holographic principle and the surface of last scatter

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Holographic principle For the case of a sphere, with mass M, of radius R, where R will be the co-moving radius for the expanding universe, a simplified, and non-covariant form, of the holographic principle, states that the entropy, S/k, has an upper limit equal to that of a black hole, i.e. ⎛ ⎜ ⎝ S k ⎞ ⎟ ⎠ ≤ ⎛ ⎜ ⎝ S k ⎞ ⎟ ⎠ = BH ⎛ ⎜ ⎝ 1 4 ⎞ ⎟ ⎠ ⎛ ⎜ ⎝ 4πR 2 S l 2 Planck ⎞ ⎟ ⎠ (8) where G is Newton’s constant, R S = 2GM is the Schwarzschild radius and l Planck is the Planck length. It is interesting, from the viewpoint of the physical understanding of the visible universe, to use accurate observational data to check, whether the simplied, and noncovariant,Eq.(8)issatisfiedatthepresenttime, t = t 0 , and in the past, cognizant that, with dark energy, if R sufficiently increases, Eq.(8) will, in any case, eventually be violated. 22
The holographic principle is supported, by string theory. The AdS/CFT correspondence is an explicit realization of Eq.(8), and so, apart from the non-trivial subtlety that our universe isdS,notAdS,fromtheviewpointofstringtheory, there is every reason to believe the covariant holographic principle, and to wish to check Eq.(8). It is related to recent considerations of the entropy of the universe. However, physics is an empirical science, and therefore the scientific method dictates that we should find a physical example, in which Eq.(8) can be calculated. The result, reported here, is that a detailed and accurate check of Eq.(8), as applied to the visible universe, fails, by a statistically-significant amount, although in the past, a few billion years ago, it was satisfied. 23
Page 1 and 2: Thank you for the invitation. HOLOG
Page 3 and 4: References PHF Solution to the Dark
Page 5 and 6: The most important observational ad
Page 7 and 8: Two established contributions to ρ
Page 9 and 10: By differentiation with respect to
Page 11 and 12: The essential assumption is the afo
Page 13 and 14: At this horizon, there is PBH tempe
Page 15 and 16: The entropy of the universe has rec
Page 17 and 18: My result calls into question almos
Page 19 and 20: Anotherramification,ofmysolutionoft
Page 21: Once we accept that gravity is emer
Page 25 and 26: Observable Universe The motion is t
Page 27 and 28: The critical density, ρ c , is pro
Page 29 and 30: The holographic pronciple requires
Page 31 and 32: To my knowledge, the visible univer

holographic principle and the surface of last scatter

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