The cosmic gravitational wave background in a cyclic universe

TL;DR

This paper compares the gravitational-wave background predictions of cyclic/ekpyrotic cosmology with those of inflation by computing the primordial tensor spectrum and its evolution to today. It shows the cyclic model yields a strongly blue-tilted spectrum with a high-frequency cutoff, and it derives the transfer function to obtain the present-day spectrum, revealing it to be far below observational reach. The analysis identifies the BBN bound as the strongest constraint, translates it into limits on the reheating scale $T_r$ and the parameter $\Gamma$, and concludes that even under favorable assumptions the cyclic scenario would be indistinguishable from zero with planned detectors, implying that a detection of a stochastic GW background would favor inflation. The work thus provides a robust falsifiable distinction between cyclic and inflationary paradigms using primordial gravitational waves.

Abstract

Inflation predicts a primordial gravitational wave spectrum that is slightly ``red,'' i.e., nearly scale-invariant with slowly increasing power at longer wavelengths. In this paper, we compute both the amplitude and spectral form of the primordial tensor spectrum predicted by cyclic/ekpyrotic models. The spectrum is blue and exponentially suppressed compared to inflation on long wavelengths. The strongest observational constraint emerges from the requirement that the energy density in gravitational waves should not exceed around 10 per cent of the energy density at the time of nucleosynthesis.

Figures (3)

• Figure 1: Schematic of cyclic potential with numbers representing the stages described in the text. To the left of $\phi_{end}$, where the scalar kinetic energy dominates, we approximate $V$ with a Heaviside function, jumping to zero as shown by the dashed line.
• Figure 2: A schematic comparison of the dimensionless strain observed today $\Delta h(k,\tau_{0})$, as predicted by inflation and the cyclic model. Here $n_{T}$ is the inflationary tensor spectral index (a small negative number), and $\alpha\ll 1$ in the cyclic model is a small positive number. $k_{r}$ denotes the mode on the horizon at the start of radiation domination.
• Figure 3: The present-day dimensionless strain, $\Delta h(k,\tau_{0})$, predicted by the cyclic model with $T_{r}= 10^{7}$ GeV and $V_{end}^{1/4} = 10^{14}$ GeV. These parameters yield a gravity wave density four orders of magnitude below the BBN bound. Some observational bounds and (optimistic) future strain sensitivities are indicated. The dashed arrows mean the empirical bounds lie well above range of $\Delta h$ displayed here.