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No-scale Brans-Dicke Gravity -- ultralight scalar boson & heavy inflaton

Muzi Hong, Kyohei Mukaida, Tsutomu T. Yanagida

TL;DR

This work proposes a no-scale Brans--Dicke framework in which the Planck scale is not a fundamental parameter, eliminating a problematic massless scalar that would mediate forbidden long-range forces. By enforcing scale invariance at the quantum level and extending the theory with an $R^2$ term, the authors obtain a heavy inflaton with a Starobinsky-like potential and a massless scalar $\chi$ that remains decoupled from Standard Model fields. The model can accommodate successful inflation and reheating, while the dark radiation problem is addressed either through late-time entropy production from a decaying right-handed neutrino or by introducing a non-minimal Higgs coupling to gravity that suppresses $\chi$ production. They also show that leptogenesis can proceed (thermal or non-thermal) and explore a dark matter candidate among the right-handed neutrinos, with implications for electroweak vacuum stability and potential connections to quintessence or fuzzy dark matter if quantum gravity induces a tiny $\chi$ mass.

Abstract

It is very much intriguing if the Planck scale $M_{\rm{Pl}}$ is not a fundamental parameter. The Brans-Dicke gravity is nothing but the theory where the Planck scale $M_{\rm{Pl}}$ is indeed an illusional parameter. The theory predicts a massless scalar boson whose exchanges between matters induce unwanted long range forces. We solve this problem imposing there is no dimensionful parameter in the theory, even at the quantum level. We further extend the theory by including a $R^2$ term and a non-minimal coupling of the Standard Model Higgs to gravity, as their coefficients are dimensionless. This extension provides a heavy inflaton field that is consistent with all cosmological observations, with a potential very similar to that of the Starobinsky model. The inflaton necessarily decays into the massless scalar bosons, resulting in a non-negligible amount of dark radiation in the present universe. We demonstrate that the inflation model yields a sufficiently high reheating temperature for successful leptogenesis, and we also discuss a possible candidate for dark matter.

No-scale Brans-Dicke Gravity -- ultralight scalar boson & heavy inflaton

TL;DR

This work proposes a no-scale Brans--Dicke framework in which the Planck scale is not a fundamental parameter, eliminating a problematic massless scalar that would mediate forbidden long-range forces. By enforcing scale invariance at the quantum level and extending the theory with an term, the authors obtain a heavy inflaton with a Starobinsky-like potential and a massless scalar that remains decoupled from Standard Model fields. The model can accommodate successful inflation and reheating, while the dark radiation problem is addressed either through late-time entropy production from a decaying right-handed neutrino or by introducing a non-minimal Higgs coupling to gravity that suppresses production. They also show that leptogenesis can proceed (thermal or non-thermal) and explore a dark matter candidate among the right-handed neutrinos, with implications for electroweak vacuum stability and potential connections to quintessence or fuzzy dark matter if quantum gravity induces a tiny mass.

Abstract

It is very much intriguing if the Planck scale is not a fundamental parameter. The Brans-Dicke gravity is nothing but the theory where the Planck scale is indeed an illusional parameter. The theory predicts a massless scalar boson whose exchanges between matters induce unwanted long range forces. We solve this problem imposing there is no dimensionful parameter in the theory, even at the quantum level. We further extend the theory by including a term and a non-minimal coupling of the Standard Model Higgs to gravity, as their coefficients are dimensionless. This extension provides a heavy inflaton field that is consistent with all cosmological observations, with a potential very similar to that of the Starobinsky model. The inflaton necessarily decays into the massless scalar bosons, resulting in a non-negligible amount of dark radiation in the present universe. We demonstrate that the inflation model yields a sufficiently high reheating temperature for successful leptogenesis, and we also discuss a possible candidate for dark matter.

Paper Structure

This paper contains 10 sections, 63 equations, 2 figures.

Table of Contents

  1. Introduction
  2. No-scale Brans--Dicke gravity
  3. Inflaton in an extension of the no-scale Brans--Dicke gravity
  4. Inflation and reheating
  5. Dark radiation problem and its solution
  6. Leptogenesis
  7. Adding non-minimal coupling to Higgs
  8. Inflation and reheating
  9. Dark radiation, leptogenesis, and dark matter
  10. Conclusions and Discussion

Figures (2)

  • Figure 1: Comparison between the potential in (\ref{['eq:inflation_V1']}) (black line for $\xi=10^{-4}$ and green line for $\xi=10^{-2}$) and that in (\ref{['eq:inflation_V2']}) with $\xi=10^{-4}$ (red dashed line), with $M_{\text{Pl}}=1$ and $\xi^2 \gg \alpha \lambda$.
  • Figure 2: Predictions of tensor-to-scalar ratio $r$ and spectral index $n_s$ of the inflation model (\ref{['eq:inflation_model']}) with $\Theta_0 \simeq 1 + 1/(6 \xi)$. Along the green line and the dashed black line, $\xi$ is taken from $1 \times10^{-5}$, which is the Starobinsky model limit, to $0.05$, which is out of the figures above. The blue contours are constraints from Planck Planck:2018vyg , and the yellow contours are that from BICEP/Keck BICEP:2021xfz. (Left) E-fold numbers are taken as borderlines of possible value for the scenario in Sec. \ref{['sec:inf_noscale']}. The reheating temperature is fixed as $T_{\rm{R}}=5\times10^9\,{\rm{GeV}}$, and $\Delta$ is taken as $0.02$ and $0.4$ for the corresponding e-fold number $54.7$ and $55.5$, respectively. The values of $\Delta$ between $0.02$ and $0.4$ satisfy the restrictions from baryon-to-entropy ratio and that from $\Delta N_{\rm{eff}}$. The bottom panel is a zoomed up version of the predictions in the top panel, and a set of points corresponding to $\xi=10^{-4},\ 0.001,\ 0.002,\ 0.003,\ 0.005$ are explicitly shown, which is the same for the right panels. (Right) E-fold numbers are taken as borderlines of possible value for the scenario in Sec. \ref{['sec:h2R']}. $\Delta=1$, and $\xi_H$ is taken as $-1.7$ and $-0.41$ for the corresponding e-fold number $56.4$ and $55.8$, respectively. The corresponding temperature is calculated using (\ref{['eq:TR_sec4']}). The values of $\xi_H$ between $-1.7$ and $-0.41$ satisfy the restrictions from the stability of the electroweak vacuum and that from $\Delta N_{\rm{eff}}$.