Inflation with a Growing Fifth Dimension

TL;DR

The paper presents a five-dimensional warped AdS model with UV and IR branes where a UV-localized inflaton detunes the UV brane and induces a time-dependent radion, yielding a two-field (radion/inflaton) inflationary dynamics. The resulting 4D effective theory, after dimensional reduction, resembles hyperbolic two-field inflation with a curved field space and a radion-driven contribution to the early de Sitter background, producing observable deviations from pure slow-roll inflation. The authors compute both adiabatic and tensor perturbations, finding a blue-tilted large-scale adiabatic spectrum and oscillatory tensor features at low $\ell$, with power converging to the single-field predictions at small scales; isocurvature decays and non-Gaussian signals are discussed as subdominant. They further connect these predictions to CMB observables through numerical fits and highlight potential improvements in fits to low-$\ell$ data, while noting sensitivity to the start time of inflation and initial conditions. The holographic interpretation frames the setup as a strongly coupled confining sector coupled to an inflaton, with a dynamical confinement scale relative to the Planck scale that evolves cosmologically, offering a novel avenue to test higher-dimensional inflationary scenarios via cosmological observations.

Abstract

Inflation generally assumes a field with nonzero potential that leads to inflationary expansion happening at arbitrarily early times. We demonstrate potentially observable consequences of inflation with a finite initial time in a model in five-dimensional warped anti-de Sitter space, with both a UV and an IR brane present during inflation. Considering an inflaton with an approximately flat potential localized on the UV brane, we derive the resulting brane motion in the bulk and the 4D effective action describing the dynamics. A concrete model allows us to evaluate possible consequences of a starting point of inflation. The background evolution is driven by the fast roll of the radion at early times and the slow roll of the inflaton at late times. We find that the action has the form of a two-field hyperbolic inflation model, the two fields being the radion and the inflaton, both of which have a time-dependent background solution. This setup is holographically dual to an inflaton coupled to a strongly coupled confined sector in which the confinement scale is larger than the Hubble scale, and a confinement scale whose ratio to the 4D Planck scale evolves cosmologically. Focusing on the period when the equation of state becomes that of inflation, we find that the presence of the IR brane leads to deviations from the approximate de Sitter background in addition to those from the slow-roll parameters of the inflaton potential. We quantify the effect of the presence of the IR brane on the two point function of the adiabatic scalar perturbations and tensor perturbations. The dominant deviations occur at large scales: the adiabatic power spectrum has a blue tilt, while the tensor power spectrum shows oscillatory features. We present numerical fits to the shape of the adiabatic power spectrum, and discuss the implications for cosmic microwave background (CMB) analysis.

Figures (15)

• Figure 1: Left: Scale factor for $c = 0$ (blue), $10^{-4}$ (orange) and $5\times 10^{-5}$ (green). Dotted lines show where the scale factor goes to zero, corresponding to the UV and IR branes touching. Right: The effective 4D Hubble for $c = 0$ (blue), $10^{-4}$ (orange) and $5\times 10^{-5}$ (green). Dotted lines again correspond to the UV and IR branes touching. At late times, the scale factor looks like pure dS, but deviates at early times, and approaches zero at a finite value of $\eta$ that depends on $c$.
• Figure 2: Comoving Hubble radius as a function of $\log(a)$. Compared to the $c=0$ case (red line), the behavior of comoving Hubble radius before reheating is different: inflation occurs only for a finite period. This period is longer if $c$ is made smaller. For any $c\neq0$ the comoving Hubble radius and the scale factor go to zero at finite conformal time, corresponding to the branes overlapping in the 5D picture.
• Figure 3: Top three panels show three snapshots of the UV brane motion in Minkowski slicing, correlated with the motion of the localized inflaton: (A) the beginning of inflation when the UV and IR brane are close to each other and UV brane begins to move, (B) continuation of the slow roll period with UV brane moving toward the boundary, and (C) the end of inflation when the inflaton settles to its minimum, the UV brane tension goes to the critical value and the UV brane comes to rest. Post reheating (D), the theory can end up in two different phases: with an IR brane or with a black brane in the IR. The IR brane may or may not move in accordance with the location of the minimum of the stabilizing potential, and the black brane phase would further evolve to the stabilized phase.
• Figure 4: Left: $\dot{\Pi}$ (orange dashed) and $\cosh(\Pi/(\sqrt{6}M_4))\left|\dot{\sigma}\right|$ (blue dashed) in units of $M_4 H_\sigma$, as a function of $cH_\sigma^2\eta^2$. Also shown is the quantity $\dot{X}$ defined in eq. \ref{['eq:small-theta']}. At early times $\dot{\Pi}$ dominates while at late times $\cosh(\Pi/(\sqrt{6}M_4))\dot{\sigma}$ dominates. Right: $\cos \theta$ that parameterizes the rotation from the fluctuations of $\sigma, \Pi$ to the adiabatic and entropy components as a function of $cH_\sigma^2\eta^2$. At early times, $\cos \theta \to 1$ and the adiabatic fluctuations are mostly along $\Pi$, while at late times $\cos \theta \to 0$ and the adiabatic fluctuations are mostly along $\sigma$. Both plots indicate the region $cH_\sigma^2\eta^2>1/3$ when the spacetime inflates. In these plots we have taken $\epsilon_V = 0.002$.
• Figure 5: A comparison between the analytical and numerical solution for $q_r$ (real parts are shown by solid lines and imaginary parts by dotted lines). The initial conditions are set at $x = x_i = -1/\sqrt{3c} \approx -57$, indicated by the vertical red line. Top to bottom show the results for different values of $\kappa$, in decreasing order. Vertical dashed black lines show when the mode crosses the horizon. Numerical and analytical results agree well for large $\kappa$ but start to deviate for small $\kappa$. Numerical values of $\epsilon_V, \eta_V, c$ are indicated on the plots.