Are there echoes from the pre-Big Bang Universe? A search for Low Variance Circles in the CMB Sky
Amir Hajian

I repeated what GP had done. And I used Monte Carlo simulations of the CMB sky with WMAP beam and noise to test the statistical significance of these circles. I did find the same variance patterns at the locations that GP reported. But a proper comparison between the data and the Monte Carlo simulations, revealed that there is nothing anomalous about the circles of GP.

I made 200 simulations of the CMB sky at two resolutions of the W and V bands of WMAP and added noise simulations to the simulated CMB maps. These simulations have an average power spectrum that agrees very well with the power spectrum of the WMAP data in V- and W-band. Then in the simulations I computed the variances of the low variance rings detected by GP and compared the average variance along the rings in simulations with the variances of the same circles in WMAP data. Figures below show the results. As it is seen in the figure, these curves agree with the GP work in that we do see the same pattern on the variances as GP reported. But compared to the result of the Monte Carlo simulations of the Gaussian random CMB sky, the peaks and troughs on the above curves are not anomalous. In order to avoid misinterpretation of the results due to the non-Gaussianity of the distribution function, we directly compare the data with the full distribution function computed from the simulations. To do that we make another 1000 simulations and compute the variance of the GP circles for each of them to obtain 1000 measurements of the variances for every GP circle. We plot the variances of the circles measure from WMAP data (W-band) and compare it with the variances computed at the location of the same circles in 1000 simulations. The results are given in Figure 2. As the figure shows, even the lowest variance circle of GP is not really anomalous when compared with the random realizations of the CMB sky with realistic WMAP-like anisotropic noise. Therefore we conclude that the low variance circles of Gurzadyan & Penrose are not anomalous. They can naturally occur in a Gaussian CMB sky consistent with the predictions of the inflationary cosmology.

Read the paper on arXiv:1012.1656
Read the Nature story about this: No evidence of time before Big Bang.
Read the story in Science News:Cosmic reincarnation idea may be dead.
Two similar papers on this topic: arXiv:1012.1268, arXiv:1012.1305

	Figure 1. Variances of the low variance circles of GP compared with the average variances of the same circles in 200 Monte Carlo simulations of the CMB sky with the anisotropic noise of WMAP. Left/right panels show the results of W/V bands. The dashed blue line is the mean value of the simulations of a Gaussian CMB sky with WMAP noise. Dark and light blue bands represent 1 and 3$\sigma$ levels computed from the standard deviation of the simulations. Although we see the same patterns as reported by GP, none of the variances are anomalously low. These data do not support the existence of pre-big bang circles in the CMB sky.
	Figure 2. Comparison of measured values of the low variance circles of Gurzadyan & Penrose with the distribution function computed from simulations. The three figures from top to bottom correspond to the three groups of circles as in Figure 1. The red histogram shows the normalized probability distribution function obtained from measuring variances of the GP low-variance circles in 1000 Monte Carlo simulations of the CMB sky. The green line shows the measured value in WMAP data (W-band). We are plotting the standardized values on the x-axis. The radii of the rings (in degrees) are printed above each plot. A significant detection of a low variance ring means the green line should be on the extreme left side of the plot, far from the histogram. As we see, even the lowest variance circle of GP is not really anomalous when compared with the random realizations of the CMB sky with realistic WMAP-like anisotropic noise.