Our understanding of the state of the universe between the end of inflation and big bang nucleosynthesis (BBN) is incomplete. The dynamics at the end of inflation are rich and a potential source of observational signatures. Reheating, the energy transfer between the inflaton and Standard Model fields (possibly through intermediaries) and their subsequent thermalization, can provide clues to how inflation fits in with known high-energy physics. We provide an overview of our current understanding of the nonperturbative, nonlinear dynamics at the end of inflation, some salient features of realistic particle physics models of reheating, and how the universe reaches a thermal state before BBN. In addition, we review the analytical and numerical tools available in the literature to study preheating and reheating and discuss potential observational signatures from this fascinating era.

We present a detailed investigation of a sub-dominant oscillating scalar field ('early dark energy', EDE) in the context of resolving the Hubble tension. Consistent with earlier work, but without relying on fluid approximations, we find that a scalar field frozen due to Hubble friction until log 10 (zc) ∼ 3.5, reaching ρEDE(zc)/ρtot ∼ 10%, and diluting faster than matter afterwards can bring cosmic microwave background (CMB), baryonic acoustic oscillations, supernovae luminosity distances, and the late-time estimate of the Hubble constant from the SH0ES collaboration into agreement. A scalar field potential which scales as V (φ) ∝ φ 2n with 2 n 3.4 around the minimum is preferred at the 68% confidence level, and the Planck polarization places additional constraints on the dynamics of perturbations in the scalar field. In particular, the data prefers a potential which flattens at large field displacements. An MCMC analysis of mock data shows that the next-generation CMB observations (i.e., CMB-S4) can unambiguously detect the presence of the EDE at very high significance. This projected sensitivity to the EDE dynamics is mainly driven by improved measurements of the E-mode polarization.We also explore new observational signatures of EDE scalar field dynamics: (i) We find that depending on the strength of the tensor-to-scalar ratio, the presence of the EDE might imply the existence of isocurvature perturbations in the CMB. (ii) We show that a strikingly rapid, scaledependent growth of EDE field perturbations can result from parametric resonance driven by the anharmonic oscillating field for n ≈ 2. This instability and ensuing potentially nonlinear, spatially inhomogenoues, dynamics may provide unique signatures of this scenario. CONTENTS

Oscillons are massive, long-lived, localized excitations of a scalar field. We show that in a class of well-motivated single-field models, inflation is followed by self resonance, leading to copious oscillon generation and a lengthy period of oscillon domination. These models are characterized by an inflaton potential which has a quadratic minimum and is shallower than quadratic away from the minimum. This set includes both string monodromy models and a class of supergravity inspired scenarios and is in good agreement with the current central values of the concordance cosmology parameters. We assume that the inflaton is weakly coupled to other fields so as not to quickly drain energy from the oscillons or prevent them from forming. An oscillon-dominated universe has a greatly enhanced primordial power spectrum on very small scales relative to that seen with a quadratic potential, possibly leading to novel gravitational effects in the early Universe.

Homogeneous oscillations of the inflaton after inflation can be unstable to small spatial perturbations even without coupling to other fields. We show that for inflaton potentials ∝ jϕj 2n near jϕj ¼ 0 and flatter beyond some jϕj ¼ M, the inflaton condensate oscillations can lead to self-resonance, followed by its complete fragmentation. We find that for nonquadratic minima (n > 1), shortly after backreaction, the equation of state parameter, w → 1=3. If M ≪ m Pl , radiation domination is established within less than an e-fold of expansion after the end of inflation. In this case self-resonance is efficient and the condensate fragments into transient, localised spherical objects which are unstable and decay, leaving behind them a virialized field with mean kinetic and gradient energies much greater than the potential energy. This end-state yields w ¼ 1=3. When M ∼ m Pl we observe slow and steady, self-resonance that can last many e-folds before backreaction eventually shuts it off, followed by fragmentation and w → 1=3. We provide analytical estimates for the duration to w → 1=3 after inflation, which can be used as an upper bound (under certain assumptions) on the duration of the transition between the inflationary and the radiation dominated states of expansion. This upper bound can reduce uncertainties in CMB observables such as the spectral tilt n s , and the tensor-to-scalar ratio r. For quadratic minima (n ¼ 1), w → 0 regardless of the value of M. This is because when M ≪ m Pl , long-lived oscillons form within an e-fold after inflation, and collectively behave as pressureless dust thereafter. For M ∼ m Pl , the self-resonance is inefficient and the condensate remains intact (ignoring longterm gravitational clustering) and keeps oscillating about the quadratic minimum, again implying w ¼ 0.

We present and employ a new kinematical approach to cosmological `dark energy' studies. We construct models in terms of the dimensionless second and third derivatives of the scale factor a(t) with respect to cosmic time t, namely the present-day value of the deceleration parameter q_0 and the cosmic jerk parameter, j(t). An elegant feature of this parameterization is that all LCDM models have j(t)=1 (constant), which facilitates simple tests for departures from the LCDM paradigm. Applying our model to the three best available sets of redshift-independent distance measurements, from type Ia supernovae and X-ray cluster gas mass fraction measurements, we obtain clear statistical evidence for a late time transition from a decelerating to an accelerating phase. For a flat model with constant jerk, j(t)=j, we measure q_0=-0.81+-0.14 and j=2.16+0.81-0.75, results that are consistent with LCDM at about the 1sigma confidence level. A standard `dynamical' analysis of the same data, employing the Friedmann equations and modeling the dark energy as a fluid with an equation of state parameter, w (constant), gives Omega_m=0.306+0.042-0.040 and w=-1.15+0.14-0.18, also consistent with LCDM at about the 1sigma level. In comparison to dynamical analyses, the kinematical approach uses a different model set and employs a minimum of prior information, being independent of any particular gravity theory. The results obtained with this new approach therefore provide important additional information and we argue that both kinematical and dynamical techniques should be employed in future dark energy studies, where possible. Our results provide further interesting support for the concordance LCDM paradigm.Comment: 12 pages, 5 figures, 2 tables. Accepted for publication in MNRA