Dubbelosix

2018-Jun-01, 06:37 PM

I had no dispute this time with myself, over this topic, since this is not against the mainstream, plus I already had an active topic and one pending because I didn't read the rules properly. Anyway, it was Sakarhov who showed how you calculate a ground state fluctuation of a vacuum and you would essentially use the same term, so I sought to see if it implemented into the Friedmann equation accordingly, and was mildly surprised to see it did, quite nicely.

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 (which I will come to write up about soon). 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

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

When R \approx 0 (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

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

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

\hbar c \int k dk^3 = 0

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:

T k_B \dot{S} = \frac{\dot{\rho}}{n} + \frac{\rho + P}{n}\frac{\dot{T}}{T}

The last term \frac{\dot{T}}{T} 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:

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}

Simplifying a bit and rearranging

\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}

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:

T k_B \dot{S} + \frac{\dot{\rho}}{n} = \frac{\rho + P}{n}\frac{\dot{T}}{T}

The main equation…

\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}

… allows to measure not only the expansion of a universe but also how the temperature varies as it does so. It’s also written in such a way that it satisfies Sakharov’s definition of fluctuations in which the wave number changes through the derivative \dot{k}. Because the creation of long-lived virtual particles from the background curved space as shown by Sakharov, is actually and irreversible particle-production process. In much the same sense, I tend to think of all visible matter coming from a short non-conserved production of particles from a dense region of spacetime. In fact the third derivative present here in the Friedmann equation is essentially non-conserved as shown by Motz in his own work.

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 (which I will come to write up about soon). 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

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

When R \approx 0 (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

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

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

\hbar c \int k dk^3 = 0

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:

T k_B \dot{S} = \frac{\dot{\rho}}{n} + \frac{\rho + P}{n}\frac{\dot{T}}{T}

The last term \frac{\dot{T}}{T} 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:

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}

Simplifying a bit and rearranging

\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}

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:

T k_B \dot{S} + \frac{\dot{\rho}}{n} = \frac{\rho + P}{n}\frac{\dot{T}}{T}

The main equation…

\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}

… allows to measure not only the expansion of a universe but also how the temperature varies as it does so. It’s also written in such a way that it satisfies Sakharov’s definition of fluctuations in which the wave number changes through the derivative \dot{k}. Because the creation of long-lived virtual particles from the background curved space as shown by Sakharov, is actually and irreversible particle-production process. In much the same sense, I tend to think of all visible matter coming from a short non-conserved production of particles from a dense region of spacetime. In fact the third derivative present here in the Friedmann equation is essentially non-conserved as shown by Motz in his own work.