Spherical Collapse in Chameleon Models

We study the gravitational collapse of an overdensity of nonrelativistic matter under the action of gravity and a chameleon scalar field. We show that the spherical collapse model is modified by the presence of a chameleon field. In particular, we find that even though the chameleon effects can be potentially large at small scales, for a large enough initial size of the inhomogeneity the collapsing region possesses a thin shell that shields the modification of gravity induced by the chameleon field, recovering the standard gravity results. We analyse the behaviour of a collapsing shell in a cosmological setting in the presence of a thin shell and find that, in contrast to the usual case, the critical density for collapse depends on the initial comoving size of the inhomogeneity.Comment: matches printed versio

Cosmological Density Perturbations From A Quantum Gravitational Model Of Inflation

We derive the implications for anisotropies in the cosmic microwave background following from a model of inflation in which a bare cosmological constant is gradually screened by an infrared process in quantum gravity. The model predicts that the amplitude of scalar perturbations is $A_S = (2.0 \pm .2) \times 10^{-5}$, that the tensor-to-scalar ratio is $r \approx 1.7 \times 10^{-3}$, and that the scalar and tensor spectral indices are $n \approx .97$ and $n_T \approx -2.8 \times 10^{-4}$, respectively. By comparing the model's power spectrum with the COBE 4-year RMS quadrupole, the mass scale of inflation is determined to be $M = (.72 \pm .03) \times 10^{16}~{\rm GeV}$. At this scale the model produces about $10^8$ e-foldings of inflation, so another prediction is $\Omega = 1$.Comment: 18 pages, LaTeX 2 epsilon, 1 eps file, uses epsfi

A Scalar Measure Of The Local Expansion Rate

We define a scalar measure of the local expansion rate based on how astronomers determine the Hubble constant. Our observable is the inverse conformal d'Alembertian acting on a unit ``standard candle.'' Because this quantity is an integral over the past lightcone of the observation point it provides a manifestly causal and covariant technique for averaging over small fluctuations. For an exactly homogeneous and isotropic spacetime our scalar gives minus one half times the inverse square of the Hubble parameter. Our proposal is that it be assigned this meaning generally and that it be employed to decide the issue of whether or not there is a significant quantum gravitational back-reaction on inflation. Several techniques are discussed for promoting the scalar to a full invariant by giving a geometrical description for the point of observation. We work out an explicit formalism for evaluating the invariant in perturbation theory. The results for two simple models are presented in subsequent papers.Comment: 25 pages, LaTeX 2 epsilon, 1 figur

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

Signature of the interaction between dark energy and dark matter in observations

We investigate the effect of an interaction between dark energy and dark matter upon the dynamics of galaxy clusters. This effect is computed through the Layser-Irvine equation, which describes how an astrophysical system reaches virial equilibrium and was modified to include the dark interactions. Using observational data from almost 100 purportedly relaxed galaxy clusters we put constraints on the strength of the couplings in the dark sector. We compare our results with those from other observations and find that a positive (in the sense of energy flow from dark energy to dark matter) non vanishing interaction is consistent with the data within several standard deviations.Comment: 13 pages, 3 figures; matches PRD published versio