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 (ϕ) = λϕ 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 reheating temperature of the universe in this case is [λ log (1/λ)] −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 (see e.g. Ref. 13), 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.2

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 lu- Within the conventional framework, 'phantom energy' with w < −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 (including w < −1) without suffering from the problems faced by phantom energy. For a sub-1 class of parameter values, braneworld dark energy and the acceleration of the universe are transient phenomena. In these models, the universe, after the current period of acceleration, re-enters the matter-dominated regime so that the deceleration parameter q(t) → 0.5 when t ≫ t 0 , where t 0 is 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.Typeset using REVT E X 1

Higher-dimensional braneworld models which contain both bulk and brane curvature terms in the action admit cosmological singularities of rather unusual form and nature. These 'quiescent' singularities, which can occur both during the contracting as well as the expanding phase, are characterised by the fact that while the matter density and Hubble parameter remain finite, all higher derivatives of the scale factor ( .. a, ... a etc.) diverge as the cosmological singularity is approached. The singularities are the result of the embedding of the (3+1)-dimensional brane in the bulk and can exist even in an empty homogeneous and isotropic (FRW) universe. The possibility that the present universe may expand into a singular state is discussed.

Abstract. For a broad range of parameter values, braneworld models display a remarkable property which we call cosmic mimicry. Cosmic mimicry is characterized by the fact that, at low redshifts, the Hubble parameter in the braneworld model is virtually indistinguishable from that in the LCDM (Λ + Cold Dark Matter) cosmology. An important point to note is that the Ω m parameters in the braneworld model and in the LCDM cosmology can nevertheless be quite different. Thus, at high redshifts (early times), the braneworld asymptotically expands like a matter-dominated universe with the value of Ω m inferred from the observations of the local matter density. At low redshifts (late times), the braneworld model behaves almost exactly like the LCDM model but with a renormalized value of the cosmological density parameter Ω is smaller (larger) than Ω m in the braneworld model with positive (negative) brane tension. The redshift which characterizes cosmic mimicry is related to the parameters in the higher-dimensional braneworld Lagrangian. Cosmic mimicry is a natural consequence of the scale-dependence of gravity in braneworld models. The change in the value of the cosmological density parameter (from Ω m at high z to Ω LCDM m at low z) is shown to be related to the spatial dependence of the effective gravitational constant G eff in braneworld theory. A subclass of mimicry models lead to an older age of the universe and also predict a redshift of reionization which is lower than z reion ≃ 17 in the LCDM cosmology. These models might therefore provide a background cosmology which is in better agreement both with the observed quasar abundance at z > ∼ 4 and with the large optical depth to reionization measured by the Wilkinson Microwave Anisotropy Probe.

We examine the behaviour of a closed oscillating universe filled with a homogeneous scalar field and find that, contrary to naive expectations, such a universe expands to larger volumes during successive expansion epochs. This intriguing behaviour introduces an arrow of time in a system which is timereversible. The increase in the maximum size of the universe is closely related to the work done on/by the scalar field during one complete oscillatory cycle which, in turn, is related to the asymmetry in the scalar field equation of state during expansion and collapse. Our analysis shows that scalar fields with polynomial potentials V (φ) = λφ q , q > 1 lead to a growing oscillation amplitude for the universe: the increase in amplitude between successive oscillations is more significant for smaller values of q. Such behaviour allows for the effective recycling of the universe. A recycled universe can be quite old and can resolve the flatness problem. These results have strong bearing on cosmological models in which the role of dark matter is played by a scalar field. They are also relevant for chaotic inflationary models of the early universe since they demonstrate that, even if the universe fails to inflate the first time around, it will eventually do so during future oscillatory cycles. Thus, the space of initial conditions favourable for chaotic inflation increases significantly.

We continue the study of the non-metric theory of gravity introduced in hep-th/0611182 and gr-qc/0703002 and obtain its general spherically symmetric vacuum solution. It respects the analog of the Birkhoff theorem, i.e., the vacuum spherically symmetric solution is necessarily static. As in general relativity, the spherically symmetric solution is seen to describe a black hole. The exterior geometry is essentially the same as in the Schwarzschild case, with power-law corrections to the Newtonian potential. The behavior inside the black-hole region is different from the Schwarzschild case in that the usual spacetime singularity gets replaced by a singular surface of a new type, where all basic fields of the theory remain finite but metric ceases to exist. The theory does not admit arbitrarily small black holes: for small objects, the curvature on the would-be horizon is so strong that non-metric modifications prevent the horizon from being formed.The theory allows for modifications of gravity of very interesting nature. We discuss three physical effects, namely, (i) correction to Newton's law in the neighborhood of the source, (ii) renormalization of effective gravitational and cosmological constants at large distances from the source, and (iii) additional redshift factor between spatial regions of different curvature. The first two effects can be responsible, respectively, for the observed anomaly in the acceleration of the Pioneer spacecraft and for the alleged missing mass in spiral galaxies and other astrophysical objects.The third effect can be used to propose a non-cosmological explanation of high redshifts of quasars and gamma-ray bursts.

We show that loitering at high redshifts (z > ∼ 6) can easily arise in braneworld models of dark energy which, in addition to being spatially flat, also accelerate at late times. Loitering is characterized by the fact that the Hubble parameter dips in value over a narrow redshift range which we shall refer to as the 'loitering epoch'. During loitering, density perturbations are expected to grow rapidly. In addition, since the expansion of the universe slows down, its age near loitering dramatically increases. An early epoch of loitering is expected to boost the formation of high redshift gravitationally bound systems such as 10 9 M ⊙ black holes at z ∼ 6 and lower-mass black holes and/or Population III stars at z > 10, whose existence could be problematic within the LCDM scenario. Loitering models also help to reduce the redshift of reionization from its currently (high) value of z reion ≃ 17 in LCDM cosmology, thus alleviating a significant source of tension between observations of the high-redshift universe and theoretical model building. Currently a loitering universe accelerates with an effective equation of state w < −1 thus mimicking phantom dark energy. Unlike phantom, however, the late-time expansion of the universe in our model is singularity free, and a universe that loitered in the past will approach a LCDM model asymptotically in the distant future.