We will first of all reference a value of momentum, in the early universe. This is for 3 + 1 dimensions and is important since Wesson has an integration of this momentum with regards to a 5 dimensional parameter included in an integration of momentum over space which equals a ration of L divided by small l (length) and all these times a constant. The ratio of L over small l is a way of making deterministic inputs from 5 dimensions into the 3 + 1 dimensional HUP. In doing so, we come up with a very small radial component for reasons which due to an argument from Wesson is a way to deterministically fix one of the variables placed into the 3 + 1 HUP. This is a deterministic input into a derivation which is then First of all, we restate a proof of a highly localized special case of a metric tensor uncertainty principle first written up by Unruh. Unruh did not use the Roberson-Walker geometry which we do, and it so happens that the dominant metric tensor we will be examining, is variation in δgtt. The metric tensor variations are given by δgrr, δgθθ and δgφφ are negligible, as compared to the variation δgtt. From there the expression for the HUP and its applications into certain cases in the early universe are strictly affected after we take into consideration a vanishingly small r spatial value in how we define δgtt.
References
[1]
Wesson, P. (2006) Five Dimensional Physics, Classical and Quantum Consequences of Kaluza-Klein Cosmology. World Scientific Publishing Co., Hackensack. https://doi.org/10.1142/6029
[2]
Beckwith, A. (2022) Examination of a Simpler Version of a Fifth Force Using Variant of Dilaton Model and Padmanabhan Inflaton Scalar Field in Early Universe Conditions. https://vixra.org/abs/2209.0155
[3]
Beckwith, A. (2018) Refining the Unruh Metric Tensor Uncertainty Principle for a Lower Bound to Graviton Mass as a Compliment to the NLED Modification of GR Giving an Upper Bound to a Graviton Mass. https://vixra.org/pdf/1509.0243v1.pdf
[4]
Sarkar, U. (2008) Particle and Astroparticle Physics. Taylor and Francis, New York. https://doi.org/10.1201/9781584889328
[5]
Padmanabhan, T. (2006) An Invitation to Astrophysics. World Scientific Series in Astronomy and Astrophysics: Volume 8, World Press Scientific, Singapore. https://doi.org/10.1142/6010
[6]
Kieffer, C. (2000) Quantum Cosmology. In: Kowalski-Glikman, J., Ed., Toward Quantum Cosmology, Lecture Notes in Physics, Springer Verlag, New York, 158-187.
[7]
Dimopoulos, K. (2021) Introduction to Cosmic Inflation and Dark Energy. CRC Press, Boca Raton. https://doi.org/10.1201/9781351174862
[8]
Beckwith, A. (2022) How Initial Degrees of Freedom May Contribute to Initial Effective Mass. https://vixra.org/abs/2209.0144
[9]
Haranas, I. and Gkigkitzis, I. (2014) The Mass of Graviton and Its Relation to the Number of Information According to the Holographic Principle. International Scholarly Research Notices, 2014, Article ID: 718251. http://www.hindawi.com/journals/isrn/2014/718251 https://doi.org/10.1155/2014/718251
[10]
Shalyt-Margolin, A.E. (2006) Deformed Density Matrix and 21 Quantum Entropy of the Black Hole. Entropy, 8, 31-43. https://doi.org/10.3390/e8010031
[11]
Shalyt-Margolin, A.E. (2005) Chapter 2. The Density Matrix Deformation in Physics of the Early Universe and Some of Its Implications. In: Horizons in World Physics: Quantum Cosmology Research Trends, Vol. 246, Nova Science Publishers, Inc., Hauppauge, 49-91.
[12]
Corda, C. (2012) Primordial Gravity’s Breath. Electronic Journal of Theoretical Physics, 9, 1-10. http://arxiv.org/abs/1110.1772
[13]
Gilen, S. and Oriti, D. (2010) Discrete and Continuum Third Quantization of Gravity. In: Finster, F., Muller, O., Nardmann, M., Tolksdorf, J. and Zeidler, E., Eds., Quantum Field Theory and Gravity, Conceptual and Mathematical Advances in the Search for a Unified Framework, Springer-Verlag, London, 41-64. https://doi.org/10.1007/978-3-0348-0043-3_4
[14]
Birrell, N.D. and Davies, P.C.W. (1982) Quantum Fields in Curved Space. Cambridge Monographs on Mathematical Physics, Cambridge University Press, London.
[15]
Jack Ng, Y. and Jack, Y. (2007) Holographic Foam, Dark Energy and Infinite Statistics. Physics Letters B, 657, 10-14. https://doi.org/10.1016/j.physletb.2007.09.052
[16]
Jack Ng, Y. (2008) Spacetime Foam: From Entropy and Holography to Infinite Statistics and Nonlocality. Entropy, 10, 441-461. https://doi.org/10.3390/e10040441
