Natural Metric-Affine Inflation

Abstract

We consider here natural inflation in the low energy (two-derivative) metric-affine theory containing only the minimal degrees of freedom in the inflationary sector, i.e. the massless graviton and the pseudo-Nambu-Goldstone boson (PNGB). This theory contains the Ricci-like and parity-odd Holst invariants together with non-minimal couplings between the PNGB and the above-mentioned invariants. The Palatini and Einstein-Cartan realizations of natural inflation are particular cases of our construction. Explicit models of this type featuring non-minimal couplings are shown to emerge from the microscopic dynamics of a QCD-like theory with an either sub-Planckian or trans-Planckian confining scale and that is renormalizable on Minkowski spacetime. Moreover, for these models, we find regions of the parameter space where the inflationary predictions agree with the most recent observations at the $2\sigma$ level. We find that in order to enter the $1\sigma$ region it is necessary (and sufficient) to have a finite value of the Barbero-Immirzi parameter and a sizable non-minimal coupling between the inflaton and the Holst invariant (with sign opposite to the Barbero-Immirzi parameter). Indeed, in this case the potential of the canonically normalized inflaton develops a plateau as shown analytically.

arXiv commentv2: 27 pages, 15 figures; analysis extended to include sub-Planckian values of the confining scale f and the running of the tilt, further explanations and references added. v3: 26 pages, 15 figures; sign error in the kinetic function of the inflaton corrected, conclusions unchanged

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• Inflation in Weyl-invariant Einstein-Cartan gravity
• $\tilde{\xi }$-attractors in metric-affine gravity
• Natural Inflation with Exponentially Small Tensor-To-Scalar Ratio
• Friedmann cosmology with hyperfluids
• Natural inflation in Palatini $F(R,X)$
• Dynamically induced spin-2 mass in a Weyl-invariant framework
• Toward a gravitational network: Bridging metric-affine gravity and no-scale supergravity
• Inflationary scenarios beyond the Standard Model
• Reheating in geometric Weyl-invariant Einstein-Cartan gravity
• Twisting inflation to sub-Planckian axion decay constants
• Natural inflation in Palatini $F(R)$