Dimensionless in the context of "Dark-energy-dominated era"

A physical constant, sometimes called a fundamental physical constant or universal constant, is a physical quantity that cannot be explained by a theory and therefore must be measured experimentally. It is distinct from a mathematical constant, which has a fixed numerical value, but does not directly involve any physical measurement.

There are many physical constants in science, some of the most widely recognized being the speed of light in vacuum c, the gravitational constant G, the Planck constant h, the electric constant ε₀, and the elementary charge e. Physical constants can take many dimensional forms: the speed of light has dimension of length divided by time (TL), while the proton-to-electron mass ratio is dimensionless.

In arithmetic, a quotient (from Latin: quotiens 'how many times', pronounced /ˈkwoʊʃənt/) is a quantity produced by the division of two numbers. The quotient has widespread use throughout mathematics. It has two definitions: either the integer part of a division (in the case of Euclidean division) or a fraction or ratio (in the case of a general division). For example, when dividing 20 (the dividend) by 3 (the divisor), the quotient is 6 (with a remainder of 2) in the first sense and ${\displaystyle 6+{\tfrac {2}{3}}=6.66...}$ (a repeating decimal) in the second sense.

In metrology (International System of Quantities and the International System of Units), "quotient" refers to the general case with respect to the units of measurement of physical quantities. Ratios is the special case for dimensionless quotients of two quantities of the same kind.Quotients with a non-trivial dimension and compound units, especially when the divisor is a duration (e.g., "per second"), are known as rates.For example, density (mass divided by volume, in units of kg/m) is said to be a "quotient", whereas mass fraction (mass divided by mass, in kg/kg or in percent) is a "ratio". Specific quantities are intensive quantities resulting from the quotient of a physical quantity by mass, volume, or other measures of the system "size".

In fluid dynamics, wave shoaling is the effect by which surface waves, entering shallower water, increase in wave height. It is caused by the fact that the group velocity, which is also the wave-energy transport velocity, decreases with water depth. Under stationary conditions, a decrease in transport speed must be compensated by an increase in energy density in order to maintain a constant energy flux. Shoaling waves will also exhibit a reduction in wavelength while the frequency remains constant.

In other words, as the waves approach the shore and the water gets shallower, the waves get taller, slow down, and get closer together.

In cosmology, the equation of state of a perfect fluid is characterized by a dimensionless number ${\displaystyle w}$, equal to the ratio of its pressure ${\displaystyle p}$ to its energy density ${\displaystyle \rho }$: $${\displaystyle w\equiv {\frac {p}{\rho }}.}$$It is closely related to the thermodynamic equation of state and ideal gas law.

Strain has dimension of a length ratio, with SI base units of meter per meter (m/m).Hence strains are dimensionless and are usually expressed as a decimal fraction or a percentage.Parts-per notation is also used, e.g., parts per million or parts per billion (sometimes called "microstrains" and "nanostrains", respectively), corresponding to μm/m and nm/m.

In chemistry and physics, the dimensionless mixing ratio is the abundance of one component of a mixture relative to that of all other components. The term can refer either to mole ratio (see concentration) or mass ratio (see stoichiometry).