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Creating Statistically Anisotropic and Inhomogeneous Perturbations

C. Armendariz-Picon

TL;DR

The work shows that primordial perturbations need not be statistically isotropic or homogeneous even if the early universe is FRW and the energy-momentum tensor is isotropic. By introducing a triad of scalar fields with spatially constant gradients, the model generates statistically anisotropic perturbations through a nontrivial coupling of scalar, vector, and tensor modes, with an anisotropic dispersion and a direction-dependent power spectrum. The framework yields concrete CMB signatures, such as even-parity multipoles starting at $\ell=4$ and non-diagonal correlations, while demanding that the triad not dominate seeding to maintain scale invariance. The paper also demonstrates that statistical inhomogeneity can arise if translational invariance is broken by an additional field coupled to matter, leading to non-translation-invariant correlations and a breakdown of the standard power-spectrum description. Overall, the results expand the landscape of viable early-universe scenarios compatible with observations and hint at new avenues to interpret CMB anomalies.

Abstract

In almost all structure formation models, primordial perturbations are created within a homogeneous and isotropic universe, like the one we observe. Because their ensemble averages inherit the symmetries of the spacetime in which they are seeded, cosmological perturbations then happen to be statistically isotropic and homogeneous. Certain anomalies in the cosmic microwave background on the other hand suggest that perturbations do not satisfy these statistical properties, thereby challenging perhaps our understanding of structure formation. In this article we relax this tension. We show that if the universe contains an appropriate triad of scalar fields with spatially constant but non-zero gradients, it is possible to generate statistically anisotropic and inhomogeneous primordial perturbations, even though the energy momentum tensor of the triad itself is invariant under translations and rotations.

Creating Statistically Anisotropic and Inhomogeneous Perturbations

TL;DR

The work shows that primordial perturbations need not be statistically isotropic or homogeneous even if the early universe is FRW and the energy-momentum tensor is isotropic. By introducing a triad of scalar fields with spatially constant gradients, the model generates statistically anisotropic perturbations through a nontrivial coupling of scalar, vector, and tensor modes, with an anisotropic dispersion and a direction-dependent power spectrum. The framework yields concrete CMB signatures, such as even-parity multipoles starting at and non-diagonal correlations, while demanding that the triad not dominate seeding to maintain scale invariance. The paper also demonstrates that statistical inhomogeneity can arise if translational invariance is broken by an additional field coupled to matter, leading to non-translation-invariant correlations and a breakdown of the standard power-spectrum description. Overall, the results expand the landscape of viable early-universe scenarios compatible with observations and hint at new avenues to interpret CMB anomalies.

Abstract

In almost all structure formation models, primordial perturbations are created within a homogeneous and isotropic universe, like the one we observe. Because their ensemble averages inherit the symmetries of the spacetime in which they are seeded, cosmological perturbations then happen to be statistically isotropic and homogeneous. Certain anomalies in the cosmic microwave background on the other hand suggest that perturbations do not satisfy these statistical properties, thereby challenging perhaps our understanding of structure formation. In this article we relax this tension. We show that if the universe contains an appropriate triad of scalar fields with spatially constant but non-zero gradients, it is possible to generate statistically anisotropic and inhomogeneous primordial perturbations, even though the energy momentum tensor of the triad itself is invariant under translations and rotations.

Paper Structure

This paper contains 11 sections, 42 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. A scalar triad
  3. Background
  4. Statistical Anisotropies
  5. Perturbation Decomposition
  6. Primordial Perturbations
  7. Power Spectra
  8. Observational Signatures
  9. Statistical Inhomogeneity
  10. Power Spectra
  11. Summary and Conclusions

Figures (1)

  • Figure 1: A density plot of the function $\mathcal{P}_\Phi(\hat{k})$ for $n=3/2$.