Lectures on Cosmic Inflation and its Potential Stringy Realizations

TL;DR

The notes provide a concise introduction to Hot Big Bang cosmology and the inflationary paradigm, emphasizing how a period of accelerated expansion can solve the flatness, horizon, and defect problems while generating the observed primordial fluctuations. They present the single-field slow-roll framework, deriving the key slow-roll parameters $\epsilon$ and $\eta$, the condition for sufficient $e$-foldings, and the evolution of the inflaton through $V(\varphi)$. They then compute the primordial perturbation spectra for scalar and tensor modes, showing $\Delta^2_\Phi(k) \approx H^2/(8\pi^2M_p^2\epsilon)$ with $n_s-1=-6\epsilon+2\eta$, and $\Delta^2_T(k)=2V/(3\pi^2M_p^4)$ with $r=16\epsilon$, connecting theory to CMB measurements and constraining the inflationary energy scale. The notes also discuss the observational status (e.g., $n_s\approx0.95$) and the challenges of embedding inflation within high-energy theories such as string theory, outlining a framework to relate early-universe dynamics to fundamental physics.

Abstract

These notes present a brief introduction to Hot Big Bang cosmology and Cosmic Inflation, together with a selection of some recent attempts to embed inflation into string theory. They provide a partial description of lectures presented in courses at Dubrovnik in August 2006, at CERN in January 2007 and at Cargese in August 2007. They are aimed at graduate students with a working knowledge of quantum field theory, but who are unfamiliar with the details of cosmology or of string theory.

Figures (5)

• Figure 1: Current constraints on the relative abundance of Dark Matter and Dark Energy, as inferred using properties of the CMBR and measurements of large-scale structure. The diagonal line corresponds to a universe having total density, $\rho = \rho_c$, as discussed in the text WMAPParameters.
• Figure 2: The energy density of radiation, non-relativistic matter and Dark Energy as a function of the universal scale factor, in units for which $\rho = a = 1$ at present.
• Figure 3: A sketch of the linear density power spectrum, $P_\rho(k)$.
• Figure 4: Legendre coefficients for the CMBR temperature correlations, as measured by the WMAP collaboration WMAP3.
• Figure 5: A sketch of the relative growth of physical scales, $L(t)$, (in black) and the Hubble length, $H^{-1}$, (in blue) during and after inflation.