One Loop Back Reaction On Power Law Inflation

We consider quantum mechanical corrections to a homogeneous, isotropic and spatially flat geometry whose scale factor expands classically as a general power of the co-moving time. The effects of both gravitons and the scalar inflaton are computed at one loop using the manifestly causal formalism of Schwinger with the Feynman rules recently developed by Iliopoulos {\it et al.} We find no significant effect, in marked contrast with the result obtained by Mukhanov {\it et al.} for chaotic inflation based on a quadratic potential. By applying the canonical technique of Mukhanov {\it et al.} to the exponential potentials of power law inflation, we show that the two methods produce the same results, within the approximations employed, for these backgrounds. We therefore conclude that the shape of the inflaton potential can have an enormous impact on the one loop back-reaction.Comment: 28 pages, LaTeX 2 epsilo

One Loop Back Reaction On Chaotic Inflation

We extend, for the case of a general scalar potential, the inflaton-graviton Feynman rules recently developed by Iliopoulos {\it et al.} As an application we compute the leading term, for late co-moving times, of the one loop back reaction on the expansion rate for $V(\phi) = \frac12 m^2 \phi^2$. This is expressed as the logarithmic time derivative of the scale factor in the coordinate system for which the expectation value of the metric has the form: $dx^{\mu} dx^{\nu} = - d{\bar t}^2 + a^2({\bar t}) d{\vec x} \cdot d{\vec x}$. This quantity should be a gauge independent observable. Our result for it agrees exactly with that inferred from the effect previously computed by Mukhanov {\it et al.} using canonical quantization. It is significant that the two calculations were made with completely different schemes for fixing the gauge, and that our computation was done using the standard formalism of covariant quantization. This should settle some of the issues recently raised by Unruh.Comment: 41 pages, LaTeX 2 epsilo

Structure formation in the presence of dark energy perturbations

We study non-linear structure formation in the presence of dark energy. The influence of dark energy on the growth of large-scale cosmological structures is exerted both through its background effect on the expansion rate, and through its perturbations as well. In order to compute the rate of formation of massive objects we employ the Spherical Collapse formalism, which we generalize to include fluids with pressure. We show that the resulting non-linear evolution equations are identical to the ones obtained in the Pseudo-Newtonian approach to cosmological perturbations, in the regime where an equation of state serves to describe both the background pressure relative to density, and the pressure perturbations relative to the density perturbations as well. We then consider a wide range of constant and time-dependent equations of state (including phantom models) parametrized in a standard way, and study their impact on the non-linear growth of structure. The main effect is the formation of dark energy structure associated with the dark matter halo: non-phantom equations of state induce the formation of a dark energy halo, damping the growth of structures; phantom models, on the other hand, generate dark energy voids, enhancing structure growth. Finally, we employ the Press-Schechter formalism to compute how dark energy affects the number of massive objects as a function of redshift.Comment: 21 pages, 8 figures. Matches published version, with caption of Fig. 6 correcte

Second Order Perturbations of Flat Dust FLRW Universes with a Cosmological Constant

We summarize recent results concerning the evolution of second order perturbations in flat dust irrotational FLRW models with $\Lambda\ne 0$. We show that asymptotically these perturbations tend to constants in time, in agreement with the cosmic no-hair conjecture. We solve numerically the second order scalar perturbation equation, and very briefly discuss its all time behaviour and some possible implications for the structure formation.Comment: 6 pages, 1 figure. to be published in "Proceedings of the 5th Alexander Friedmann Seminar on Gravitation and Cosmology", Int. Journ. Mod. Phys. A (2002). Macros: ws-ijmpa.cls, ws-p9-75x6-50.cl

General plane wave mode functions for scalar-driven cosmology

We give a solution for plane wave scalar, vector and tensor mode functions in the presence of any homogeneous, isotropic and spatially flat cosmology which is driven by a single, minimally coupled scalar. The solution is obtained by rescaling the various mode functions so that they reduce, with a suitable scale factor and a suitable time variable, to those of a massless, minimally coupled scalar. We then express the general solution in terms of co-moving time and the original scale factor.Comment: 6 pages, revtex4, no figures, revised version corrects an embarrassing mistake (in the published version) for the parameter q_C. Affected eqns are 45 and 6

On Metric Preheating

We consider the generation of super-horizon metric fluctuations during an epoch of preheating in the presence of a scalar field \chi quadratically coupled to the inflaton. We find that the requirement of efficient broad resonance is concomitant with a severe damping of super-horizon \delta\chi quantum fluctuations during inflation. Employing perturbation theory with backreaction included as spatial averages to second order in the scalar fields and in the metric, we argue that the usual inflationary prediction for metric perturbations on scales relevant for structure formation is not strongly modified.Comment: 5 latex pages, 1 postscript figure included, uses revtex.sty in two column format and epsf.sty, some typos corrected and references added. Links and further material at http://astro.uchicago.edu/home/web/sigl/r4.htm

Back-Reaction In Lightcone QED

We consider the back-reaction of quantum electrodynamics upon an electric field E(x_+) = - A'_-(x_+) which is parallel to x^3 and depends only on the lightcone coordinate x_+ = (x^0 + x^3)/\sqrt{2}. Novel features are that the mode functions have simple expressions for arbitrary A_-(x_+), and that one cannot ignore the usual lightcone ambiguity at zero + momentum. Each mode of definite canonical momenta k_+ experiences pair creation at the instant when its kinetic momentum p_+=k_+ - e A_-(x_+) vanishes, at which point operators from the surface at x_- =-\infty play a crucial role. Our formalism permits a more explicit and complete derivation of the rate of particle production than is usually given. We show that the system can be understood as the infinite boost limit of the analogous problem of an electric field which is homogeneous on surfaces of constant x^0.Comment: 37 pages, 2 figures, LaTeX 2 epsilo

Spherical collapse of dark energy with an arbitrary sound speed

We consider a generic type of dark energy fluid, characterised by a constant equation of state parameter w and sound speed c_s, and investigate the impact of dark energy clustering on cosmic structure formation using the spherical collapse model. Along the way, we also discuss in detail the evolution of dark energy perturbations in the linear regime. We find that the introduction of a finite sound speed into the picture necessarily induces a scale-dependence in the dark energy clustering, which in turn affects the dynamics of the spherical collapse in a scale-dependent way. As with other, more conventional fluids, we can define a Jeans scale for the dark energy clustering, and hence a Jeans mass M_J for the dark matter which feels the effect of dark energy clustering via gravitational interactions. For bound objects (halos) with masses M >> M_J, the effect of dark energy clustering is maximal. For those with M << M_J, the dark energy component is effectively homogeneous, and its role in the formation of these structures is reduced to its effects on the Hubble expansion rate. To compute quantitatively the virial density and the linearly extrapolated threshold density, we use a quasi-linear approach which is expected to be valid up to around the Jeans mass. We find an interesting dependence of these quantities on the halo mass M, given some w and c_s. The dependence is the strongest for masses lying in the vicinity of M ~ M_J. Observing this M-dependence will be a tell-tale sign that dark energy is dynamic, and a great leap towards pinning down its clustering properties.Comment: 25 pages, 6 figures, matches version published in JCA

Inflationary cosmology with scalar field and radiation

We present a simple, exact and self-consistent cosmology with a phenomenological model of quantum creation of radiation due to decay of the scalar field. The decay drives a non-isentropic inflationary epoch, which exits smoothly to the radiation era, without reheating. The initial vacuum for radiation is a regular Minkowski vacuum. The created radiation obeys standard thermodynamic laws, and the total entropy produced is consistent with the accepted value. We analyze the difference between the present model and a model with decaying cosmological constant previously considered.Comment: 13 pages Latex; to appear Gen. Rel. Gra