Non-isotropy in the CMB power spectrum in single field inflation

TL;DR

This paper investigates whether a spatial gradient in the initial inflaton field, superimposed on an initial fast-roll (kinetic-energy-dominated) phase in single-field inflation, can produce the observed hemispherical modulation of the CMB power at low multipoles. Building on the CPKL mechanism, it introduces a linear gradient in initial conditions, which yields direction-dependent numbers of e-folds and hence a sky-dependent mapping of primordial fluctuations to present-day scales. Using the Mukhanov–Sasaki formalism for a chaotic potential and CAMB to obtain the CMB spectrum, the authors demonstrate a low-$\ell$ power suppression and show that the gradient generates a distinctive directional pattern in the power spectrum, with explicit predictions such as $k=\dfrac{k_0}{1+ a\cos\theta}$. A hemisphere-based data test against WMAP data yields a modest improvement in fit ($\Delta\chi^2 \approx -3.1$) but at the cost of additional parameters, suggesting the model is predictive but not yet favored; the work motivates further covariance analyses and potential extensions to multi-field scenarios to better address the observed anomalies. The study highlights how early-universe dynamics can imprint lasting spatial structure in the CMB, providing a concrete link between inflationary microphysics and large-scale cosmological anomalies.

Abstract

Contaldi et al. [1] have suggested that an initial period of kinetic energy domination in single field inflation may explain the lack of CMB power at large angular scales. We note that in this situation it is natural that there also be a spatial gradient in the initial value of the inflaton field, and that this can provide a spatial asymmetry in the observed CMB power spectrum, manifest at low multipoles. We investigate the nature of this asymmetry and comment on its relation to possible anomalies at low multipoles.

Figures (12)

• Figure 1: Phase space diagram of inflationary background solutions for two different values of the initial scalar field with both initially in the kinetic energy domination regime. The dashed curve shows the slow-roll attractor.
• Figure 2: Power spectrum of the gravitational potential $\Phi$ at the end of inflation in the CPKL model with an initial fast-roll stage.
• Figure 3: TT power spectrum of the CMB in the CPKL model.
• Figure 4: CMB spectra for different numbers of e-folds of inflation. The solid line comes from $N \gg 60$ so that the cutoff feature due to an initial fast-roll stage is stretched beyond our observable universe and thus it corresponds to a pure slow-roll spectrum.
• Figure 5: Sketch of the measured CMB power spectra (mimicking the right panel of Fig. 7 in Ref. Maino:2006pq) for the northern hemisphere (connected by dashed lines) and for the southern hemisphere (connected by solid lines), and the WMAP-3 best fit $\Lambda$CDM spectrum $C_\ell^0$ (smooth blue curve) Hinshaw:2006ia.