Fluctuations as Cosmic Seeds

[Dubbelosix]

I have noted in the past, if a vacuum is not truly Newtonian and it does indeed expand (new space appearing) then there will be new fluctuations added to spacetime as well. Fluctuations can also act as the seeds of the universe to explain a primordial gravitational clumping, giving rise to the large scale structure, albeit, this uses the notion of some rapid expansion phase. We too have the same phase characterized by the centrifugal force the universe experienced when it was very young from a furiously fast spin. In fact, Wald and Harren have shown it is possible to retrieve the cosmic seeds without inflation.

 

In their model the inhomogeneities of the universe arises while in the radiation phase – their model also requires that all fluctuation modes would have been in their ground state and that the fluctuations are “born” in the ground state at an appropriate time which is early enough so that their physical length is very small compared to the Hubble radius, in which case, they can “freeze out” when these two lengths become equal.

 

It has been noted in literature that there is clearly a need for some process that would be responsible for the so called “birth” of the fluctuations. I have a mechanism in my own model, which we will discuss at the end - today I want to show how you can talk about fluctuations within the context of expanding space, which is required within a sensible approach to unify the cosmic seeds with the dynamics of spacetime. It is possible to construct a form of the Friedmann equation with what is called the Sakharov fluctuation term, which is the modes of the zero point fluctuations

 

 

[math]m\dot{R}^2 + 2\hbar c R \int k dk = \frac{8 \pi GmR^2}{3}\rho[/math]

 

 

When [math]R \approx 0[/math](but not pointlike) then the fluctuations are in their ground state. Though inflation is not required to explain the cosmic seeding, there are alternatives themselves to cosmic inflation such as one particular subject I have investigated with a passion; rotation can mimic dark energy perfectly which is thought to explain the expansion and perhaps even acceleration (if such a thing exists). It is possible to expand the Langrangian of the zero point modes on the background spacetime curvatuture in a power series

 

 

[math]\mathcal{L} = \hbar c R \int k dk... + \hbar c R^n \int \frac{dk}{k^{n-1}} + C[/math]

 

 

Where C is a renormalizing constant which is set to zero for flat space. It had been believed at one point that the forth power over the momenta of the particles would be zero

 

 

[math]\hbar c \int k dk^3 = 0[/math]

 

 

But interesting things happen in the curvature of spacetime, such a condition doesn't need to hold.The anisotropies may arise in an interesting way when I refer back to equations I investigated in the rotating model. An equation of state with thermodynamic definition can be given as:

 

[math]T k_B \dot{S} = \frac{\dot{\rho}}{n} + \frac{\rho + P}{n}\frac{\dot{T}}{T}[/math]

 

The last term [math]\frac{\dot{T}}{T}[/math] calculates the temperature variations that arise, even in the presence of the cosmic seed and we can therefore change the effective density coefficient in the following way:

 

[math]2m\dot{R}\ddot{R} + 2\hbar c R \int k \dot{k} = \frac{8 \pi GmR^2}{3}(\rho + \frac{3P}{c^2})\frac{\dot{T}}{T}[/math]

 

 

Simplifying a bit and rearranging

 

 

[math]\frac{\dot{R}}{R}\frac{\ddot{R}}{R} + \frac{\hbar c}{mR} \int k \dot{k} = \frac{8 \pi G}{6}(\rho + \frac{3P}{c^2})\frac{\dot{T}}{T}[/math]

 

 

 

 

 

 

ref http://sci-hub.bz/10.1007/BF00637768

 

Also, read Sivaram and Arun

Edited September 21, 2017 by Dubbelosix

[Mordred]

Lol I can see your topics are all related, gonna make life interesting to correlate the threads together. Lambda is your focal point it appears in your recent threads.

Not sure why you needed the first paragraph, of course fluctuations can give rise to particle production, any field anistropies can do so under the right conditions, there is countless examples such as Hawking, Hawking Berkenstein, Parker (Cosmology not xray associated) radiation. 

 Even quasi particles such as the inflation being another example.

I asked on one of your other threads if your familiar with S-matrix, and how the creation and annihilation operators correlate to particle production. In that field anistropies gives rise to particle number density.

What is wrong with the use of those creation/annihilation opetators under QFT to the above?

( your knowledgable enough, that I don't have to waste time clearing misconceptions). The math you post is accurately done, so my time is better spent asking pertinent questions to see how you address them. (Hopefully in doing so aiding your direction of possible research)

Edited September 23, 2017 by Mordred

[Dubbelosix]

There is nothing wrong, in fact, I have already applied the creation and annihilation operators in some attempts). Certainly, in the diabatic model in my other thread, the creation and annihilation operators will play a role.