Edmund J. Copeland

Dynamics of dark energy

We review in detail a number of approaches that have been adopted to try and explain the remarkable observation of our accelerating universe. In particular we discuss the arguments for and recent progress made towards understanding the nature of dark energy. We review the observational evidence for the current accelerated expansion of the universe and present a number of dark energy models in addition to the conventional cosmological constant, paying particular attention to scalar field models such as quintessence, K-essence, tachyon, phantom and dilatonic models. The importance of cosmological scaling solutions is emphasized when studying the dynamical system of scalar fields including coupled dark energy. We study the evolution of cosmological perturbations allowing us to confront them with the observation of the Cosmic Microwave Background and Large Scale Structure and demonstrate how it is possible in principle to reconstruct the equation of state of dark energy by also using Supernovae Ia observational data. We also discuss in detail the nature of tracking solutions in cosmology, particle physics and braneworld models of dark energy, the nature of possible future singularities, the effect of higher order curvature terms to avoid a Big Rip singularity, and approaches to modifying gravity which leads to a late-time accelerated expansion without recourse to a new form of dark energy.

Exponential potentials and cosmological scaling solutions

Scalar fields have come to play a central role in current models of the early universe. The self-interaction potential energy density of such a field is undiluted by the expansion of the universe and hence can act like an effective cosmological constant driving a period of inflation. The detailed evolution is dependent upon the specific form of the potential V as a function of the scalar field’s expectation value φ. A common functional form for the self-interaction potential is an exponential dependence upon the scalar field. It is to be found in higher-order [1] or higher-dimensional gravity theories [2]. In string or Kaluza–Klein type models the moduli fields associated with the geometry of the extra dimensions may have effective exponential potentials due to curvature of the internal spaces, or the interaction of moduli with form fields on the internal spaces. Exponential potentials can also arise due to nonperturbative effects such as gaugino condensation [3]. The possible cosmological roles of exponential potentials have been investigated before, but almost always as a means of driving a period of cosmological inflation [4,5]. This requires potentials that are much flatter than those usually found in particle physics models. The purpose of this paper is to emphasize that scalar fields with exponential potentials may still have important cosmological consequences even if they are too steep to drive a period of inflation [6–8]. We will present a phase-plane analysis to show that scalar fields with exponential potentials contribute a non-negligible energy density at nucleosynthesis unless they are unusually steep. This ‘relic density’ problem is not alleviated by standard models of inflation.

Cosmic F- and D-strings

Macroscopic fundamental and Dirichlet strings have several potential instabilities: breakage, tachyon decays, and confinement by axion domain walls. We investigate the conditions under which metastable strings can exist, and we find that such strings are present in many models. There are various possibilities, the most notable being a network of (p,q) strings. Cosmic strings give a potentially large window into string physics.

Quintessence arising from exponential potentials

We demonstrate how the properties of the attractor solutions of exponential potentials can lead to models of quintessence with the currently observationally favored equation of state. Moreover, we show that these properties hold for a wide range of initial conditions and for natural values of model parameters. PACS number~s!: 98.80.Cq

General second-order scalar-tensor theory and self-tuning

Starting from the most general scalar-tensor theory with second order field equations in four dimensions, we establish the unique action that will allow for the existence of a consistent selftuning mechanism on FLRW backgrounds, and show how it can be understood as a combination of just four base Lagrangians with an intriguing geometric structure dependent on the Ricci scalar, the Einstein tensor, the double dual of the Riemann tensor and the Gauss-Bonnet combination. Spacetime curvature can be screened from the net cosmological constant at any given moment because we allow the scalar field to break Poincaré invariance on the self-tuning vacua, thereby evading the Weinberg no-go theorem. We show how the four arbitrary functions of the scalar field combine in an elegant way opening up the possibility of obtaining non-trivial cosmological solutions.

What is needed of a tachyon if it is to be the dark energy

We study a dark energy scenario in the presence of a tachyon field {phi} with potential V({phi}) and a barotropic perfect fluid. The cosmological dynamics crucially depends on the asymptotic behavior of the quantity {lambda}=-M{sub p}V{sub {phi}}/V{sup 3/2}. If {lambda} is a constant, which corresponds to an inverse square potential V({phi}){proportional_to}{phi}{sup -2}, there exists one stable critical point that gives an acceleration of the Universe at late times. When {lambda}{yields}0 asymptotically, we can have a viable dark energy scenario in which the system approaches an instantaneous critical point that dynamically changes with {lambda}. If |{lambda}| approaches infinity asymptotically, the Universe does not exhibit an acceleration at late times. In this case, however, we find an interesting possibility that a transient acceleration occurs in a regime where |{lambda}| is smaller than of order unity.

Foundations of observing dark energy dynamics with the Wilkinson Microwave Anisotropy Probe

Detecting dark energy dynamics is the main quest of current dark energy research. Addressing the issue demands a fully consistent analysis of cosmic microwave background, large-scale structure and SN-Ia data with multiparameter freedom valid for all redshifts. Here we undertake a ten parameter analysis of general dark energy confronted with the first year Wilkinson Microwave Anisotropy Probe, 2dF galaxy survey and latest SN-Ia data. Despite the huge freedom in dark energy dynamics there are no new degeneracies with standard cosmic parameters apart from a mild degeneracy between reionization and the redshift of acceleration, both of which effectively suppress small scale power. Breaking this degeneracy will help significantly in detecting dynamics, if it exists. Our best-fit model to the data has significant late-time evolution at z<1.5. Phantom models are also considered and we find that the best-fit crosses w =-1 which, if confirmed, would be a clear signal for radically new physics. Treatment of such rapidly varying models requires careful integration of the dark energy density usually not implemented in standard codes, leading to crucial errors of up to 5%. Nevertheless cosmic variance means that standard Lambda cold dark matter models are still a very good fit to the data and evidence for dynamics is currently very weak. Independent tests of reionization or the epoch of acceleration (e.g., integrated Sachs-Wolfelarge scale structure correlations) or reduction of cosmic variance at large scales (e.g., cluster polarization at high redshift) may prove key in the hunt for dynamics.

A new view of k-essence

K-essence models, relying on scalar fields with non-canonical kinetic terms, have been proposed as an alternative to quintessence in explaining the observed acceleration of the Universe. We consider the use of field redefinitions to cast k-essence in a more familiar form. While k-essence models cannot in general be rewritten in the form of quintessence models, we show that in certain dynamical regimes an equivalence can be made, which in particular can shed light on the tracking behaviour of k-essence. In several cases, k-essence cannot be observationally distinguished from quintessence using the homogeneous evolution, though there may be small effects on the perturbation spectrum. We make a detailed analysis of two k-essence models from the literature and comment on the nature of the fine tuning arising in the models.

Steep inflation: ending braneworld inflation by gravitational particle production

We propose a scenario for inflation based upon the braneworld picture, in which high-energy corrections to the Friedmann equation permit inflation to take place with potentials ordinarily too steep to sustain it. Inflation ends when the braneworld corrections begin to lose their dominance. Reheating may naturally be brought about via gravitational particle production, rather than the usual inflaton decay mechanism; the reheat temperature may be low enough to satisfy the gravitino bound and the Universe becomes radiation dominated early enough for nucleosynthesis. We illustrate the idea by considering steep exponential potentials, and show they can give satisfactory density perturbations (both amplitude and slope) and reheat successfully. The scalar field may survive to the present epoch without violating observational bounds, and could be invoked in the quintessential inflation scenario of Peebles and Vilenkin.

Low energy effective string cosmology

We give the general analytic solutions derived from the low energy string effective action for four-dimensional Friedmann-Robertson-Walker models with a dilaton and antisymmetric tensor field, considering both long and short wavelength modes of the [ital H] field. The presence of a homogeneous [ital H] field significantly modifies the evolution of the scale factor and dilaton. In particular it places a lower bound on the allowed value of the dilaton. The scale factor also has a lower bound but our solutions remain singular as they all contain regions where the spacetime curvature diverges signalling a breakdown in the validity of the effective action. We extend our results to the simplest Bianchi type I metric in higher dimensions with only two scale factors. We again give the general analytic solutions for long and short wavelength modes for the [ital H] field restricted to the three-dimensional space, which produces an anisotropic expansion. In the case of [ital H] field radiation (wavelengths within the Hubble length) we obtain the usual four-dimensional radiation-dominated FRW model as the unique late time attractor.