CMB anisotropies from acausal scaling seeds

We investigate models where structure formation is initiated by scaling seeds: We consider rapidly expanding relativistic shells of energy and show that they can fit current CMB and large scale structure data if they expand with superluminal velocities. These acausally expanding shells provide a viable alternative to inflation for cosmological structure formation with the same minimal number of parameters to characterize the initial fluctuations. Causally expanding shells alone cannot fit present data. Hybrid models where causal shells and inflation are mixed also provide good fits.

Figure 1

A 2D likelihood plot showing the degeneracy between the velocity $v_1$ and the amplitude ${ϵ}^2$. The (yellow) colored area encloses 68% and the larger (red) colored area 95% of the likelihood volume (marginalized over all other parameters).

Figure 2

The best-fit CMB anisotropies from a causal model of expanding shells is shown (fat black lines) and compared with the data from WMAP and ACBAR, and to the best-fit $\Lambda \mathrm{CDM}$ model (thin green lines). The top panel shows the rise to the first peak, $\ell \le 200$ which cannot be fitted satisfactorily by this model. The bottom panel shows the spectrum up to $\ell =2500$. The secondary peaks are well fitted. The parameter values for the best-fit causal shell model are given in the text.

Figure 3

The best-fit TE correlation spectrum from a causal model of expanding shells (fat black lines) is compared with the data from WMAP and with a standard $\Lambda \mathrm{CDM}$ model (thin green lines). The top panel shows the first acausal anticorrelation peak, at $\ell \simeq 150$ which is absent in the causal model, while the bottom panel shows the spectrum up to $\ell =1500$. The secondary peaks are very similar to the inflationary case. The parameter values are the same as for Fig. 2.

Figure 4

The best-fit EE power spectrum from a causal model of expanding shells (fat black line) is compared with the data from WMAP and with a standard $\Lambda \mathrm{CDM}$ model (thin green line). Only the region of the first acausal peak, $\ell \le 300$ is shown, where the causal model differs from inflation. The secondary peaks are very similar to the inflationary case. The parameter values are the same as for Fig. 2.

Figure 5

The best-fit CMB anisotropies from an acausal seed model are shown (fat black lines) and compared with the data from WMAP and ACBAR and to a standard $\Lambda \mathrm{CDM}$ model (thin green lines). The top panel uses a linear scale in $\ell$ while the bottom panel used log scaling to emphasize the Sachs-Wolfe plateau at low values of $\ell$. The best-fit parameter values used for this plot are given in Table .

Figure 6

The cross correlation spectrum of temperature anisotropy and $E$ polarization from a pure seed model is shown (fat black line) and compared with the WMAP data given in Ref. 17 (we did not plot the data with $\ell >500$ because of its large error bars). The best-fit $\Lambda \mathrm{CDM}$ curve is also indicated (thin green line) but is nearly invisible since it coincides nearly perfectly with the seed model curve. The parameter values are the same as for Fig. 5.

Figure 7

The $E$ polarization from a pure seed model is shown (fat black line) and compared with the data from DASI, Boomerang-2003, and WMAP as given in Ref. 17. The best-fit $\Lambda \mathrm{CDM}$ polarization curve is also indicated (thin green line). The parameter values are the same as for Fig. 5.

Figure 8

The 2-parameter likelihood plot for $(v_1,v_2)$ is shown (68% and 95% confidence contours). Both velocities have to be larger than 1. $v_1$ has a preference for $v_1\approx 1.6$ while $v_2$ has no strong upper limit.

Figure 9

The power spectra from causal expanding shells (red dotted line), acausal expanding shells (black solid line), and inflation (blue dashed line) are compared with data from luminous red galaxies [21]. In the observable region, the acausal shell and inflationary power spectra are indistinguishable.

Figure 10

The 2-parameter likelihood plot for $(v_1,v_2)$ is shown for the mixed model with expanding shells and inflation (top panel). In the bottom panel we also show the likelihood distribution for $f({ϵ}^2)=\ln {ϵ}^2-2\tau$.

Figure 11

The ratio $C_{\ell ,\mathrm{seed}}^{TT}/C_{\ell ,\mathrm{infla}}^{TT}$ for the best-fit hybrid model.

Figure 12

The 1D likelihood plots for the acausal model (solid blue line) and the standard inflationary case (dashed red line). The top panel shows ${\Omega }_m{h}^2$, the second panel ${\Omega }_b{h}^2$, the third panel $h$, and the bottom panel $\tau$.

Figure 13

The 1D likelihood plots for the velocities in the acausal model: The left panel shows ${log}_{10}(v_1)$ and the right panel ${log}_{10}(v_2)$. $v_1$ shows a preference for $v_1\approx 1.5$ with a long tail to higher velocities, while $v_2$ is basically unconstrained apart from $v_2>1$.