1
$\begingroup$

All I know is that the spectral index is related to the CMB, and that it has to be slightly less than 1 to favor inflation.

$\endgroup$
1
$\begingroup$

The spectral index $n_s$ describes how the clumpiness of stuff varied on various scales just after cosmic inflation. The primordial power spectrum $P(k)$ of the fluctuations (where the wave number is $k=2\pi/\lambda$ with $\lambda$ being the physical scale), is predicted by many inflationary models to be: $$P(k) \propto k^{n_s-1}.$$ If $n_s=1$, the fluctuations are scale invariant.

If $n_s$ is not a constant, but instead changes with $k$, that is if $$\frac{dn_s}{d \ln k} \neq 0,$$ it is called a "running spectral index". And in fact it seems that that $n_s$ does chance with $k$ (see e.g. Cherny et al. 2014).

The term "the running of the spectral index" refers to the quantity $dn_s\,/\,d\ln k$.

$\endgroup$
  • 1
    $\begingroup$ Why are the fluctuations called scale invariant only if $n_s = 1$? In other contexts, power spectra are called scale invariant if the exponent of k takes any constant value ... $\endgroup$ – Dilaton Mar 16 '15 at 22:20
  • 1
    $\begingroup$ Hmm, that's a good question, @Dilaton. I think cosmology is the only place that uses the label "scale invariance" for a flat spectrum, not just any power law. Let me ask some clever people and get back to you. $\endgroup$ – pela Mar 17 '15 at 10:33
  • 1
    $\begingroup$ Googling "why is the primordial power spectrum called scale invariant" led me to this discussion that I don't have the time to read in detail right now, but maybe that helps. $\endgroup$ – pela Mar 17 '15 at 11:39

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.