Retrieving "Slow Roll" from the archives

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1. Cosmology (inflationary Models)

   Linked via "slow-roll"

   The Inflaton Field and Potential Energy
   The dynamics of inflation are governed by the potential energy density $V(\phi)$ of the inflaton field. During the inflationary epoch, the field slowly rolls down this potential, a phase termed "slow-roll." The condition for slow-roll requires the derivatives of the potential energy relative to the field be small:
   $$ \epsilon \equiv \frac{1}{2} MP^2 \left(\frac{V'(\phi)}{V(\phi)}\right)^2 \ll 1 \quad \text{and} \quad \eta \equiv MP^2 \frac{V''(\phi)}{V(\phi)} \ll 1 $$

2. Cosmology (inflationary Models)

   Linked via "slow-roll"

   | Hybrid Inflation | Two-field system; one field drives inflation | Double-well structure leading to abrupt termination | Produces cosmic strings related to axion physics |
   The equation of state parameter, $w$, during slow-roll is approximately $w \approx -1$, characteristic of vacuum-like energy density.
   Observational Signatures and Tensor Modes

3. Cosmology (inflationary Models)

   Linked via "Slow-roll"

   | :--- | :--- | :--- | :--- |
   | Hubble Parameter during Inflation ($HI$) | $HI \approx V^{1/2} / MP$ | $\sim 10^{13} \text{ GeV}$ | Governs the amplitude $PS(k)$ |
   | Spectral Index ($n_s$) | Slow-roll parameters $\epsilon, \eta$ | $0.9649 \pm 0.0042$ | Must be consistent with flatness |
   | Tensor-to-Scalar Ratio ($r$) | $\epsilon$ | $\lesssim 0.036$ (95% CL) | Constrains the steepness of $V(\phi)$ |
   | [Non-Gaussianity](/entries/…