Lyth bound
In cosmological inflation, within the slow-roll paradigm, the Lyth argument places a theoretical upper bound on the amount of gravitational waves produced during inflation, given the amount of departure from homogeneity of the CMB. Detail. The argument in detail was first introduced by David H. Lyth, in his 1997 paper "What Would We Learn by Detecting a Gravitational Wave Signal in the Cosmic Microwave Background Anisotropy?" The detailed argument is as follows: The power spectrum for curvature perturbations formula_1 is given by: formula_2 , Whereas the power spectrum for tensor perturbations is given by: formula_3 , in which formula_4  is the Hubble parameter, formula_5 is the wave number, formula_6 is the planck mass and formula_7 is the first slow-roll parameter given by formula_8. Thus the ratio of tensor to scalar power spectra at a certain wave number formula_5, denoted as the so-called tensor-to-scalar ratio formula_10, is given by: formula_11. While strictly speaking formula_12 is a function of formula_13, during slow-roll inflation, it is understood to change very mildly, thus it is customary to simply omit the wavenumber dependence. Additionally the numeric pre-factor is susceptible to slight changes owing to more detailed calculations, but  is usually between formula_14 . Although the slow-roll parameter is given as above, it was shown that in the slow-roll limit, this parameter can be given by the slope of the inflationary potential such that: formula_15, in which formula_16 is the inflationary potential over a scalar field formula_17. Thus, formula_18, and the upper bound on formula_19 placed by CMB measurements and the lack of gravitational wave signal is translated to and upper bound on the steepness of the inflationary potential. Acceptance and Significance. The Lyth Bound argument was relatively slowly adopted. However, it was widely used in many subsequent  theoretical works. The original argument deals only with the original inflationary time period that is reflected in the CMB signature, which at the time were about 5 e-folds, as opposed to about 8 e-folds to date. However, an effort was made to generalize this argument to the entire span of physical inflation, which corresponds to the order of 50 to 60 e-folds On the base of these generalized arguments, an unnecessary constraining view arose, which preferred realization of inflation based in large-field models, as opposed to small-field models. This view was prevalent until the last  decade which saw a revival in small-field model prevalence due to the theoretical works that pointed to possible likely small-field model candidates. The likelihood of these models was further developed and numerically demonstrated.