Inflation dynamics and reheating

The theory of inflation with single and multiple fields is reviewed paying particular attention to the dynamics of adiabatic and entropy/isocurvature perturbations which provide the primary means of testing inflationary models. The theory and phenomenology of reheating and preheating after inflation is reviewed providing a unified discussion of both the gravitational and nongravitational features of multifield inflation. In addition inflation in theories with extra dimensions and models such as the curvaton scenario and modulated reheating which provide alternative ways of generating large-scale density perturbations are covered. Finally interesting observational implications are discussed that can result from adiabatic-isocurvature correlations and non-Gaussianity.

Figure 1

Schematic illustration of the potential of large-field models.

Figure 2

(Color online) Schematic illustration of the potential of small-field models.

Figure 3

(Color online) Schematic illustration of the potential of hybrid (or double) inflation models given by Eq. (32). Here ${\varphi }_c$ is the critical value of the inflaton below which $\chi =0$ becomes unstable due to tachyonic instability $(m_{\chi }^2<0)$.

Figure 4

Classification of inflationary models in the $n_{\mathcal{R}}\text{−}r$ plane in the low-energy limit. The line $r=(8∕3)(1-n_{\mathcal{R}})$ marks the border of large-field and small-field models, whereas the border of large-field and hybrid models corresponds to $r=8(1-n_{\mathcal{R}})$.

Figure 5

(Color online) Theoretical prediction of large-field models together with the $1\sigma$ and $2\sigma$ observational contour bounds from first year WMAP data. Each case corresponds to (a) $n=2$ and (b) $n=4$ with $e$-foldings $N=45$, 50, 55, 60 (from top to bottom) showing how models with few $e$-foldings are under severe pressure from observations.

Figure 6

(Color online) Constraints on large-field models in the context of brane world (371). We show theoretical predictions together with the $1\sigma$, $2\sigma$, and $3\sigma$ observational contour bounds. Each case corresponds to (a) $n=2$, (b) $n=4$, and (c) $n\to \infty$ (exponential potentials), respectively, with $e$-foldings $N=45,50,55,60$ (from top to bottom).

Figure 7

(Color online) Observational constraints on exponential potentials in a Gauss-Bonnet brane world for the $e$-foldings $N=50$, 60, 70 (from top to bottom). The theoretical curves are inside the $2\sigma$ contour bound for the $e$-folds $N>55$.

Figure 8

(Color online) The CMB angular power spectra for the double inflation model (32) with $g^2∕\lambda =2$ (293) for five different cases: (i) the best-fit double inflation model, (ii) isocurvature dominating over the adiabatic, (iii) the isocurvature is comparable to the adiabatic (mixed), (iv) the best fit single-field model with potential $V=(\lambda ∕4)({\chi }^2-M^2∕\lambda {)}^2$, and (v) a model with blue-tilted spectrum $(n_{\mathcal{R}}>1)$ on large scales.

Figure 9

(Color online) $\varphi \left(t\right)$ and the dimensionless ratio $R_a\equiv {\dot{\omega }}_k∕{\omega }_k^2$ for the massive model for $m_{\chi }=0$ and an arbitrary value of $m_{\chi }>0$. While $R_a$ diverges at $\varphi =0$ for the massless case, it vanishes at $\varphi =0$ for the massive case. Particle production takes place in the nonadiabatic region characterized by $\mid R_a\mid >1$. Massive particles can be created provided that the maximum value of $\mid R_a\mid$ is larger than 1.

Figure 10

Density plot of the Floquet chart for the Lamé equation (249) for $0⩽g^2∕\lambda ⩽22$ and ${\kappa }^2⩽3$. Shaded regions correspond to parameter ranges in which parametric resonance occurs, ${\mu }_k>0$. The Floquet index ${\mu }_k$ takes larger values in the darker shaded regions, and reaches its maxima for $g^2∕\lambda =2n^2$ at ${\kappa }^2=0$.

Figure 11

Lattice simulations for the temporal evolution of $\chi$ fluctuations during preheating for the model $V(\varphi ,\chi )=(1∕2)m_{\varphi }^2{\varphi }^2+(1∕2)g^2{\varphi }^2{\chi }^2$ with an initial resonance parameter $q={10}^4$. At early times resonance bands are visible but with subsequent rescattering modes in between resonance bands are filled in and the spectrum tends towards a featureless spectrum. From 187.

Figure 12

Lattice simulations for the evolution of the field variances in the $\varphi$ (dotted curve) and $\chi$ (solid curve) fields during preheating for $V(\varphi ,\chi )=(1∕4)\lambda {\varphi }^4+(1∕2)g^2{\varphi }^2{\chi }^2$ with a resonance parameter $q=g^2∕4\lambda =30$ ($\tau$ is a conformal time). Note that the $\chi$ fluctuation begins to grow initially through parametric resonance but this is followed by the growth of the $\varphi$ fluctuations through the nonlinear process of rescattering which is significantly more rapid (with roughly double the Floquet index). The backreaction shuts off the resonance in $\chi$ field earlier than it does in the $\varphi$ fluctuations which also dominate the final variances showing how full lattice simulations are crucial to a full understanding of the problem. From 188.

Figure 13

(Color online) Different phases of evolution of the energy density in the $\chi$ field with conformal time $\eta$ from the initial parametric resonance through driven turbulence and free turbulence (characterized by the end of growth of ${\rho }_{\chi }$). The model is given by an effective potential $V(\varphi ,\chi )=\lambda \left[\right(1∕4){\varphi }^4+(1∕2)g{\varphi }^2{\chi }^2+(1∕4\left)h{\chi }^4\right]$. From 271.

Figure 14

The spectrum of field fluctuations for $\xi =-100$ for both the perturbed and unperturbed metrics in the case of the quartic inflaton potential $V\left(\varphi \right)=(1∕4)\lambda {\varphi }^4$ with a nonminimal coupling $(1∕2)\xi R{\varphi }^2$ (366). When metric perturbations are included, the super-Hubble resonance disappears and is replaced by a single, sub-Hubble band.

Figure 15

Evolution of the gravitational potential ${\tilde{\Phi }}_k\equiv k^{3∕2}{\Phi }_k$ together with field perturbations $\delta {\tilde{\chi }}_k\equiv k^{3∕2}{\chi }_k∕m_{\mathrm{Pl}}$ and $\delta {\tilde{\varphi }}_k\equiv k^{3∕2}{\varphi }_k∕m_{\mathrm{pl}}$ on cosmological scales during inflation and preheating for $g^2∕\lambda =2$. With the use of the Hartree approximation we find that super-Hubble metric perturbations are amplified during preheating.

Figure 16

The evolution of $\zeta$, ${\zeta }_{\varphi }$, and ${\zeta }_{\gamma }$ (normalized by $\delta \Gamma ∕\Gamma$) in the modulated reheating scenario with initial conditions ${\Omega }_{\varphi }\left(0\right)=0.99$, ${\Omega }_{\gamma }\left(0\right)=0.01$, $g=0.01$, $\zeta \left(0\right)=0.0$, and ${\zeta }_{\varphi }\left(0\right)=0.0$.