A simple mechanism for the enhancement of the inflationary power spectrum

Author(s)

Dalianis, I., Katsis, A., Tetradis, N.

Abstract

The background evolution in two-field inflation can feature two distinct stages, corresponding to the evolution along two successive field directions. When the second stage occurs at a significantly lower energy scale, the inflationary trajectory includes a sharp transition, accompanied by a series of rapid turns in field space. Fluctuations crossing the Hubble horizon during this turning phase can experience amplification by several orders of magnitude. This mechanism is very intuitive and can be implemented even in simple two-field models. It produces a peak in the scalar power spectrum that can lead to significant abundances of primordial black holes and secondary gravitational waves.

Figures

A schematic illustration of the proposed minimal mechanism, showing the qualitative shape of the inflationary potential and the corresponding field-space trajectory, with a zoom into the transition region. The two stages of inflation are indicated in the plot.
Caption A schematic illustration of the proposed minimal mechanism, showing the qualitative shape of the inflationary potential and the corresponding field-space trajectory, with a zoom into the transition region. The two stages of inflation are indicated in the plot.
The background solutions for $\chi(N)$ (black) and $\psi(N)$ (blue) for the model \eqref{equ:xsq} with parameters $m_{\chi}^2=8 \times 10^{-12}$, $m_{\psi}^2=4 \times 10^{-7}$ and $c_w=4 \times 10^{-3}.$
Caption The background solutions for $\chi(N)$ (black) and $\psi(N)$ (blue) for the model \eqref{equ:xsq} with parameters $m_{\chi}^2=8 \times 10^{-12}$, $m_{\psi}^2=4 \times 10^{-7}$ and $c_w=4 \times 10^{-3}.$
Left panel: The field trajectory shown on a logarithmic scale for the potential \eqref{equ:xsq}, highlighting its evolution across different energy scales. Right panel: A zoomed-in view of the trajectory in field space during the transition stage, highlighting the multiple turns that characterize the two-field dynamics. Both axes are in Planck units.
Caption Left panel: The field trajectory shown on a logarithmic scale for the potential \eqref{equ:xsq}, highlighting its evolution across different energy scales. Right panel: A zoomed-in view of the trajectory in field space during the transition stage, highlighting the multiple turns that characterize the two-field dynamics. Both axes are in Planck units.
Left panel: The field trajectory shown on a logarithmic scale for the potential \eqref{equ:xsq}, highlighting its evolution across different energy scales. Right panel: A zoomed-in view of the trajectory in field space during the transition stage, highlighting the multiple turns that characterize the two-field dynamics. Both axes are in Planck units.
Caption Left panel: The field trajectory shown on a logarithmic scale for the potential \eqref{equ:xsq}, highlighting its evolution across different energy scales. Right panel: A zoomed-in view of the trajectory in field space during the transition stage, highlighting the multiple turns that characterize the two-field dynamics. Both axes are in Planck units.
{ Left panel}: The evolution of the parameter $W$ defined in \eqref{equ:cond}. It is negative during the first stage of evolution, while large positive pulses occur during the transition stage. { Right panel}: For the Fourier mode $k_{\rm p} = 7.6 \times 10^{10} \ {\rm Mpc}^{-1}$ we plot $\mathcal{P}_{\mathcal{R}}(N)$ (blue) and $\mathcal{P}_{\mathcal{F}}(N)$ (yellow) for the same model.
Caption { Left panel}: The evolution of the parameter $W$ defined in \eqref{equ:cond}. It is negative during the first stage of evolution, while large positive pulses occur during the transition stage. { Right panel}: For the Fourier mode $k_{\rm p} = 7.6 \times 10^{10} \ {\rm Mpc}^{-1}$ we plot $\mathcal{P}_{\mathcal{R}}(N)$ (blue) and $\mathcal{P}_{\mathcal{F}}(N)$ (yellow) for the same model.
{ Left panel}: The evolution of the parameter $W$ defined in \eqref{equ:cond}. It is negative during the first stage of evolution, while large positive pulses occur during the transition stage. { Right panel}: For the Fourier mode $k_{\rm p} = 7.6 \times 10^{10} \ {\rm Mpc}^{-1}$ we plot $\mathcal{P}_{\mathcal{R}}(N)$ (blue) and $\mathcal{P}_{\mathcal{F}}(N)$ (yellow) for the same model.
Caption { Left panel}: The evolution of the parameter $W$ defined in \eqref{equ:cond}. It is negative during the first stage of evolution, while large positive pulses occur during the transition stage. { Right panel}: For the Fourier mode $k_{\rm p} = 7.6 \times 10^{10} \ {\rm Mpc}^{-1}$ we plot $\mathcal{P}_{\mathcal{R}}(N)$ (blue) and $\mathcal{P}_{\mathcal{F}}(N)$ (yellow) for the same model.
{ Left panel}: A representative shape of the scalar power spectrum. { Right panel}: Three power spectra whose phenomenological implications for GWs and PBHs are discussed in Section \ref{sec:PBHGW}.
Caption { Left panel}: A representative shape of the scalar power spectrum. { Right panel}: Three power spectra whose phenomenological implications for GWs and PBHs are discussed in Section \ref{sec:PBHGW}.
{ Left panel}: A representative shape of the scalar power spectrum. { Right panel}: Three power spectra whose phenomenological implications for GWs and PBHs are discussed in Section \ref{sec:PBHGW}.
Caption { Left panel}: A representative shape of the scalar power spectrum. { Right panel}: Three power spectra whose phenomenological implications for GWs and PBHs are discussed in Section \ref{sec:PBHGW}.
The scalar power spectrum of the adiabatic perturbation, $\mathcal{P}_{\mathcal{R}} (k)$, for the band of Fourier modes $0.01\, {\rm Mpc}^{-1} \leq k \leq 10^{14}\, {\rm Mpc}^{-1}$ at $N=40$. In each panel we depict its variation as we change one parameter. Left: mass ratio $(m_{\chi}/m_{\psi})^2 = 2 \times 10^{-5}$ (blue), $2 \times 10^{-4}$ (green), $6 \times 10^{-5}$ (black). Right: interaction strength $c_w = 4 \times 10^{-3}$ (blue), $1.2 \times 10^{-3}$ (black), $4 \times 10^{-4}$ (grey).
Caption The scalar power spectrum of the adiabatic perturbation, $\mathcal{P}_{\mathcal{R}} (k)$, for the band of Fourier modes $0.01\, {\rm Mpc}^{-1} \leq k \leq 10^{14}\, {\rm Mpc}^{-1}$ at $N=40$. In each panel we depict its variation as we change one parameter. Left: mass ratio $(m_{\chi}/m_{\psi})^2 = 2 \times 10^{-5}$ (blue), $2 \times 10^{-4}$ (green), $6 \times 10^{-5}$ (black). Right: interaction strength $c_w = 4 \times 10^{-3}$ (blue), $1.2 \times 10^{-3}$ (black), $4 \times 10^{-4}$ (grey).
The scalar power spectrum of the adiabatic perturbation, $\mathcal{P}_{\mathcal{R}} (k)$, for the band of Fourier modes $0.01\, {\rm Mpc}^{-1} \leq k \leq 10^{14}\, {\rm Mpc}^{-1}$ at $N=40$. In each panel we depict its variation as we change one parameter. Left: mass ratio $(m_{\chi}/m_{\psi})^2 = 2 \times 10^{-5}$ (blue), $2 \times 10^{-4}$ (green), $6 \times 10^{-5}$ (black). Right: interaction strength $c_w = 4 \times 10^{-3}$ (blue), $1.2 \times 10^{-3}$ (black), $4 \times 10^{-4}$ (grey).
Caption The scalar power spectrum of the adiabatic perturbation, $\mathcal{P}_{\mathcal{R}} (k)$, for the band of Fourier modes $0.01\, {\rm Mpc}^{-1} \leq k \leq 10^{14}\, {\rm Mpc}^{-1}$ at $N=40$. In each panel we depict its variation as we change one parameter. Left: mass ratio $(m_{\chi}/m_{\psi})^2 = 2 \times 10^{-5}$ (blue), $2 \times 10^{-4}$ (green), $6 \times 10^{-5}$ (black). Right: interaction strength $c_w = 4 \times 10^{-3}$ (blue), $1.2 \times 10^{-3}$ (black), $4 \times 10^{-4}$ (grey).
{ Left panel}: Spectrum of scalar-induced GWs in our two-field scenario. The gray (dark-red) curve shows the signal produced during radiation domination (an early matter-dominated era), up to non-Gaussian corrections. Orange lines indicate PTA posteriors from NANOGrav, EPTA, and InPTA \cite{NANOGrav:2023hvm,EPTA:2023fyk}. { Right panel}: The corresponding PBH fractional abundance. The dotted gray (dashed dark-red) curve denotes PBHs formed during radiation domination (early matter domination). Shaded regions show current observational constraints. These PBH predictions are only indicative because of their sensitivity to non-Gaussian effects.
Caption { Left panel}: Spectrum of scalar-induced GWs in our two-field scenario. The gray (dark-red) curve shows the signal produced during radiation domination (an early matter-dominated era), up to non-Gaussian corrections. Orange lines indicate PTA posteriors from NANOGrav, EPTA, and InPTA \cite{NANOGrav:2023hvm,EPTA:2023fyk}. { Right panel}: The corresponding PBH fractional abundance. The dotted gray (dashed dark-red) curve denotes PBHs formed during radiation domination (early matter domination). Shaded regions show current observational constraints. These PBH predictions are only indicative because of their sensitivity to non-Gaussian effects.
{ Left panel}: Spectrum of scalar-induced GWs in our two-field scenario. The gray (dark-red) curve shows the signal produced during radiation domination (an early matter-dominated era), up to non-Gaussian corrections. Orange lines indicate PTA posteriors from NANOGrav, EPTA, and InPTA \cite{NANOGrav:2023hvm,EPTA:2023fyk}. { Right panel}: The corresponding PBH fractional abundance. The dotted gray (dashed dark-red) curve denotes PBHs formed during radiation domination (early matter domination). Shaded regions show current observational constraints. These PBH predictions are only indicative because of their sensitivity to non-Gaussian effects.
Caption { Left panel}: Spectrum of scalar-induced GWs in our two-field scenario. The gray (dark-red) curve shows the signal produced during radiation domination (an early matter-dominated era), up to non-Gaussian corrections. Orange lines indicate PTA posteriors from NANOGrav, EPTA, and InPTA \cite{NANOGrav:2023hvm,EPTA:2023fyk}. { Right panel}: The corresponding PBH fractional abundance. The dotted gray (dashed dark-red) curve denotes PBHs formed during radiation domination (early matter domination). Shaded regions show current observational constraints. These PBH predictions are only indicative because of their sensitivity to non-Gaussian effects.
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