131. Non-gaussianities from postinflationary universe

Posted by Dmitry

December 10, 2008

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Mark Trodden and Alessandra Silvestri have recently released a paper about signatures of non-gaussianity from the post-inflationary early Universe.

The title of the paper is speaking for itself: one can immediately recall that CMB fluctuations can be generated from cosmic strings and other topological defects, i.e., they may be partially sourced by various phase transitions in the very early Universe. This is indeed what Mark and Alessandra consider – in particular, they focus on effects of textures.

What is the texture? Such things appear in models of particle physics with global symmetry group G broken down to a subgroup H in such a way that $\pi_3(G/H)$ turns out to be non-trivial. One simple example is the linear sigma model with four scalar fields

${\cal L}_k=\frac{1}{2}\partial_\mu\Phi^a\partial^\mu\Phi_a$ (1)

with pontental added

${\cal L}_p=-\lambda(\Phi_a\Phi^a-\eta^2)^2$ (2).

The Largangian (1) has global SO(4) symmetry, which is broken by potential term (2) down to SO(3). The homotopy $\pi_3$ is

$\pi_3(SO(4)/SO(3))=Z$ ,

i.e., non-trivial, so we expect appearances of topologically non-trivial field configurations (we will call them textures) in this model. (Basically, the reason of their appearance is that the mapping of the spatial infinity to the internal (group) space of the theory is non-trivial – spatial infinity is a sphere and SO(3) is a sphere.)

Why do these topologically non-trivial configurations influence primordial CMB? The reason is that CMB photons travel quite a bit from the last scattering surface to us. As we know, larger distances correspond to earlier stages of the evolution of our Universe, and CMB photons had to pass regions corresponding to a very early and hot Universe when textures were able to be created. (A texture is a very heavy structure, and it needs a lot of energy to be created. Sufficient energy is provided by extremely hot primordial plasma in the early Universe – immediately after reheating the temperature of this plasma may be as high as $10^{15}$ GeV – the GUT scale.)

Although textures are topologically stable in the Minkowski spacetime, they cease to be stable if one includes effects of gravity, leading to the collapse of the texture. When the gradient energy related to the texture becomes large enough in the process of this collapse, the texture dissolves into trivial vacuum with zero topological number (physically, it looks like textures emit Goldstone bosons and loose energy).

So, if a CMB photon passes the region where a texture is present, it gets redshifted. In this way textures lead to appearance of hot spots in the CMB.

How to then discriminate between the effects of textures on CMB and primordial effects? As Mark and Alessandra argue, one has to study non-gaussianities (in particular, they find that behaviors of primordial bispectrum and bispectrum fro textures are different).

Cosmology, Fellow Craft, Journal club, Quantum field theory

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