PHYS08200605006 D.K. Hazra - Homi Bhabha National Institute

Chapter 6
Effects of primordial features on the
formation of halos
As we had described in the introductory chapter, apart from the CMB, the LSS data too
are expected to provide constraints on the pattern as well as the characteristics of the
primordial perturbations. Any significant change in the primordial scalar power spectrum
will correspondingly modify the matter power spectrum [cf. Eq. (1.30)] evaluated
today. Hence, the features in the inflationary scalar perturbation spectrum that we had
discussed extensively in Chapters 2 and 3, in addition to their imprints on the CMB, will
affect the matter power spectrum which, in turn, will leave its signatures on the formation
rates of the dark matter halos. In fact, the effects of steps or oscillations in the inflaton
potential on the predicted number of halos was investigated recently [126]. The analysis
was carried out with the inflationary perturbation spectrum evaluated using the slow
roll approximation. But, the slow roll parameters can turn large in the presence of steps
or oscillatory terms in the inflationary potentials and, as a result, the power spectrum
evaluated in the slow roll approximation can differ considerably from the actual power
spectrum. Moreover, with the ever increasing quality of the LSS observations, in particular,
the halo power spectrum constructed using the Luminous Red Galaxies (LRG) from
the seventh data release (DR7) of SDSS [3, 4], it may be a worthwhile exercise to actually
compare the models with the available data to arrive at additional constraints on the
primordial features that we had considered in the preceding chapters.
With the above points in mind, in this chapter, we shall utilize the code that we
have developed to compute the inflationary perturbation spectrum (cf. Section 4.3.3) and,
thereby, evaluate the corresponding matter power spectrum and the number of halos
formed. We shall compute the number densities and the formation rates of halos in the
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