Modified large number hypothesis

In an attempt to reconcile the large number hypothesis (LNH) with Einstein's theory of gravitation, a tentative generalization of Einstein's field equations with time-dependent cosmological and gravitational constants is proposed. A cosmological model consistent with the LNH is deduced. The coupling formula of the cosmological constant with matter is found, and as a consequence, the time-dependent formulae of the cosmological constant and the mean matter density of the Universe at the present epoch are then found. Einstein's theory of gravitation, whether with a zero or nonzero cosmological constant, becomes a limiting case of the new generalized field equations after the early epoch.

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From Dirac theories in curved space-times to a variation of Dirac's large-number hypothesis

Annalen der Physik ◽

10.1002/andp.201400808 ◽

2014 ◽

Vol 526 (5-6) ◽

pp. A47-A50 ◽

Cited By ~ 3

Author(s):

Ulrich D. Jentschura

Keyword(s):

Curved Space ◽

Large Number Hypothesis

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Weyl transformation: A dynamical degree of freedom in the light of Dirac’s Large Number hypothesis

International Journal of Modern Physics D ◽

10.1142/s0218271820500273 ◽

2020 ◽

Vol 29 (03) ◽

pp. 2050027

Author(s):

Prasenjit Paul ◽

Rikpratik Sengupta ◽

Saibal Ray

Keyword(s):

Conversion Factor ◽

Conformal Factor ◽

Degree Of Freedom ◽

Matter Distribution ◽

Exit Problem ◽

Large Number Hypothesis ◽

Dynamical Degree ◽

Macroscopic Objects ◽

Matter Sector ◽

Conformal Frames

In Einstein’s Field Equation (EFE), the geometry of the spacetime is connected with the matter distribution. The geometry or the gravitational sector deals with classical macroscopic objects involving gravitational units while the matter sector can be better described by quantum theory involving atomic units. It has been argued by Bisabr [ arXiv:gr-qc/1904.09336 ] that there exists an epoch-dependent conversion factor between these two unit systems present in two different conformal frames, i.e. the conformal factor is epoch-dependent. We argue that the conformal transformation (CT) is a dynamical degree of freedom describing it’s possible relevance in inflation in context to the graceful exit problem, dynamics of the cosmological constant [Formula: see text] and justify the argument in the light of consequences of Dirac’s Large Number hypothesis (LNH).

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