We study the problem of scalar particle production after inflation by an inflaton field which is oscillating rapidly relative to the expansion of the universe. We use the framework of the chaotic inflation scenario with quartic and quadratic inflaton potentials. Particles produced are described by a quantum scalar field χ, which is coupled to the inflaton via linear and quadratic couplings. The particle production effect is studied using the standard technique of Bogolyubov transformations. Particular attention is paid to parametric resonance phenomena which take place in the presence of the quickly oscillating inflaton field. We have found that in the region of applicability of perturbation theory the effects of parametric resonance are crucial, and estimates based on first-order Born approximation often underestimate the particle production. In the case of the quartic inflaton potential V(cphi)=λ${\mathit{cphi}}^4$, the particle production process is very efficient for either type of coupling between the inflaton field and the scalar field χ even for small values of coupling constants. The energy density of the universe after the decay of the inflaton oscillations is in this case a factor [λ ln(1/λ)${]}^{\mathrm{-}1}$ times larger than the corresponding estimates based on first-order Born approximation. In the case of the quadratic inflaton potential the reheating process depends crucially on the type of coupling between the inflaton and the scalar field χ and on the magnitudes of the coupling constants. If the inflaton coupling to fermions and its linear (in inflaton field) coupling to scalar fields are suppressed, then, as previously discussed by Kofman, Linde, and Starobinsky, the inflaton field will eventually decouple from the rest of the matter, and the residual inflaton oscillations may provide the (cold) dark matter of the universe. In the case of the quadratic inflaton potential we obtain the lowest and the highest possible bounds on the effective energy density of the inflaton field when it freezes out.

We explore a new class of braneworld models in which the scalar curvature of the (induced) brane metric contributes to the brane action. The scalar curvature term arises generically on account of one-loop effects induced by matter fields residing on the brane. Spatially flat braneworld models can enter into a regime of accelerated expansion at late times. This is true even if the brane tension and the bulk cosmological constant are tuned to satisfy the Randall–Sundrum constraint on the brane. Braneworld models admit a wider range of possibilities for dark energy than standard LCDM. In these models the luminosity distance can be both smaller and larger than the luminosity distance in LCDM. Whereas models withd_L⩽d_L(LCDM) implyw=p/ρ ⩾ −1 and have frequently been discussed in the literature, models withd_L>d_L(LCDM) have traditionally been ignored, perhaps because, within the general-relativistic framework, the luminosity distance has this propertyonly ifthe equation of state of matter is strongly negative (w< −1). Within the conventional framework, `phantom energy' withw< −1 is beset with a host of undesirable properties, which makes this model of dark energy unattractive. Braneworld models, on the other hand, have the capacity to endow dark energy with exciting new possibilities (includingw< −1) without suffering from the problems faced by phantom energy. For a subclass of parameter values, braneworld dark energy and the acceleration of the universe aretransientphenomena. In these models, the universe, after the current period of acceleration, re-enters the matter-dominated regime so that the deceleration parameterq(t) → 0.5 whent>>t₀, wheret₀is the present epoch. Such models could help reconcile an accelerating universe with the requirements of string/M-theory.

We study cosmological braneworld models with a single timelike extra dimension. Such models admit the intriguing possibility that a contracting braneworld experiences a natural bounce without ever reaching a singular state. This feature persists in the case of anisotropic braneworlds under some additional and not very restrictive assumptions. Generalizing our study to braneworld models containing an induced brane curvature term, we find that a FRW-type singularity is once again absent if the bulk extra dimension is timelike. In this case, the universe either has a non-singular origin or commences its expansion from a quasi-singular state during which both the Hubble parameter and the energy density and pressure remain finite while the curvature tensor diverges. The non-singular and quasi-singular behaviour which we have discovered differs both qualitatively and quantitatively from what is usually observed in braneworld models with spacelike extra dimensions and could have interesting cosmological implications.