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

Back-Reaction Is For Real

We demonstrate the existence of a secular back-reaction on inflation using a simple scalar model. The model consists of a massless, minimally coupled scalar with a quartic self-interaction which is a spectator to $\Lambda$-driven inflation. To avoid problems with coincident propagators, and to make the scalars interact more like gravitons, we impose a covariant normal ordering prescription which has the effect of removing tadpole graphs. This version of the theory exhibits a secular slowing at three loop order due to interactions between virtual infrared scalars which are ripped apart by the inflating background. The effect is quantified using an invariant observable and all orders bounds are given. We also argue that, although stochastic effects can have either sign, the slowing mechanism is superimposed upon them.Comment: 35 pages, LaTeX 2 epsilon, 8 figure

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

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

Energy-Momentum Tensor of Cosmological Fluctuations during Inflation

We study the renormalized energy-momentum tensor (EMT) of cosmological scalar fluctuations during the slow-rollover regime for chaotic inflation with a quadratic potential and find that it is characterized by a negative energy density which grows during slow-rollover. We also approach the back-reaction problem as a second-order calculation in perturbation theory finding no evidence that the back-reaction of cosmological fluctuations is a gauge artifact. In agreement with the results on the EMT, the average expansion rate is decreased by the back-reaction of cosmological fluctuations.Comment: 19 pages, no figures.An appendix and references added, conclusions unchanged, version accepted for publication in PR

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

Back Reaction Problem in the Inflationary Universe

We investigate the back reaction of cosmological perturbations on an inflationary universe using the renormalization-group method. The second-order zero mode solution which appears by the nonlinearity of the Einstein equation is regarded as a secular term of a perturbative expansion, we renormalized a constant of integration contained in the background solution and absorbed the secular term to this constant in a gauge-invariant manner. The resultant renormalization-group equation describes the back reaction effect of inhomogeneity on the background universe. For scalar type classical perturbation, by solving the renormalization-group equation, we find that the back reaction of the long wavelength fluctuation works as a positive spatial curvature, and the short wavelength fluctuation works as a radiation fluid. For the long wavelength quantum fluctuation, the effect of back reaction is equivalent to a negative spatial curvature.Comment: 17 page

The back reaction and the effective Einstein's equation for the Universe with ideal fluid cosmological perturbations

We investigate the back reaction of cosmological perturbations on the evolution of the Universe using the renormalization group method. Starting from the second order perturbed Einstein's equation, we renormalize a scale factor of the Universe and derive the evolution equation for the effective scale factor which includes back reaction due to inhomogeneities of the Universe. The resulting equation has the same form as the standard Friedman-Robertson-Walker equation with the effective energy density and pressure which represent the back reaction effect.Comment: 16 pages, to appear in Phys. Rev.