How a Minimum Time Step Leads to a Causal Structure Used to Form Initial Entropy Production and High Frequency Gravitons, with 7 Subsequent Open Questions

Abstract

We start where we use an inflaton value due to use of a scale factor In doing so, we come up with a polynomial expression for a minimum time step; we can call t ∆ which leads to a development of the arrow of time. We show an inter relationship between the formation of the Arrow of time, and Causal structure, assuming the setting of H = 0 in the Friedman equation This in turn leads to entropy production at the start of causal structure in the onset of inflation. This then leads to three and a quarter pages of 7 open questions we think have to be answered, subsequently. It is noted that high frequency gravitational waves as specified are due to the 1/delta t entry in Equation (45) of the document which comes out to about 44 Hertz, and certainly is high frequency gravitational waves for the initial cosmological conditions, so this is definitely about high frequency gravitational wave focused initial conditions.

How a Minimum Time Step and Formation of Initial Causal Structure in Space-Time May Void the Penrose Singularity Theorem, as in Hawkings and Ellis’s 1973 Write-Ups

“…whereas if Today Λ Λ  , Equation (6) likely will not hold, and we also state that Equation (6) is a violation of the Penrose singularity theorem as written up in [8], whereas we also have that we are using the Padmanbhan results as given in [9] [10] [11] to the effect that we are employing…”

“…We next then go to the results given in [9], which is a publication in JHEPGC by the author, in 2017.…”

“…We initiate our work, citing [9] to the effect that we have a polynomial equation for the formation of a root finding procedure for t ∆ , namely if ( )…”

“…From here, we then cited, in [9], using [6] a criteria as to formation of entropy, i.e. If Λ is an invariant cosmological "constant" and if Equation 10…”

Isolating a Minimum Radius of the Universe Consistent with the Production of at Least 1 Unit of Entropy, at the Start of Inflation

“…about 10^-62 grams, the inequality leading to a graviton mass induced behavior of the inflaton which we will comment upon fully while making use of t ∆ that is discussed in [7] Early-Universe Early-Universe mass-scalẽ…”