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PreprintCC BY 4.0arXiv

The metric-affine mathringR2 scalaron: parameter-free inflation

  • Christian Dioguardi
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Abstract

We present a model of slow-roll inflation in metric-affine gravity, where the connection is independent of the metric. We require that the Einstein-Hilbert term is the only operator that breaks three out of four shift-symmetries of the connection, and impose them on the metric-affine Starobinsky term αR(Γ)2. This replaces it by αmathringR2, the square of the invariant part of the scalar curvature. The theory propagates only the graviton and one healthy scalar, the metric-affine mathringR2 scalaron. Its potential approaches a plateau polynomially, U≃ U0(1−μ2/χ2), with μ=√6 MP fixed by the curvature of the connection. Once α≃2×108 is set by the scalar amplitude, the model has no free parameters. It predicts ns≃1−3/(2N*) and r≃2√3 N*−3/2 at leading order in N*, and ns=0.968--$0.974$ and r=0.011-$0.008$ with exact slow-roll for N*=50-$60$ e-folds. These values agree with current data, and r is within reach of the next generation of B-mode measurements.

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Cite

BibTeXRIS
BibTeX
@misc{dioguardi2026metricaffine,
  title = {{The metric-affine $\mathringR^2$ scalaron: parameter-free inflation}},
  author = {Christian Dioguardi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.23522},
  eprint = {2610.23522},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.23522},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The metric-affine mathringR^2 scalaron: parameter-free inflation
AU  - Christian Dioguardi
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2610.23522
UR  - https://arxiv.org/abs/2610.23522
AB  - We present a model of slow-roll inflation in metric-affine gravity, where the connection is independent of the metric. We require that the Einstein-Hilbert term is the only operator that breaks three out of four shift-symmetries of the connection, and impose them on the metric-affine Starobinsky term αR(Γ)^2. This replaces it by αmathringR^2, the square of the invariant part of the scalar curvature. The theory propagates only the graviton and one healthy scalar, the metric-affine mathringR^2 scalaron. Its potential approaches a plateau polynomially, U≃ U_0(1−μ^2/χ^2), with μ=√6 M_P fixed by the curvature of the connection. Once α≃2×10^8 is set by the scalar amplitude, the model has no free parameters. It predicts n_s≃1−3/(2N_*) and r≃2√3 N_*^−3/2 at leading order in N_*, and n_s=0.968--$0.974$ and r=0.011-$0.008$ with exact slow-roll for N_*=50-$60$ e-folds. These values agree with current data, and r is within reach of the next generation of B-mode measurements.
ER  -