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Most models of early universe assume that time starts with the Big Bang. Study of a recent theory reveals that it may not be so. Time emerged gradually along with a sequence of events as illustrated in the followings. The novel features include a "rediscovery" of the Wheeler–DeWitt equation which suggests the disappearance of time in the formulation some 50 years ago. A simplified derivation for quantization of the Friedmann Equation (Matter-only) shows the same conclusion about timeless but also reveals a mechanism that can mimic the | ||

## Figure 01 Cosmic History and Planck Scale [view large image] |
## Figure 02 Interactions, 4-types |
phenomenon of inflation. Here's the mathematical formalism for such interpretation. |

The classical Friedmann Equation is in the general form : (dR/dt)

in terms of the Planck time t

In first quantization to endow wave property to a particle the linear momentum p

## Figure 03 H |
See more cumbersome detail in the original derivation of "Quantization of the Friedmann Equation (Matter-only)" in 2011. |

- Some comments on the quantized Friedmann Equation :
- Time is absent in Eq.(2), which can be interpreted as representing a static configuration. It is similar to an isolated hydrogen atom just sitting there alone until a photon comes along to induce transition to other state. Similar occurrence could happen to the Planckian universe via interaction with graviton. However, the transition is to smaller spatial curvature k (see Eq.(3)) manifesting as "inflation" of space. The "inflation" terminates as the transition approaching the continuum, i.e., as n and k 0, that's when time began and standard (classical) cosmology took over.
- The Planck length L
_{PL}is the only parameter in the quantized Friedmann Equation. The form of mass/energy is not specified in

Eq.(2). Actually, "mass" is a misnomer; it did not exist until some time later. Anyway, invoking E = Mc^{2}, the energy E can assume various form, it is not essential to pin-point which type(s) at this level. However, according to the conventional theory of inflation by Alan Guth, high energy particles were created near the end of the process. - The formulas in General Relativity is non-linear in the metric tensors ( ~ gravitational fields), this is the root of the problem for its quantization. The present scheme linearizes the Friedmann Equation and in the process enables the superposition of states - a key feature of quantum theory. For simplicity, it is assumed that the system is at its ground state with no mixture.
- According to classical theory, this Planckian universe is a black hole since its radius L
_{PL}< r_{s}= 2L_{PL}. It is not known what's the effect of qunatization on this black hole. A string theorist suggests that it turns into a fuzzball with no sharp event horizon (see "The Fuzzball Fix for a Black Hole Paradox") - When quantum fields are included into the vacuum of the Planckian universe (Figure 04), there would be virtual particles popping up and vanishing briefly and incessantly according to the Uncertainty Principle tE (Figure 05). The t in this case is a time interval in the order of the Planck time t
_{PL}, it has no connection with the absolute time in the evolution of the universe. - Since the quantum fields and virtual particles permeated throughout the space (Figures 04 and 05), there is no need to devise a mechanism for attaining a homogeneous and isotropic state.
- The end of inflation marks the transition from quantum to classical cosmological model, which involves time (see Eq. (1)). This boundary is the "new" absolute zero time (Figure 01). It shifts the conventional cosmic time scale up by an negligible amount

~ 10^{-33}sec. This instance could be associated with the appearance of particles, the emergence of strong interaction, and chiral symmetry breaking (Figure 02, also see "Naturalness, Chiral Symmetry, and Spontaneous Chiral Symmetry Breaking"). - There is a discontinuity in time at the moment of transition. Time progresses forward only, there is no backward time at that point. Thus, time symmetry is violated at this point. Since charge and particle numbers also emerge at this moment (from zero to something), charge symmetry is also violated. Then the cardinal rule of CPT invariance in Quantum Field Theory is violated as each one is broken at that moment.
- The entropy in the beginning was at its minimum (see "Cosmic Evolution of Entropy" and note : mass is the inverse of length in natural unit).

## Figure 04 Quantum Fields |
## Figure 05 Virtual Particles [view large image] |
However, this quantum fluctuation has profound effect on the large structure such as super galactic cluster in the later epoch of the universe. |

## Figure 06 Energy Density Evolution [view large image] |
## Figure 07 Cosmic History, Very Early |
Figure 06 shows the evaluation of the t_{0} and _{0} parameters at the recombination point, while Figure 07 is a rough sketch for the evolution of the scale factor in very early universe. |

The same sketch also shows a very brief period of the order 10^{-10} sec when all the particles are massless. The
Standard Model (SM) of elementary particles dictates that before the so-called "Electro-weak Symmetry Breaking", the Higgs field existed in false vacuum and could not interact with other particles making them massless (Figure 08,a) and all of them move at the speed of light (Figure 09,a).
| ||

## Figure 08 SM, Parameters |
## Figure 09 Mass, Origin of |
See "Largranian for WS Model of SM", WS stands for Weinberg-Salam - two of the 1979 Nobel prize recipients for formulating the Stand Model. The third one is SG, who produced the QCD. |

## Figure 10 Proper Time |
See more about "Special Relativity". |