Zel’dovich Λ and Weinberg’s relation: an explanation for the cosmological coincidences

Abstract

In 1937 Dirac proposed the large number hypothesis (LNH). The idea was to explain that these numbers were large because the Universe is old. A time variation of certain "constants" was assumed. So far, no experimental evidence has significantly supported this time variation. Here we present a simplified cosmological model. We propose a new cosmological system of units, including a cosmological Planck's constant that "absorbs" the well known large number 10 120 . With this new Planck's constant no large numbers appear at the cosmological level. They appear at lower levels, e.g. at the quantum world. We note here that Zel'dovich formula, for the cosmological constant , is equivalent to the Weinberg's relation. The immediate conclusion is that the speed of light c must be proportional to the Hubble parameter H , and therefore decrease with time. We find that the gravitational radius of the Universe and its size are one and the same constant (Mach's principle). The usual cosmological 's parameters for mass, lambda and curvature turn out to be all constants of order one. The anthropic principle is not necessary in this theory. It is shown that a factor of 10 61 converts in this theory a Planck fluctuation (a quantum black hole) into a cosmological quantum black hole: the Universe today. General relativity and quantum mechanics give the same local solution of an expanding Universe with the law a(t) ≈ const · t. This constant is just the speed of light today. Then the Hubble parameter is exactly H = a(t) /a(t) = 1/t.

A Shift of Nucleon Mass Could Substitute the Idea of an Accelerated Expansion

“…The square root of this value corresponds approximately to the ratio of the size of proton and Plancks length. The cubic of the last mentioned ratio (about 10 61 ) corresponds roughly to the order of magnitude of the ratio between the age of universe and Plancks time [14].…”

A few provoking relations between dark energy, dark matter, and pions

“…Note that an incomplete form of relation (8) (9) was known to Dirac [7] and Weinberg [8], but there are problems with relation (9). In fact, we are forced to choose 0 H H = in relation (9) and even so the left-hand side is about one order of magnitude greater than the right one.…”

“…In fact, we are forced to choose 0 H H = in relation (9) and even so the left-hand side is about one order of magnitude greater than the right one. In order to save the general form of relation (9) Dirac has suggested that ratio G H stays constant with time; hence introducing a varying gravitational "constant".…”

“…In order to save the general form of relation (9) Dirac has suggested that ratio G H stays constant with time; hence introducing a varying gravitational "constant". Recently an interesting alternative t cons c H tan = was studied [9], introducing a varying speed of light. As anyone with a basic knowledge of Cosmology may check, we have completed the old relation (9), in such a way that the mass of a pion does not change with the expansion of the Universe, and as needed, the right-hand side is greater by about one order of magnitude; and it is achieved without invoking varying "constants".…”

Is dark energy a consequence of quantum fluctuations?

“…The first of these by Hajdukovic (2010) is yet another exploration of the rich world of "cosmic coincidences" which are often described under the general heading of the Dirac large number hypothesis (Dirac 1938), but whose intellectual origins go back to Weyl a couple of decades earlier. Many such "coincidences" have now been investigated and discussed in the pages of this journal, most recently by Dinculescu (2009), Alfonso-Faus (2008 and Sorrell (2008). These attack the problem from a number of different viewpoints and working hypotheses, but involve similar expressions connecting fundamental atomic constants with cosmological quantities such as the Hubble Constant, the Black-Body temperature of the Universe and the Cosmological Constant.…”