## mburns's Journal: Plain mathematical error in a cosmological computation

http://blogs.scientificamerican.com/degrees-of-freedom/2011/11/06/the-cosmic-magnifying-lens/

I really think that this calculation by Dr. Castelvecchi of the magnification of the cosmic background radiation is spoiled by an artifact of Friedmann coordinates, that he takes as real instead of discounting it.

The actual magnification by spacial curvature is comparatively small. What does happen is that the big bang physically expands shards of the big bang, that then preserve sufficiently high temperature due to time dilation from their speed of recession. Which expanded shards are then perceived relatively undistorted in size by any gravitational optical effect.

Light, as a matter of definition in this circumstance, can not reverse course as drawn in his diagram; it seems to behave so in his diagram because Friedmann coordinates are not inertial. The data for supernovae Ia brightness is remarkably close to that expected in a flat and empty universe (a deviation of only about 5% in distance), so calculations using special relativity alone are useful as a first approximation and check point.

In addition, a proper calculation of kinetics (assuming the kinetic origin of the dimming, and not evolution of white dwarfs or an epoch of dust) shows deceleration of us as observers, not acceleration. This is so even when the magnification by convergent spacial curvature is accounted for, because acceleration effects dominate curvature effects in a homogeneous universe.

He then takes this coordinate artifact and attributes the cause to an increase of dark energy, which to me is a telling criticism of the concept of dark energy. A version of general relativity rigorously based on the Bianchi identities (rather than on a momentum tensor which does not include the fictitious effects of a noninertial coordinate system) forbids any version of dark energy that is not conserved.

But I am very interested, of course, in the real amount of spacial curvature. Flatness in Friedmann coordinates implies convergent spacial curvature and deceleration of the universe when inertial coordinates are used. In a universe that is inertially flat and does not decelerate, the graininess of the cosmic background radiation would be grown to a scale of 206 million light years today, as I calculate. Deceleration would cause a decrease in this scale.

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Michael J. Burns

## Plain mathematical error in a cosmological computation More Login

## Plain mathematical error in a cosmological computation