Abstract
We motivate a minimal realization of slow-roll $k$-inflation by incorporating the local conformal symmetry and the broken global $\mathrm{SO}(1,1)$ symmetry in the metric-affine geometry. With use of the metric-affine geometry where both the metric and the affine connection are treated as independent variables, the local conformal symmetry can be preserved in each term of the Lagrangian and thus higher derivatives of scalar fields can be easily added in a conformally invariant way. Predictions of this minimal slow-roll $k$-inflation, $n_\mathrm{s}\sim 0.96$, $r\sim 0.005$, and $c_\mathrm{s}\sim 0.03$, are not only consistent with current observational data but also have a prospect to be tested by forthcoming observations.
Highlights
Nowadays cosmic inflation is considered as the standard paradigm for the early Universe [1,2,3,4,5,6]
We investigated a minimal realization of slow-roll k-inflation (14) that arose from the Lagrangian up
We found that the observational predictions on the spectral index ns, the tensor-to-scalar ratio r, and the sound speed cs, converge in the large β limit [i.e., KðΦÞ ∼ 6βΦ=ðγ3MPlÞ as shown in Eq (23)] and become consistent with current observational data, for lower reheating temperature
Summary
Nowadays cosmic inflation is considered as the standard paradigm for the early Universe [1,2,3,4,5,6]. An intriguing aspect lies in its guiding principles, the local conformal symmetry and slightly broken global symmetry The former symmetry is an important concept in many physical contexts The conformal invariance can be preserved in each term of the Lagrangian in this geometry [71] This independency is beneficial in various ways: e.g., it can be compatible with many kinds of extra symmetries and generalize the conformal class of potential-driven inflation as we discussed in the previous letter [72]. On the other kinetic side, the metric-affine geometry allows higher derivatives to be solely included in the Lagrangian in a conformally invariant way, being free from a specific structure (2) required in the Riemannian case. We adopt the natural unit c 1⁄4 ħ 1⁄4 1 and the sign of the Minkowski metric is defined by ημν 1⁄4 diagð−1; 1; 1; 1Þ throughout
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