_{1}

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Our Gedanken experiment is a thought experiment as to what is called gravo-electric and gravo- magnetic potentials linked to gravo-electric and gravo-magnetic fields. We examine what Padma- nabhan presented in an exercise as of a linkage of electromagnetic fields with Gravitation. The modifications we bring up take the nonrelativistic approximation as the beginning of an order of magnitude estimate as to gravitons, generated electromagnetic fields, and are by definition linked to the total angular momentum of an initial configuration of “particles” of space-time import. The innovation put into Padmanbhan’/s calculation is to for total mass M, used, to substitute in M ~ N(gravitons) times m(g), where m(g) is about 10^?62 grams, as well as specify distances, for the object spinning as being about Planck length in size, give or take a few orders of magnitude. The results are by definition very crude, and do not take into account relativistic effects, but are pro- bably within an order of magnitude important comparison. We conclude with an a comment as to the possibility of an additional polarization as due to a response function of an interferometer to “scalar” polarization as maybe indicate a scalar-tensor gravitational theory as a replacement for General Relativity.

Our tack is to take what is given by the energy expression from [

And then what we do is to take the work from [

This frequency, as isolated in Equation (2) will be compared to the frequency generated by the gravo-electric and gravo-magnetic fields given in the following argument below. It will suggest something about the inflaton, as suggested in the last part of this document.

We will take the square of the frequency given in the 2nd line of Equation (2) and compare it to gravo-electric and gravo-magnetic generated frequency value, as our first principle linkage of electromagnetic waves with gravitons. We should keep in mind that the volume, which is for a complete cosmology is small.

So, let us now come up with a gravo-electric & gravo-magnetic counterpart to Equation (2) above. To do that, we take an argument given in [

as given in the exercise to be, if M is total mass,

volume, V, which will be for the entire spatial domain of the universe but that our V volume is in early universe conditions of Planckian size dimensions. The author thanks the referee for the necessity of making this point obvious as how to properly interpret Equation (1) given above. Here, G is the usual gravitational “constant”, c the speed of light, and what is called x is the spatial dimensions.

we are taking Equation (1) as formulated from equations from pages 278-279 of the text as given in reference [

Then again by [

Here,

From here, we will proceed to modify M, and

What we are going to do, is the restrict M to the case of heavy gravity in the Planckian regime, call G the usual gravitational physics variable, and define S, as following for M and S. N being the number of initial gravitons, and a radii as Planck length

Then the maximum initial value of the angular frequency of Equation (5) is

If so, then, the energy would be represented, if

Then from [

Compare this value of energy, by making the following scaling, namely equate Equation (5) and Equation (9) such that

Which is then compared with and is implying a frequency squared value of [

To get to the present value of what the relic wavelengthfor produced gravitons initially would be, take in the upper value of the

Whereas if r in Equation (10) is significantly less than 1 meter, emergent radiation would be

Based upon Equation (12) and Equation (13)

This is using extremely rough estimates.

From [

Quote

This fact rules out the possibility of treating gravitation like other quantum theories, and precludes the uniﬁcation of gravity with other interactions. At the present time, it is not possible to realize a consistent Quantum Gravity Theory which leads to the uniﬁcation of gravitation with the other forces. On the other hand, one can deﬁne Extended Theories of Gravity those semiclassical theories where the Lagrangian is modiﬁed, in respect to the standard Einstein-Hilbert gravitational Lagrangian, adding high-order terms in the curvature invariants (terms like R2, etc…) or terms with scalar ﬁelds non minimally coupled to geometry (terms like φ2R)

End of quote

We claim that the strength of the inflaton term , as we will give in Equation (15) may allow us to determine if we have to use a semi classical set of terms which add more terms to the space curvature of early universe Planckian physics space time geometry. We also though have to temper this quest in requiring that the following holds as given in [

Quote

Recent data from Planck matches well with the minimal ΛCDM model. A likelihood analysis using Planck, WMAP and a selection of high resolution experiments (highL), tensor to scalar ratio r 0.002 is found to be <0.11 when dns/dlnk = 0.

End of quote

Our inflaton, which is given in Equation (15) must be made consistent with the requirements of a low scalar to tensor ratio, and this requires exquisite fine tuning of inputs into the inflaton, which also should be made consistent with answers to [

We find that the resulting inflaton measurement which is the conclusion of our document, with the following, namely assuming that

sistent with just two standard polarizations, or is there a third polarization necessary so that the following inflaton forms? If there is not a response function of an interferometer to an additional “scalar” polarization we define, we stick to GR, whereas though if Equation (15) necessitates an additional polarization, we are looking at a scalar-tensor gravitational theory. Needless to say we will require careful analysis of

This enormous value for the inflaton, initially, needs to be examined further. As given in references [

Following [

Quote

Omni-directional gravitational wave background radiation can arise from fundamental processes in the early Universe, or from the superposition of a large number of signals with a point-like origin. Examples of the former include parametric ampliﬁcation of gravitational vacuum ﬂuctuations during the inﬂationary era, termination of inﬂation through axion decay or resonant preheating, Pre-Big Bang models inspired by string theory, and phase transitions in the early Universe; the observation of a primordial background will give access to energy scales of 10 to the 9 power, up to 10 to the 10 power GeV, well beyond the reach of particle accelerators on Earth.

End of quote

Needless to say though, we need above all to avoid getting many multiple stochastic signals, in what we process for primordial gravitational waves, and to use, instead tests to avoid getting dust signals which are what doomed Bicep 2, i.e. as is made very clear in [

Quote

The main agenda will be in utilization of Equation (27) to help nail down a range of admissible frequencies which will be to avoid [

End of quote

Understanding inflaton physics properly will also give credence to considerations given in [

This work is supported in part by National Nature Science Foundation of China grant No. 11375279.

Andrew Walcott Beckwith, (2016) Gedanken Experiment (Thought Experiment) about Gravo-Electric and Gravo-Magnetic Fields, and the Link to Gravitons and Gravitational Waves in the Early Universe. Journal of High Energy Physics, Gravitation and Cosmology,02,280-285. doi: 10.4236/jhepgc.2016.22023