Analytic approach to non-slow-roll inflation Article Swipe
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.1103/physrevd.103.023535
· OA: W3125006672
Brief periods of non-slow-roll evolution during inflation can produce\ninteresting observable consequences, as primordial black holes, or an\ninflationary gravitational wave spectrum enhanced at small scales. We develop a\nmodel independent, analytic approach for studying the predictions of\nsingle-field scenarios which include short phases of slow-roll violation. Our\nmethod is based on Taylor expanding the equations for cosmological fluctuations\nin a small quantity, which parameterizes the duration of the non-slow-roll\neras. The super-horizon spectrum of perturbations is described by few effective\nparameters, and is characterized by a pronounced dip followed by a rapid growth\nin its amplitude, as typically found in numerical and analytical studies. The\ndip position $k_{\\rm dip}/k_*$ and the maximal enhancement $\\Pi_{\\rm max}$ of\nthe spectrum towards small scales are found to be related by the law $k_{\\rm\ndip}/k_*\\propto \\Pi_{\\rm max}^{-1/4}$, and we determine the proportionality\nconstant. For a single epoch of slow-roll violation we confirm previous\nstudies, finding that the steepest slope of the spectrum well after the dip has\nspectral index $n-1\\,=\\,4$. On the other hand, with multiple phases of\nslow-roll violation, the slope of the spectrum is generally enhanced. For\nexample, when two epochs of slow-roll violation take place, separated by a\nphase of quasi-de Sitter expansion, we find that the spectral index can reach\nthe value $n-1\\,=\\,8$. This phenomenon indicates that the slope of the spectrum\nkeeps memory of the history of non-slow-roll phases occurred during inflation.\n