Free energy determination of phase coexistence in model C60: A comprehensive Monte Carlo study

The free energy of the solid and fluid phases of the Girifalco C60 model are determined through extensive Monte Carlo simulations. In this model the molecules interact through a spherical pair potential, characterized by a narrow and attractive well, adjacent to a harshly repulsive core. We have used the Widom test particle method and a mapping from an Einstein crystal, in order to estimate the absolute free energy in the fluid and solid phases, respectively; we have then determined the free energy along several isotherms, and the whole phase diagram, by means of standard thermodynamic integrations. We highlight how the interplay between the liquid-vapor and the liquid-solid coexistence conditions determines the existence of a narrow liquid pocket in the phase diagram, whose stability is assessed and confirmed in agreement with previous studies. In particular, the critical temperature follows closely an extended corresponding-states rule recently outlined by Noro and Frenkel [J. Chem. Phys. 113:2941 (2000)]. We discuss the emerging "energetic" properties of the system, which drive the phase behavior in systems interacting through short-range forces [A. A. Louis, Phil. Trans. R. Soc. A 359:939 (2001)], in order to explain the discrepancy between the predictions of several structural indicators and the results of full free energy calculations, to locate the fluid phase boundaries. More generally, we aim to provide extended reference data for calculations of the free energy of the C60 fullerite in the low temperature regime, as for the determination of the phase diagram of higher order fullerenes and other fullerene-related materials, whose description is based on the same model adopted in this work.Comment: RevTeX, 11 pages, 9 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

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

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

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