The Eternal Sunshine of the Spotless Mind

We extend the worldline measure for pocket formation in eternal inflation to allow for time-ordered bubble formation. Such a time-ordering is equivalent to imposing a preferred time-slicing on the "parent" de Sitter space. Using this measure, we describe a covariant version of the youngness paradox and show that the youngness paradox is a gauge artifact if the parent spacetime is an unbroken de Sitter space, due to the lack of an explicit time-ordering for the bubble nucleation events. We then show that one can add a "clock" to the de Sitter space, in the form of a vector field with a spontaneously broken symmetry that defines a unique timelike direction accessible to all observers. Once this is done, the existence of a preferred slicing means that the youngness paradox cannot be easily resolved. We use this to elucidate the apparent "persistence of memory" discussed recently by Garriga, Guth and Vilenkin, for inflationary universes produced by bubble nucleation.Comment: 18 pages, 5 figure

Haloes of k-Essence

We study gravitationally bound static and spherically symmetric configurations of k-essence fields. In particular, we investigate whether these configurations can reproduce the properties of dark matter haloes. The classes of Lagrangians we consider lead to non-isotropic fluids with barotropic and polytropic equations of state. The latter include microscopic realizations of the often-considered Chaplygin gases, which we find can cluster into dark matter halo-like objects with flat rotation curves, while exhibiting a dark energy-like negative pressure on cosmological scales. We complement our studies with a series of formal general results about the stability and initial value formulation of non-canonical scalar field theories, and we also discuss a new class of de Sitter solutions with spacelike field gradients.Comment: 34pages, single column double spacing, 7 figures, 3 Tables, RevTex4. Additional references and minor clarifications. To be submitted to JCA

Formulating Weak Lensing from the Boltzmann Equation and Application to Lens-lens Couplings

The Planck mission has conclusively detected lensing of the Cosmic Microwave Background (CMB) radiation from foreground sources to an overall significance of greater than $25\sigma$. The high precision of this measurement motivates the development of a more complete formulation of the calculation of this effect. While most effects on the CMB anisotropies are widely studied through direct solutions of the Boltzmann equation, the non-linear effect of CMB lensing is formulated through the solutions of the geodesic equation. In this paper, we present a new formalism to the calculation of the lensing effect by \emph{directly solving the Boltzmann equation}, as we did in the calculation of the CMB anisotropies at recombination. In particular, we developed a diagrammatic approach to efficiently keep track of all the interaction terms and calculate all possible non-trivial correlations to arbitrary high orders. Using this formalism, we explicitly articulate the approximations required to recover the usual remapping approach used in current studies of the weak lensing. In addition, we point out additional unexplored corrections that are manifest in our formalism to which experiments may be sensitive. As an example, we calculate the correction to the CMB temperature power spectrum for the \emph{lens-lens} coupling effects which are neglected in standard calculations. We find that the correction is $\lesssim 0.1\%$ of the CMB temperature power spectrum for $\ell$ up to 3000 and thus is comparable to the cosmic variance.Comment: 25 pages, 3 figures, 4 tables, CMB, lensin

Lorentz-Violating Vector Fields Slow the Universe Down

We consider the gravitational effects of a single, fixed-norm, Lorentz-violating timelike vector field. In a cosmological background, such a vector field acts to rescale the effective value of Newton's constant. The energy density of this vector field precisely tracks the energy density of the rest of the universe, but with the opposite sign, so that the universe experiences a slower rate of expansion for a given matter content. This vector field similarly rescales Newton's constant in the Newtonian limit, although by a different factor. We put constraints on the parameters of the theory using the predictions of primordial nucleosynthesis, demonstrating that the norm of the vector field should be less than the Planck scale by an order of magnitude or more.Comment: 15 pages, Revtex4, updated version. Added References. Minor Typos corrected. Older version published in PR

Dust of Dark Energy

We introduce a novel class of field theories where energy always flows along timelike geodesics, mimicking in that respect dust, yet which possess non-zero pressure. This theory comprises two scalar fields, one of which is a Lagrange multiplier enforcing a constraint between the other's field value and derivative. We show that this system possesses no wave-like modes but retains a single dynamical degree of freedom. Thus, the sound speed is always identically zero on all backgrounds. In particular, cosmological perturbations reproduce the standard behaviour for hydrodynamics with vanishing sound speed. Using all these properties we propose a model unifying Dark Matter and Dark Energy in a single degree of freedom. In a certain limit this model exactly reproduces the evolution history of Lambda-CDM, while deviations away from the standard expansion history produce a potentially measurable difference in the evolution of structure.Comment: 13 pages, 3 figures. Added references, corrected language

3-pt Statistics of Cosmological Stochastic Gravitational Waves

We consider the 3-pt function (i.e. the bispectrum or non-Gaussianity) for stochastic backgrounds of gravitational waves. We estimate the amplitude of this signal for the primordial inflationary background, gravitational waves generated during preheating, and for gravitational waves produced by self-ordering scalar fields following a global phase transition. To assess detectability, we describe how to extract the 3-pt signal from an idealized interferometric experiment and compute the signal to noise ratio as a function of integration time. The 3-pt signal for the stochastic gravitational wave background generated by inflation is unsurprisingly tiny. For gravitational radiation generated by purely causal, classical mechanisms we find that, no matter how non-linear the process is, the 3-pt correlations produced vanish in direct detection experiments. On the other hand, we show that in scenarios where the B-mode of the CMB is sourced by gravitational waves generated by a global phase transition, a strong 3-pt signal among the polarization modes could also be produced. This may provide another method of distinguishing inflationary B-modes. To carry out this computation, we have developed a diagrammatic approach to the calculation of stochastic gravitational waves sourced by scalar fluids, which has applications beyond the present scenario.Comment: 16 pages, 5 figure

A scattering theory of ultrarelativistic solitons

We construct a perturbative framework for understanding the collision of solitons (more precisely, solitary waves) in relativistic scalar field theories. Our perturbative framework is based on the suppression of the space-time interaction area proportional to $1/(\gamma v)$, where $v$ is the relative velocity of an incoming solitary wave and $\gamma = 1/\sqrt{1-v^2} \gg 1$. We calculate the leading order results for collisions of (1+1) dimensional kinks in periodic potentials, and provide explicit, closed form expressions for the phase shift and the velocity change after the collisions. We find excellent agreement between our results and detailed numerical simulations. Crucially, our perturbation series is controlled by a kinematic parameter, and hence not restricted to small deviations around integrable cases such as the Sine-Gordon model.Comment: v3: 43 pages, 10 figures, references added, matches version accepted for publication in PR

Gravitational Wave Production At The End Of Inflation

We consider gravitational wave production due to parametric resonance at the end of inflation, or ``preheating''. This leads to large inhomogeneities which source a stochastic background of gravitational waves at scales inside the comoving Hubble horizon at the end of inflation. We confirm that the present amplitude of these gravitational waves need not depend on the inflationary energy scale. We analyze an explicit model where the inflationary energy scale is ~10^9 GeV, yielding a signal close to the sensitivity of Advanced LIGO and BBO. This signal highlights the possibility of a new observational ``window'' into inflationary physics, and provides significant motivation for searches for stochastic backgrounds of gravitational waves in the Hz to GHz range, with an amplitude on the order of \Omega_{gw}(k)h^2 ~ 10^-11. Finally, the strategy used in our numerical computations is applicable to the gravitational waves generated by many inhomogeneous processes in the early universe.Comment: 4 pages, Revtex, 2 figures. v2 References added, discussion clarified and improved. v3 further clarification, typo regarding source corrected. Basic results unchange