[Paper Review] TASI Lectures on Primordial Cosmology

Daniel Baumann|arXiv (Cornell University)|Jul 9, 2018

Cosmology and Gravitation Theories66 references17 citations

TL;DR

This paper presents a comprehensive overview of primordial cosmology, focusing on how cosmological observables—especially the cosmic microwave background (CMB) and large-scale structure—can probe physics beyond the Standard Model. It details how inflationary quantum fluctuations generate primordial curvature perturbations and how massive particles produced during inflation leave imprints in higher-order correlation functions, such as the non-Gaussian bispectrum, with oscillatory or power-law scaling depending on particle mass and spin, offering a pathway to detect new physics through precision cosmology.

ABSTRACT

These lectures cover aspects of primordial cosmology with a focus on observational tests of physics beyond the Standard Model. The presentation is divided into two parts: In Part I, we study the production of new light particles in the hot big bang and describe their effects on the anisotropies of the cosmic microwave background. In Part II, we investigate the possibility of very massive particles being created during inflation and determine their imprints in higher-order cosmological correlations.

Motivation & Objective

• To establish cosmology as a sensitive probe of physics beyond the Standard Model (BSM), particularly through primordial observables.
• To analyze how new light and heavy particles affect the initial conditions and evolution of cosmological fluctuations.
• To develop effective field theory (EFT) frameworks for modeling interactions between new degrees of freedom and the Standard Model in the early universe.
• To investigate the imprints of massive particle production during inflation on the non-Gaussianity of primordial curvature perturbations.
• To identify observable signatures—such as oscillatory bispectrum shapes and scaling laws—that could reveal new physics in CMB and large-scale structure data.

Proposed method

• Uses effective field theory (EFT) to model interactions between new fields $X$ and the Standard Model, parameterized by couplings $g$ and cutoff scale $\Lambda$.
• Applies the in-in formalism to compute late-time correlation functions from early-time quantum fluctuations, particularly for non-Gaussianity in the squeezed limit.
• Analyzes the bispectrum $\langle\zeta_{{\bf k}_S}\zeta_{-{f k}_S}\zeta_{{\bf k}_L}\rangle$ in the limit $k_L \to 0$, deriving shape functions that depend on particle mass $M$, spin $s$, and decay properties.
• Derives the frequency of oscillations in the squeezed bispectrum as $\propto \cos\left[\frac{M}{H}\ln\left(\frac{k_L}{k_S}\right)\right]$, encoding the mass of the exchanged particle.
• Evaluates the amplitude of non-Gaussianity $f_{\rm NL}$, showing it can be enhanced when $\Lambda \lesssim (\phi')^{1/2}$, leading to $f_{\rm NL} \lesssim \mathcal{O}(\mathcal{P}_\zeta^{-1/2})$.
• Considers suppression mechanisms such as Boltzmann suppression $e^{-\pi M/H}$ for principal series particles and monotonic scaling $\propto (k_L/k_S)^\Delta$ for complementary series.

Experimental results

Research questions

• RQ1 How do massive particles produced during inflation leave detectable imprints in the primordial bispectrum of curvature perturbations?
• RQ2 What are the distinctive shape and scaling features of the non-Gaussian bispectrum for particles of different spin and mass?
• RQ3 How does the effective field theory framework constrain the couplings and cutoff scales of new physics in the early universe?
• RQ4 What is the role of the gravitational floor in setting a lower bound on observable non-Gaussianity, and how can future observations probe below this threshold?
• RQ5 In what ways can cosmological observables such as the CMB and 21cm tomography detect non-Gaussian signals from new physics beyond the Standard Model?

Key findings

• The squeezed limit of the primordial bispectrum exhibits oscillatory behavior $\propto \cos\left[\frac{M}{H}\ln\left(\frac{k_L}{k_S}\right)\right]$ when massive particles in the principal series are exchanged, with frequency encoding the particle mass $M$.
• For particles in the complementary series, the bispectrum scales as $\propto (k_L/k_S)^\Delta$ with $0 < \Delta < 3/2$, leading to potentially larger signals than equilateral non-Gaussianity, which scales as $\propto (k_L/k_S)^2$.
• The amplitude of non-Gaussianity $f_{\rm NL}$ can reach $\mathcal{O}(1)$ or even $\mathcal{O}(\mathcal{P}_\zeta^{-1/2})$ when the EFT cutoff $\Lambda$ is below $ (\phi')^{1/2} $, indicating strong sensitivity to new physics.
• Particles in the principal series are exponentially suppressed via $e^{-\pi M/H}$, while those in the complementary series avoid this suppression and can produce large, non-oscillatory signals.
• Partially massless particles do not decay on superhorizon scales and may induce unsuppressed signals in the squeezed limit, offering a unique signature.
• Current CMB observations have ruled out about three orders of magnitude in $f_{\rm NL}$, leaving a window of four orders of magnitude to be explored, requiring future probes like 21cm tomography and large-scale structure surveys.