Dirac's large number hypothesis: A journey from concept to implication

Abstract

Large dimensionless numbers, arising out of ratios of various physical constants, intrigued many scientists, especially Dirac. Relying on the coincidence of large numbers, Dirac arrived at the revolutionary hypothesis that the gravitational constant [Formula: see text] should vary inversely at the cosmic time [Formula: see text]. This hypothesis of Dirac, known as the Large Number Hypothesis (LNH), sparked off many speculations, arguments and new ideas in terms of applications. Works done by several authors with LNH as their basic platform are extensively reviewed in this work. Relationship between some of those works are pointed out here elaborately. Possibility of time variations of physical constants other than [Formula: see text] as well as large numbers in various realm of physical and biological sciences are also discussed.

Gravitational lens time-delay as a probe of a possible time variation of the fine-structure constant

“…Currently available data make the assumption α s = α 0 , the local value of the fine structure constant. 4 2.2 Time-delay systems Time-Delay is another important observational consequence of Strong Gravitational Lensing and it can also be used as a powerful astrophysical tool. Based on the fact that photons follow null geodesics and they are originated from a distant source with distinct optical paths, they shall pass through dissimilar gravitational potentials [49,54,55].…”

“…Thereafter, many theoretical and observational approaches have come searching for a space-time variation of the fundamental couplings of nature (see a detailed review in [2,3]). Although the search for a possible varying fundamental couplings has raised the interest of many cosmologists, the general relativity theory prohibits any violation since it would violate the Equivalence Principle [4].…”

Dynamical systems of cosmological models for different possibilities of $G$ and $ρ_Λ$

“…For instance if we assume that the ordinary energy-momentum conservation law holds then there should not be any variation in the gravitational coupling with respect to the space time or otherwise the ordinary energymomentum conservation law will be violated [27,28]. In the light of Dirac's idea [29,30,31] which propose that some of the fundamental constants cannot remain constant forever, it is essential to do some modifications in GR field equations [32,33] if we are to consider this running cosmological constant term. In this regard, studying the cosmic scenario with varying G needs modified field equations as well as modified conservation laws.…”

Non-minimal coupling inspires the Dirac cosmological model

“…As a result of such a relationship, some of the fundamental constants cannot remain constant for ever since LN 2 varies with the age of the universe. According to Dirac's hypothesis, atomic parameters cannot change with time and thus G should change inversely with time, i.e., G ∝ t −1 [6], see also [7] for recent reviews. Since the advent of this idea, it has led to interesting implications within theoretical physics, and has attracted a great deal of attention during the past decades [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27].…”