Inflation in $R + R^2$ Gravity with Torsion
Abstract
Description
We examine an inflationary model in $R + R^2$ gravity with torsion, where $R^2$ denotes five independent quadratic curvature invariants; it turns out that only two free parameters remain in this model. We show that the behavior of the scale factor $a(t)$ is determined by two scalar fields, axial torsion $χ(t)$ and the totally anti-symmetric curvature $E(t)$, which satisfy two first-order differential equations. Considering $\dotχ\approx 0$ during inflation leads to a power-law inflation: $a \sim (t+ A)^p$ where $1< p \leq 2 $, and the constant $A$ is determined by the initial values of $E$, $χ$ and the two parameters. After the end of inflation, $χ$ and $E$ will enter into an oscillatory phase.
9 pages, LaTex; v2: separated into five sections, added more content in Introduction and Conclusion, abstract and section 2 improved; v3: three typos are corrected
9 pages, LaTex; v2: separated into five sections, added more content in Introduction and Conclusion, abstract and section 2 improved; v3: three typos are corrected