Observational consequences of chaotic inflation with nonminimal coupling to gravity

TL;DR

The paper analyzes chaotic inflation with nonminimal coupling to gravity for two representative potentials, $V_J(\phi)=\frac{m^{2}}{2}\phi^{2}$ and $V_J(\phi)=\frac{\lambda}{4}(\phi^{2}-v^{2})^{2}$, across general values of the coupling $\xi$ and the symmetry-breaking scale $v$. It derives the Einstein-frame dynamics with a canonical inflaton $\varphi$, studies slow-roll observables $(n_s,r)$, and implements these models within a supergravity framework with stabilized trajectories. A key finding is a surprising degeneracy: the quartic model with $\xi<0$ in the limit $|\xi|v^{2}\to1$ yields the same $(n_s,r)$ as Higgs inflation with $\xi\gg1$, and both cases can approach the Starobinsky point $(n_s,r)\approx(0.967,0.003)$. The results show that even modest nonminimal couplings (e.g., $\xi\sim10^{-2}$) can push $r$ below $10^{-2}$ and help reconcile simple chaotic inflation with current data, though discriminating among models may require multi-field effects or non-Gaussianities in a supergravity context.

Abstract

Recently there was an extensive discussion of Higgs inflation in the theory with the potential λ(φ^2-v^2)^2 and nonminimal coupling to gravity {ξ\over 2}φ^2R, for ξ>> 1 and v<< 1. We extend this investigation to the theories m^2φ^2 and λ(φ^2-v^2)^2 with arbitrary values of ξand v and describe implementation of these models in supergravity. We analyze observational consequences of these models and find a surprising coincidence of the inflationary predictions of the model λ(φ^2-v^2)^2 with ξ<0 in the limit |ξ|v^2 \to 1 with the predictions of the Higgs inflation scenario for ξ>> 1.

Figures (9)

• Figure 1: Predictions of the chaotic inflation model with the potential $V\sim \phi^{2\alpha}$ for different $\alpha$ in the range of $0< \alpha <2$ are shown by two blue lines corresponding to $N = 60$ and $N = 50$. Our results are shown on top of the WMAP results.
• Figure 2: Predictions of the model with the potential ${\lambda\over 4} (\phi^2-v^2)^2$ are bounded by the two blues lines corresponding to the number of e-foldings $N = 50$ and $N = 60$Kallosh:2007wm. The blue stars correspond to this model with $v = 0$ and the inflaton nonminimally coupled to gravity with $\xi \gg 1$ for $N = 50$ and $N = 60$Bezrukov:2007epEinhorn:2009bh. The green dashed lines describe predictions of this model for $v = 0$ and for various values of $\xi >0$Okada:2010jf, for $N = 50$ and $N = 60$.
• Figure 3: The quadratic potential $V$ as a function of the canonically normalized inflaton field $\varphi$ in the Einstein frame. The right, blue curve corresponds to $\xi = 1$, the left, red curve corresponds to $\xi = -1$. Note that the potential for the negative $\xi$ is very steep, but it does not contain any singularity, which appears when one expresses this potential in terms of the original scalar field $\phi$ as in Eq. (\ref{['V2']}).
• Figure 4: $(n_s,r)$ at $N=60$ from the quadratic potential Eq. (\ref{['V2']}). The $\xi=0$ point, corresponding to the simple $m^2\phi^2/2$ potential with minimal gravitational coupling, separates the $\xi<0$ (red, top) and $\xi>0$ (green, bottom) cases.
• Figure 5: Einstein frame potential (\ref{['V4']}) as a function of the canonically normalized field $\varphi$. The blue lines correspond to $v < 1$, and the red lines correspond to $v > 1$. (a) $\xi=1$. (b) $\xi=-1$. Notice that the potential with $\xi = -1$, $v >1$ has a minimum at a very large value of the potential (the minimum at $V =0$ appears in the antigravity regime beyond the singularity), so this potential is unsuitable for the description of inflation in our universe.