arXiv subjects

Neil Barnaby

Publications and source records attributed to Neil Barnaby.

28 records · Page 2Linked to original sources

arXiv2008

Dynamics with Infinitely Many Derivatives: Variable Coefficient Equations

Infinite order differential equations have come to play an increasingly significant role in theoretical physics. Field theories with infinitely many derivatives are ubiquitous in string field theory and have attracted interest recently also from cosmologists. Crucial to any application is a firm understanding of the mathematical structure of infinite order partial differential equations. In our previous work we developed a formalism to study the initial value problem for linear infinite order equations with constant coefficients. Our approach relied on the use of a contour integral representation for the functions under consideration. In many applications, including the study of cosmological perturbations in nonlocal inflation, one must solve linearized partial differential equations about some time-dependent background. This typically leads to variable coefficient equations, in which case the contour integral methods employed previously become inappropriate. In this paper we develop the theory of a particular class of linear infinite order partial differential equations with variable coefficients. Our formalism is particularly well suited to the types of equations that arise in nonlocal cosmological perturbation theory. As an example to illustrate our formalism we compute the leading corrections to the scalar field perturbations in p-adic inflation and show explicitly that these are small on large scales.

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arXiv2008

Predictions for Nongaussianity from Nonlocal Inflation

In our previous work the nonlinearity parameter f_NL, which characterizes nongaussianity in the cosmic microwave background, was estimated for a class of inflationary models based on nonlocal field theory. These models include p-adic inflation and generically have the remarkable property that slow roll inflation can proceed even with an extremely steep potential. Previous calculations found that large nongaussianity is possible; however, the technical complications associated with studying perturbations in theories with infinitely many derivatives forced us to provide only an order of magnitude estimate for f_NL. We reconsider the problem of computing f_NL in nonlocal inflation models, showing that a particular choice of field basis and recent progress in cosmological perturbation theory makes an exact computation possible. We provide the first quantitatively accurate computation of the bispectrum in nonlocal inflation, confirming our previous claim that it can be observably large. We show that the shape of the bispectrum in this class of models makes it observationally distinguishable from Dirac-Born-Infeld inflation models.

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arXiv2008

Dynamics with Infinitely Many Derivatives: The Initial Value Problem

Differential equations of infinite order are an increasingly important class of equations in theoretical physics. Such equations are ubiquitous in string field theory and have recently attracted considerable interest also from cosmologists. Though these equations have been studied in the classical mathematical literature, it appears that the physics community is largely unaware of the relevant formalism. Of particular importance is the fate of the initial value problem. Under what circumstances do infinite order differential equations possess a well-defined initial value problem and how many initial data are required? In this paper we study the initial value problem for infinite order differential equations in the mathematical framework of the formal operator calculus, with analytic initial data. This formalism allows us to handle simultaneously a wide array of different nonlocal equations within a single framework and also admits a transparent physical interpretation. We show that differential equations of infinite order do not generically admit infinitely many initial data. Rather, each pole of the propagator contributes two initial data to the final solution. Though it is possible to find differential equations of infinite order which admit well-defined initial value problem with only two initial data, neither the dynamical equations of p-adic string theory nor string field theory seem to belong to this class. However, both theories can be rendered ghost-free by suitable definition of the action of the formal pseudo-differential operator. This prescription restricts the theory to frequencies within some contour in the complex plane and hence may be thought of as a sort of ultra-violet cut-off.

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arXiv2007

p-adic Inflation

We construct approximate inflationary solutions rolling away from the unstable maximum of p-adic string theory, a nonlocal theory with derivatives of all orders. Novel features include the existence of slow-roll solutions even when the slow-roll parameters, as usually defined, are much greater than unity, as well as the need for the Hubble parameter to exceed the string mass scale m_s. We show that the theory can be compatible with CMB observations if g_s / \sqrt{p} ~ 10^{-7}, where g_s is the string coupling, and if m_s < 10^{-6} M_p. A red-tilted spectrum is predicted, and the scalar-to-tensor ratio is bounded from above as r < 0.006. The p-adic theory is shown to have identical inflationary predictions to a local theory with superPlanckian parameter values, but with the advantage that the p-adic theory is ultraviolet complete.

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arXiv2007

Nongaussianity from Tachyonic Preheating in Hybrid Inflation

In a previous work we showed that large nongaussianities and nonscale-invariant distortions in the CMB power spectrum can be generated in hybrid inflation models, due to the contributions of the tachyon (waterfall) field to the second order curvature perturbation. Here we clarify, correct, and extend those results. We show that large nongaussianity occurs only when the tachyon remains light throughout inflation, whereas n=4 contamination to the spectrum is the dominant effect when the tachyon is heavy. We find constraints on the parameters of warped-throat brane-antibrane inflation from nongaussianity. For F-term and D-term inflation models from supergravity, we obtain nontrivial constraints from the spectral distortion effect. We also establish that our analysis applies to complex tachyon fields.

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arXiv2006

Nongaussian and nonscale-invariant perturbations from tachyonic preheating in hybrid inflation

We show that in hybrid inflation it is possible to generate large second-order perturbations in the cosmic microwave background due to the instability of the tachyonic field during preheating. We carefully calculate this effect from the tachyon contribution to the gauge-invariant curvature perturbation, clarifying some confusion in the literature concerning nonlocal terms in the tachyon curvature perturbation; we show explicitly that such terms are absent. We quantitatively compute the nongaussianity generated by the tachyon field during the preheating phase and translate the experimental constraints on the nonlinearity parameter f_{NL} into constraints on the parameters of the model. We also show that nonscale-invariant second-order perturbations from the tachyon field can become larger than the inflaton-generated first-order perturbations, leading to stronger constraints than those coming from nongaussianity. The width of the excluded region in terms of the logarithm of the dimensionless coupling g, grows linearly with the log of the ratio of the Planck mass to the tachyon VEV, \log(M_p/v); hence very large regions are ruled out if the inflationary scale v is small. We apply these results to string-theoretic brane-antibrane inflation, and find a stringent upper bound on the string coupling, g_s < 10^{-4.5}.

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arXiv2005

Overproduction of cosmic superstrings

We show that the naive application of the Kibble mechanism seriously underestimates the initial density of cosmic superstrings that can be formed during the annihilation of D-branes in the early universe, as in models of brane-antibrane inflation. We study the formation of defects in effective field theories of the string theory tachyon both analytically, by solving the equation of motion of the tachyon field near the core of the defect, and numerically, by evolving the tachyon field on a lattice. We find that defects generically form with correlation lengths of order M_s^{-1} rather than H^{-1}. Hence, defects localized in extra dimensions may be formed at the end of inflation. This implies that brane-antibrane inflation models where inflation is driven by branes which wrap the compact manifold may have problems with overclosure by cosmological relics, such as domain walls and monopoles.

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arXiv2004

Tachyon Defect Formation and Reheating in Brane-Antibrane Inflation

We study analytically the dynamical formation of lower dimensional branes at the endpoint of brane-antibrane inflation through the condensation of topological defects of the tachyon field which describes the instability of the initial state. We then use this information to quantify the efficiency of the reheating which is due to the coupling of time dependent tachyon background to massless gauge fields which will be localized on the final state branes. We improve upon previous estimates indicating that this can be an efficient reheating mechanism for observers on the brane.

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arXiv2004

Caustic Formation in Tachyon Effective Field Theories

Certain configurations of D-branes, for example wrong dimensional branes or the brane-antibrane system, are unstable to decay. This instability is described by the appearance of a tachyonic mode in the spectrum of open strings ending on the brane(s). The decay of these unstable systems is described by the rolling of the tachyon field from the unstable maximum to the minimum of its potential. We analytically study the dynamics of the inhomogeneous tachyon field as it rolls towards the true vacuum of the theory in the context of several different tachyon effective actions. We find that the vacuum dynamics of these theories is remarkably similar and in particular we show that in all cases the tachyon field forms caustics where second and higher derivatives of the field blow up. The formation of caustics signals a pathology in the evolution since each of the effective actions considered is not reliable in the vicinity of a caustic. We speculate that the formation of caustics is an artifact of truncating the tachyon action, which should contain all orders of derivatives acting on the field, to a finite number of derivatives. Finally, we consider inhomogeneous solutions in p-adic string theory, a toy model of the bosonic tachyon which contains derivatives of all orders acting on the field. For a large class of initial conditions we conclusively show that the evolution is well behaved in this case. It is unclear if these caustics are a genuine prediction of string theory or not.

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arXiv2004

Creating the Universe from Brane-Antibrane Annihilation

When p-dimensional branes annihilate with antibranes in the early universe, as in brane-antibrane inflation, stable (p-2)-dimensional branes can appear in the final state. We reexamine the possibility that one of these (p-2)-branes could be our universe. In the low energy effective theory, the final state branes are cosmic string defects of the complex tachyon field which describes the instability of the initial state. We quantify the dynamics of formation of these vortices. This information is then used to estimate the production of massless gauge bosons on the final branes, due to their coupling to the time-dependent tachyon background, which would provide a mechanism for reheating after inflation. We improve upon previous estimates indicating that this can be an efficient reheating mechanism for observers on the brane.

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