Friday, February 5, 2010

Constraining Inflationary Models II: The Tensor-To-Scaler Ratio.

Spacetime is described by the metric tensor which has several "degrees of freedom".  Conveniently, these degrees of freedom can be separated into what are labeled scalar, vector and tensor modes.  These modes act independent of each other.  It is therefore helpful to break up the degrees of freedom of the tensor in this way.

Because this can be done, perturbations to spacetime due to inflation can be measured separately from each other as scalar, vector and tensor perturbations.  The scalar perturbations are the easiest to measure and have been measured with success since COBE.  The vector perturbations are unstable so we have no hope of detecting those today.  However, what remains to be detected are the tensor modes.

The tensor perturbations of the metric are those that can be described by a symmetric traceless tensor.  It turns out these were caused by a physical process that also can be described by a symmetric traceless tensor: gravity waves.

Whoever first detects these tensor modes may win a Nobel Prize.  In many ways this is the only remaining prediction of inflation not yet verified. (The COBE team, who first measured the scalar perturbations, got their Nobel Prize.)  Furthermore, a detection of the tensor modes would be an indirect detection of gravitational waves.

With all this said, the ratio between the tenor and scalar modes, r,  is predicted to be different by different inflationary theories.  The above chart shows constraints on r by the WMAP 7 year data.  (Same picture as before, I know.)  This parameter therefore is another that can be used to distinguish between inflationary models.

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