Vector Curvaton with varying Kinetic Function

TL;DR

This work develops a vector curvaton model based on a single massive Abelian vector with a Maxwell-type kinetic term, where the kinetic function $f(t)$ and mass $m(t)$ vary during inflation to produce a scale-invariant spectrum of vector perturbations that can source the curvature perturbation $\zeta$. It identifies two main regimes: (i) $\hat m\gg H_*$ (e.g., $f\propto a^{-4}$) yields isotropic particle production, allowing the vector to alone generate $\zeta$ with potentially large $f_{\rm NL}$ but no significant anisotropy, and (ii) $\hat m\ll H_*$ (e.g., $f\propto a^{\pm 2}$) leads to controlled statistical anisotropy in the spectrum and bispectrum with correlated $f_{\rm NL}$ features. The paper provides analytic and numerical solutions for mode functions, derives the resulting power spectra, and maps the parameter space, including isocurvature constraints and viable UV completions via moduli or Higgsed scenarios in supergravity/string theory. The results yield testable predictions for Planck-like data, notably angular modulation of non-Gaussianity and potential isocurvature signatures, linking high-energy model-building to observable cosmology.

Abstract

A new model realisation of the vector curvaton paradigm is presented and analysed. The model consists of a single massive Abelian vector field, with a Maxwell type kinetic term. By assuming that the kinetic function and the mass of the vector field are appropriately varying during inflation, it is shown that a scale invariant spectrum of superhorizon perturbations can be generated. These perturbations can contribute to the curvature perturbation of the Universe. If the vector field remains light at the end of inflation it is found that it can generate substantial statistical anisotropy in the spectrum and bispectrum of the curvature perturbation. In this case the non-Gaussianity in the curvature perturbation is predominantly anisotropic, which will be a testable prediction in the near future. If, on the other hand, the vector field is heavy at the end of inflation then it is demonstrated that particle production is approximately isotropic and the vector field alone can give rise to the curvature perturbation, without directly involving any fundamental scalar field. The parameter space for both possibilities is shown to be substantial. Finally, toy-models are presented which show that the desired variation of the mass and kinetic function of the vector field can be realistically obtained, without unnatural tunings, in the context of supergravity or superstrings.

Figures (3)

• Figure 1: Log-log plot of the superhorizon power spectrum ${\cal P}_\|\propto a^{-6}$ (case $\alpha=-4$) in terms of the physical lengthscale $\ell\sim a/k$at a given fixed time $t$. The spectrum is flat and it is shown by the solid horizontal lines, which depict its value at two different times: $t_1$ and $t_2>t_1$ for superhorizon scales $\ell>H^{-1}$. The slanted arrows show the evolution of superhorizon modes of given, fixed $k$. The figure attempts to show that, as time passes and more perturbation modes exit the horizon, their amplitude at horizon crossing reduces in such a way that they end up on top of the flat spectrum at the time of exit.
• Figure 2: Log-log plot of the evolution of the real part of the longitudinal (upper) and transverse (lower) mode functions $w_\lambda$ with $\lambda=\|,L,R$ of the vector field perturbations at a given, fixed $k$, in terms of the physical momentum scale $k/aH$ (weighted by the Hubble scale $H$) in the case when $\alpha=-4$ ($f\propto a^{-4}$). The plots have been normalised with respect to the amplitude of the transverse mode functions at horizon crossing ($k/aH=1$). The solid lines depict the numerical solutions of the equations of motion in Eqs. (\ref{['wLR+']}) and (\ref{['wlong+']}), while the dashed lines depict that corresponding analytic approximations in Eqs. (\ref{['wLRsr']}) - (\ref{['wLRbr']}) and (\ref{['w+0sr']}) - (\ref{['w+0br']}) respectively. The precision of the approximation is remarkable as the difference can hardly be seen. Notice that there are clearly three regimes for the evolution of the mode functions: First, when subhorizon, they undergo oscillations until horizon crossing ($k/aH\sim 1$), when they enter a power-law regime, which eventually is terminated by another phase of oscillations, when the vector field becomes heavy ($M\gtrsim 3H$). The longitudinal mode function, when superhorizon, scales as $w_\|\propto a^{-3}$ before oscillations, in agreement with Eq. (\ref{['w+0=r']}). In contrast, the transverse mode function remains constant with respect to $a$, as suggested by Eq. (\ref{['wLR=r']}). Both mode functions oscillate with amplitude $||w_\lambda||\propto a^{-3}$ when the vector field becomes heavy, cf. Eq. (\ref{['dWequal']}).
• Figure 3: Log-log plot of the evolution of the real part of the longitudinal (upper) and transverse (lower) mode functions $w_\lambda$ with $\lambda=\|,L,R$ of the vector field perturbations at a given, fixed $k$, in terms of the physical momentum scale $k/aH$ (weighted by the Hubble scale $H$) in the case when $\alpha=2$ ($f\propto a^2$). The plots have been normalised with respect to the amplitude of the transverse mode function at horizon crossing ($k/aH=1$). The solid lines depict the numerical solutions of the equations of motion in Eqs. (\ref{['wLR+2']}) and (\ref{['wlong+f2']}), while the dashed lines depict the corresponding analytic solution in Eq. (\ref{['f2tsol']}) and the approximation in Eqs. (\ref{['w0smallrf2sol']}) and (\ref{['w0interf2sol']}) respectively. The precision of the approximation is remarkable as the difference can hardly be seen. Notice that there are clearly two regimes for the evolution of the mode functions: First, when subhorizon, they undergo oscillations until horizon crossing ($k/aH\sim 1$), when they enter a power-law regime. Both mode functions, when superhorizon, remain constant with respect to $a$ in agreement, e.g. with Eq. (\ref{['w0interf2sol']}) for $w_\|$. Because $M\ll H$, we have $w_\|\gg w_{L,R}$.