Scale Invariance via a Phase of Slow Expansion

We consider a cosmological scenario in which a scale-invariant spectrum of curvature perturbations is generated by a rapidly-evolving equation of state on a slowly expanding background. This scenario generalizes the "adiabatic ekpyrotic" mechanism proposed recently in arXiv:0910.2230. Whereas the original proposal assumed a slowly contracting background, the present work shows that the mechanism works equally well on an expanding background. This greatly expands the realm of broader cosmological scenarios in which this mechanism can be embedded. We present a phase space analysis and show that both the expanding and contracting versions of the scenario are dynamical attractors, with the expanding branch having a broader basin of attraction. In both cases, a finite range of scale invariant modes can be generated within the regime of validity of perturbation theory.Comment: 34 pages, 5 figure

Strong Coupling Problem with Time-Varying Sound Speed

For a single scalar field with unit sound speed minimally coupled to Einstein gravity, there are exactly three distinct cosmological solutions which produce a scale invariant spectrum of curvature perturbations in a dynamical attractor background, assuming vacuum initial conditions: slow-roll inflation; a slowly contracting adiabatic ekpyrotic phase, described by a rapidly-varying equation of state; and an adiabatic ekpyrotic phase on a slowly expanding background. Of these three, only inflation remains weakly coupled over a wide range of modes, the other scenarios can produce at most 12 e-folds of scale invariant and gaussian modes. In this paper, we investigate how allowing the speed of sound of fluctuations to evolve in time affects this classification. While in the presence of a variable sound speed there are many more scenarios which are scale invariant at the level of the two-point function, they generically suffer from strong coupling problems similar to those in the canonical case. There is, however, an exceptional case with superluminal sound speed, which suppresses non-gaussianities and somewhat alleviates strong coupling issues. We focus on a particular realization of this limit and show these scenarios are constrained and only able to produce at most 28 e-folds of scale invariant and gaussian perturbations. A similar bound should hold more generally --- the condition results from the combined requirements of matching the observed amplitude of curvature perturbations, demanding that the Hubble parameter remain sub-Planckian and keeping non-gaussianities under control. We therefore conclude that inflation remains the unique scenario, assuming a single degree of freedom on an attractor background, capable of producing arbitrarily many scale invariant modes while remaining weakly coupled. Alternative mechanisms must inevitably be unstable or rely on multiple degrees of freedom.Comment: 23 pages, 1 figure, v2: minor edits, version to appear in PR

Dark Energy vs. Modified Gravity

Understanding the reason for the observed accelerated expansion of the Universe represents one of the fundamental open questions in physics. In cosmology, a classification has emerged among physical models for the acceleration, distinguishing between Dark Energy and Modified Gravity. In this review, we give a brief overview of models in both categories as well as their phenomenology and characteristic observable signatures in cosmology. We also introduce a rigorous distinction between Dark Energy and Modified Gravity based on the strong and weak equivalence principles.Comment: 29 pages, 4 figures; invited review submitted to Annual Reviews of Nuclear and Particle Science; v2: some pertinent references added; v3: table with constraints added, reflects published version; v4 [trivial]: fixed missing references in arxiv versio

Massive Spin-2 Scattering and Asymptotic Superluminality

We place model-independent constraints on theories of massive spin-2 particles by considering the positivity of the phase shift in eikonal scattering. The phase shift is an asymptotic $S$-matrix observable, related to the time delay/advance experienced by a particle during scattering. Demanding the absence of a time advance leads to constraints on the cubic vertices present in the theory. We find that, in theories with massive spin-2 particles, requiring no time advance means that either: (i) the cubic vertices must appear as a particular linear combination of the Einstein-Hilbert cubic vertex and an $h_{\mu\nu}^3$ potential term or (ii) new degrees of freedom or strong coupling must enter at parametrically the mass of the massive spin-2 field. These conclusions have implications for a variety of situations. Applied to theories of large-$N$ QCD, this indicates that any spectrum with an isolated massive spin-2 at the bottom must have these particular cubic self-couplings. Applied to de Rham-Gabadadze-Tolley massive gravity, the constraint is in accord with and generalizes previous results obtained from a shockwave calculation: of the two free dimensionless parameters in the theory there is a one parameter line consistent with a subluminal phase shift.Comment: 46 pages, 1 figure. v2: Minor corrections. v3: Minor edits; orthogonalized \oplus tensor polarizations. Results are unaffecte

Conformality Lost: Broken Symmetries in the Early Universe

In this dissertation, we introduce and investigate a general framework to describe the dynamics of the early universe. This mechanism is based on spontaneously broken conformal symmetry; we find that spectator fields in the theory can acquire a scale invariant spectrum of perturbations under generic conditions. Before introducing the conformal mechanism, we first consider the landscape of cosmologies involving a single scalar field which can address the canonical early universe puzzles. We find that, generically, single field non-inflationary solutions become strongly-coupled. We are therefore led to consider theories with multiple fields. We introduce the conformal mechanism via specific examples before constructing the most general effective theory for the conformal mechanism by utilizing the coset construction familiar from particle physics to construct the lagrangian for the Goldstone field of the broken conformal symmetry. This theory may be observationally distinguished from inflation by considering the non-linearly realized conformal symmetries. We systematically derive the Ward identities associated to the non-linearly realized symmetries, which relate (N+1)-point correlation functions with a soft external Goldstone to N-point functions, and discuss observational implications, which cannot be mimicked by inflation. Finally, we consider violating the null energy condition (NEC) within the general framework considered. We show that the DBI conformal galileons, derived from the world-volume theory of a 3-brane moving in an Anti-de Sitter bulk, admit a background which violates the NEC. Unlike other known examples of NEC violation, such as ghost condensation and conformal galileons, this theory also admits a stable, Poincaré-invariant vacuum. However, perturbations around deformations of this solution propagate superluminally

Consistency Relations for the Conformal Mechanism

We systematically derive the consistency relations associated to the non-linearly realized symmetries of theories with spontaneously broken conformal symmetry but with a linearly-realized de Sitter subalgebra. These identities relate (N+1)-point correlation functions with a soft external Goldstone to N-point functions. These relations have direct implications for the recently proposed conformal mechanism for generating density perturbations in the early universe. We study the observational consequences, in particular a novel one-loop contribution to the four-point function, relevant for the stochastic scale-dependent bias and CMB mu-distortion.Comment: 34 pages, 3 figures. v2: minor changes, version appearing in JCA