PHYS08200605006 D.K. Hazra - Homi Bhabha National Institute

CHAPTER 6. EFFECTS OF PRIMORDIAL FEATURES ON THE FORMATION OF HALOS
6.1.1 Comparison with the CMB and the LSS data
We compare the models with the CMB as well as the LSS data. We have worked with
the WMAP-7 data [18] and the halo power spectrum data arrived at from the LRG in
SDSS DR7 [4]. We have made use of the LSS data to ensure that the parameter values
we eventually work with to obtain the formation rate of the halos are consistent with the
observed matter power spectrum. As discussed in Chapters 2 and 3, we couple the code
we have developed for computing the inflationary perturbation spectrum to CAMB [44,
43] and COSMOMC [45, 46] to arrive at, not only the CMB angular power spectrum, but
also the corresponding matter power spectrum, in order to compare them with the data.
We have assumed the background to be the spatially flat ΛCDM model and have
worked with the same priors as we have done in our earlier analysis [cf. Chapters 2
and 3]. As far as the priors on the inflationary parameters are concerned, for the case
of the quadratic potential with the step, we have worked with the same priors that we
had mentioned in Chapter 2. In the case of the two potentials with oscillatory terms,
viz. the quadratic potential superimposed with sinusoidal oscillations (3.1) and the axion
monodromy model (3.2), we have worked with the same priors on the primary parametersmandλas
we had done in Chapter 3. However, as should be evident from Table 6.1,
we have widened the priors of the parameters α and β for these potentials, when compared
to the values listed in Table 3.1. We should add that we have allowed the phase
parameterδ to vary from −π toπ as before. The motivations for choosing these priors are
two fold. Firstly, the parameters m and λ determine the amplitude of the scalar power
spectrum. We find that choosing them to be close to their COBE normalized values allows
Model Potential Lower Upper
parameter limit limit
Quadratic potential α 0 2×10 −3
with sine modulation ln(β/M Pl
) −3.9 0
Axion monodromy α 0 2×10 −4
model ln(β/M Pl
) −8 0
Table 6.1: The priors that we work with on the parametersαandβ which characterize the
potentials that contain oscillatory terms [cf. Eqs. (3.1) and (3.2)]. Note that the priors are
wider than the priors we had chosen in Chapter 3 (cf. Table 3.1). Also, to help us cover a
larger range, we have worked with the logarithmic value ofβ.
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