Hubble scale
so . Therefore, the formula for the mass of the Universe in terms of fundamental constants is
and the expression for the cosmic energy follows up from special relativity greatest formula as
Also, defining and , you get
Remark: the cosmological constant fixes not only the biggest mass as the Universal mass of the Universe (I am sorry for pedantic expression), but also fixes the smallest possible mass (the so-called Garidi mass in de Sitter group or de Sitter relativity):
And you can thus prove that
See you in other blog post!!!!!