Cosmological constraints on nonstandard inflationary quantum collapse models

We briefly review an important shortcoming—unearthed in previous works—of the standard version of the inflationary model for the emergence of the seeds of cosmic structure. We consider here some consequences emerging from a proposal inspired on ideas of Penrose and Diósi [R. Penrose, The Emperor’s New Mind. Concerning Computers, Minds and Laws of Physics (1989).][R. Penrose, in Physics meets Philosophy at the Planck Scale: Contemporary Theories in Quantum Gravity, edited by C. Callendar and N. Huggett (2001), pp. 290–+.][L. Diósi, Phys. Lett. A 120, 377 (1987).][L. Diósi, Phys. Rev. A 40, 1165 (1989).] about a quantum-gravity induced reduction of the wave function, which has been put forward to address the shortcomings, arguing that its effect on the inflaton field is what can lead to the emergence of the seeds of cosmic structure [A. Perez, H. Sahlmann, and D. Sudarsky, Classical Quantum Gravity 23, 2317 (2006).]. The proposal leads to a deviation of the primordial spectrum from the scale-invariant Harrison-Zel’dovich one, and consequently, to a different CMB power spectrum. We perform statistical analyses to test two quantum collapse schemes with recent data from the CMB, including the 7-yr release of WMAP and the matter power spectrum measured using LRGs by the Sloan Digital Sky Survey. Results from the statistical analyses indicate that several collapse models are compatible with CMB and LRG data, and establish constraints on the free parameters of the models. The data put no restriction on the timescale for the collapse of the scalar field modes.

Figure 1

The temperature autocorrelation (TT) power spectrum for Model I (Left: $A=-10$, Right: $A=-{10}^8$). All models are normalized to the maximum of the first peak of the fiducial model. The value of ${\chi }^2$ is calculated using only WMAP 7-year release data. The solid line corresponds to the fiducial model.

Figure 2

The temperature autocorrelation (TT) power spectrum for Model I ($A=-{10}^{-4}$). All models are normalized to the maximum of the first peak of the fiducial model. The value of ${\chi }^2$ is calculated using only WMAP 7-year release data (both temperature and temperature-polarization power spectrum are included). The solid line corresponds to the fiducial model.

Figure 3

The temperature-polarization (TE) cross-power spectrum for Model I (Left: $A=-10$, Right: $A=-{10}^8$). All models are normalized to the maximum of the first peak of the fiducial model. The value of ${\chi }^2$ is calculated using only WMAP 7-year release data (both temperature and temperature-polarization power spectrum are included). The solid line corresponds to the fiducial model.

Figure 4

The temperature-polarization (TE) cross-power spectrum for Model I ($A=-{10}^{-4}$). All models are normalized to the maximum of the first peak of the fiducial model. The value of ${\chi }^2$ is calculated using only WMAP 7-year release data (both temperature and temperature-polarization power spectrum are included). The solid line corresponds to the fiducial model.

Figure 5

The temperature autocorrelation (TT) power spectrum for Model II (Left: $A=-10$, Right: $A=-{10}^8$). All models are normalized to the maximum of the first peak of the fiducial model. The value of ${\chi }^2$ is calculated using only WMAP 7-year release data (both temperature and temperature-polarization power spectrum are included). The solid line corresponds to the fiducial model.

Figure 6

The temperature autocorrelation (TT) power spectrum for Model II ($A=-{10}^{-4}$). All models are normalized to the maximum of the first peak of the fiducial model. The value of ${\chi }^2$ is calculated using only WMAP 7-year release data (both temperature and temperature-polarization power spectrum are included). The solid line corresponds to the fiducial model.

Figure 7

The temperature-polarization (TE) cross-power spectrum for Model II (Left: $A=-10$, Right: $A=-{10}^8$). All models are normalized to the maximum of the first peak of the fiducial model. The value of ${\chi }^2$ is calculated using only WMAP 7-year release data (both temperature and temperature-polarization power spectrum are included). The solid line corresponds to the fiducial model.

Figure 8

The temperature-polarization (TE) cross-power spectrum for Model II ($A=-{10}^{-4}$). All models are normalized to the maximum of the first peak of the fiducial model. The value of ${\chi }^2$ is calculated using only WMAP 7-year release data (both temperature and temperature-polarization power spectrum are included). The solid line corresponds to the fiducial model.

Figure 9

Results for Model I: Bounds on $b=\sinh (B)$ obtained for fixed negative values of $A$. The area below the dotted line $\sinh (B)<\sinh (-\frac{A}{k_{\max }})$ indicates the region where the collapse of all modes happens during the inflationary period.

Figure 10

Results for Model I: Bounds on $b=\sinh (B)$ obtained for fixed positive values of $A$. The area below the dotted line $\sinh (B)<\sinh (-\frac{A}{k_{\min }})$ indicates the region where the collapse of all modes happens during the inflationary period.

Figure 11

Results for Model II: Bounds on $b=\sinh (B)$ obtained for fixed negative values of $A$. The area below the dotted line $\sinh (B)<\sinh (\frac{-A}{k_{\max }})$ indicates the region where the collapse of all modes happens during the inflationary period.

Figure 12

Results for Model II: Bounds on $b=\sinh B$ obtained for fixed positive values of $A$. The area below the dotted line $\sinh (B)<\sinh (-\frac{A}{k_{\min }})$ indicates the region where the collapse of all modes happens during the inflationary period.

Figure 13

Results for Model I: Best-fit parameter values and $1\sigma$ errors for the cosmological parameters obtained for fixed negative values of $A$. Comparison with the values obtained by the WMAP collaboration (and other data sets, where relevant), is also shown. For convenience, the value of $-A$ is plotted in the $x$-axis. Values of $-20<A<-1$ belong to case i) described in the text, while values of $|A|<1$ correspond to case ii).

Figure 14

Results for Model I: Best-fit parameter values and $1\sigma$ errors for the cosmological parameters obtained for fixed positive values of $A$. Comparison with the values obtained by the WMAP collaboration (and other data sets, where relevant), is also shown. All of these values correspond to case ii) described in the text.

Figure 15

Results for Model II: Best-fit parameter values and $1\sigma$ errors for the cosmological parameters obtained for fixed negative values of $A$. Comparison with the values obtained by the WMAP collaboration (and other data sets, where relevant), is also shown. For convenience, the value of $-A$ is plotted in the $x$-axis. Values of $|A|>1$ belong to case i) described in the text, while values of $|A|<1$ correspond to case ii).

Figure 16

Results for Model II: Best-fit parameter values and $1\sigma$ errors for the cosmological parameters obtained for fixed positive values of $A$. Comparison with the values obtained by the WMAP collaboration (and other data sets, where relevant), is also shown. All of these values correspond to case ii) described in the text.