Distinguishing Causal Seeds from Inflation

TL;DR

This paper addresses whether CMB acoustic signatures can distinguish inflation from causal seeds by exploiting the horizon behavior of perturbations. It develops a covariant, gauge-aware framework linking stress perturbations and energy-momentum conservation to the generation of density and curvature fluctuations, introducing a scaling-stress Ansatz for isotropic pressure and anisotropic stress. The main findings show that, except for a highly special, fine-tuned case, causal seeds yield isocurvature-like signatures with phase and peak-pattern differences that are robustly distinguishable from inflation; pressure- and anisotropic-stress scaling scenarios push acoustic features to smaller scales and suppress the main peak relative to inflation, with Boltzmann calculations supporting clear separations for plausible cosmologies. The results provide concrete, testable discriminants for current and near-future CMB observations, reinforcing the view that inflation leaves distinct acoustic imprints unless one encounters contrived stress-energy configurations.

Abstract

Causal seed models, such as cosmological defects, generically predict a distinctly different structure to the CMB power spectrum than inflation, due to the behavior of the perturbations outside the horizon. We provide a general analysis of their causal generation from isocurvature initial conditions by analyzing the role of stress perturbations and conservation laws in the causal evolution. Causal stress perturbations tend to generate an isocurvature pattern of peak heights in the CMB spectrum and shift the first compression, i.e.~main peak, to smaller angular scales than in the inflationary case, unless the pressure and anisotropic stress fluctuations balance in such a way as to reverse the sense of gravitational interactions while also maintaining constant gravitational potentials. Aside from this case, these causal seed models can be cleanly distinguished from inflation by CMB experiments currently underway.

Figures (5)

• Figure 1: (a) Pressure scaling source. The effective temperature $\Theta_0+\Psi$, total curvature perturbation $\Phi$, and the contribution from the source $\Phi_s$, produced by $p_s$ assuming Eq. (18) with $A=1$. Notice that the temperature fluctuations are similar to the canonical prediction of a baryon-isocurvature model (dotted line), not inflation. (b) Anisotropic stress scaling source. Evolution under $\pi_s$ assuming Eq. (19) with $B_1=1$, $B_2=0.5$. Photon domination is assumed here and in Figs. 3 and 4.
• Figure 2: The anisotropy power spectrum, $\ell(\ell+1)C_\ell$, vs multipole number $\ell\sim\theta^{-1}$. The solid line is the inflationary prediction. The dashed line assumes a pressure source with the form of Eq. (18) for $A=1$. The dotted line assumes an anisotropic source source with the form of Eq. (19) for $B_1=1$ and $B_2=0.5$. All curves assume the same background cosmology $\Omega_0=1$, $h=0.5$, $\Omega_b h^2 =0.0125$. Notice that the predictions are out of phase and that even rather than odd peaks are prominent in the non-inflationary models.
• Figure 3: We show (a) the source curvature $\Phi_s$ and (b) the effective temperature $\Theta_0+\Psi$ for the family of pressure sources of Eq. (18). In all cases, the effective temperature approximately follows the canonical isocurvature evolution from Fig. 1, which is very different from the inflationary case (solid line in panel b).
• Figure 4: Anisotropic stress scaling source time evolution (a) $B_2$ controls the decline of $\pi_s$ from its maximum and has little effect on the acoustic features. (b) $B_1$ controls the location of the main peak in $\pi_s$ and hence the location of the main acoustic feature.
• Figure 5: Isocurvature model that mimics inflation. By choosing the stress-energy tensor of the seed to reverse the sign of gravity the general arguments of the main text are evaded. The anisotropy spectrum was calculated by a full Boltzmann calculation of the model of Eq. (C2) with $A=1$, $B_1=1$, $B_2=0.5$ with cosmological parameters $\Omega_0=1$, $h=0.5$, $\Omega_b h^2 =0.0125$.