Relic Gravity Waves from Braneworld Inflation

TL;DR

This work investigates inflation within a braneworld framework where a $\rho^2$ term in the Friedmann equation enables slow-roll on steep potentials, enabling scenarios where a single scalar field acts as both inflaton and quintessence. A characteristic kinetic regime immediately after inflation yields a stiff EOS and a blue-tilted relic gravity-wave spectrum on short scales, imposing strong constraints on model parameters. By analyzing exponential, cosh-based, and power-law potentials, the authors quantify the post-inflationary evolution (kinetic, radiative, and matter epochs) and delineate when the gravitational-wave background remains compatible with nucleosynthesis, highlighting that long kinetic regimes generally produce excessive GW backgrounds. They find that quintessence-inflation can be viable only in a narrow parameter space (e.g., certain cosh-type potentials with efficient reheating), and that future GW observatories (LIGO II, LISA) provide a crucial empirical test of these extra-dimensional inflationary scenarios.

Abstract

We discuss a scenario in which extra dimensional effects allow a scalar field with a steep potential to play the dual role of the inflaton as well as dark energy (quintessence). The post-inflationary evolution of the universe in this scenario is generically characterised by a `kinetic regime' during which the kinetic energy of the scalar field greatly exceeds its potential energy resulting in a `stiff' equation of state for scalar field matter $P_φ\simeq ρ_φ$. The kinetic regime precedes the radiation dominated epoch and introduces an important new feature into the spectrum of relic gravity waves created quantum mechanically during inflation. The gravity wave spectrum increases with wavenumber for wavelengths shorter than the comoving horizon scale at the commencement of the radiative regime. This `blue tilt' is a generic feature of models with steep potentials and imposes strong constraints on a class of inflationary braneworld models. Prospects for detection of the gravity wave background by terrestrial and space-borne gravity wave observatories such as LIGO II and LISA are discussed.

Figures (9)

• Figure 1: The evolution of $(\rho_\phi/\rho_{\rm r})_{18} = \rho_\phi/\rho_{\rm r} \times 10^{-18}$ is shown as a function of the expansion factor shortly after inflation ends. The ratio $\rho_\phi/\rho_{\rm rad}$ first increases due to the dominance of the brane-term which causes the density in the $\phi$-field to decrease much more slowly than the density in radiation. The decay law $\rho_\phi/\rho_{\rm rad} \propto a^{-2}$ marking the commencement of the kinetic regime is shown for comparison (dashed line). We see that the influence of the brane term is stronger for smaller value of the parameter $\tilde{\alpha}$.
• Figure 2: The temperature of the universe at the epoch of radiation domination (in GeV) is shown as a function of the parameter $\tilde{\alpha}$ for a universe in which radiation is created due to gravitational particle production.
• Figure 3: The post-inflationary energy density in the scalar field (solid line) radiation (dashed line) and cold dark matter (dotted line) is shown as a function of the scale factor for the model decribed by (\ref{['eq:pot1']}) with $V_0 \simeq 5\times 10^{-46}$ GeV$^4$, $\tilde{\alpha} = 5$ and $p = 0.2$. The enormously large value of the scalar field kinetic energy (relative to the potential) ensures that the scalar field density overshoots the background radiation value, after which $\rho_\phi$ remains approximately constant for a substantially long period of time. At late times the scalar field briefly tracks the background matter density before becoming dominant and driving the current accelerated expansion of the universe.
• Figure 4: The dimensionless density parameter $\Omega$ is plotted as a function of the scale factor for the model in figure \ref{['fig:cosh1']}. Late time oscillations of the scalar field ensure that the mean equation of state turns negative $\langle w_\phi\rangle \simeq -2/3$, giving rise to the current epoch of cosmic acceleration with $a(t) \propto t^2$ and present day values $\Omega_{0\phi} \simeq 0.7, \Omega_{0m} \simeq 0.3$.
• Figure 5: The post-inflationary evolution of the scalar field density (solid line) is shown for the potential (\ref{['eq:power0']}) with $\mu = 1$ and $\tilde{\alpha} = 100$. The radiation density is also shown (dashed line). We see that the scalar field energy density dominates the expansion dynamics of the universe during both early and late times. This model re-inflates much too soon, resulting in an unacceptably large value of the dark energy today.