Dark Matter with Time-Dependent Mass

We propose a simple model in which the cosmological dark matter consists of particles whose mass increases with the scale factor of the universe. The particle mass is generated by the expectation value of a scalar field which does not have a stable vacuum state, but which is effectively stabilized by the rest energy of the ambient particles. As the universe expands, the density of particles decreases, leading to an increase in the vacuum expectation value of the scalar (and hence the mass of the particle). The energy density of the coupled system of variable-mass particles (``vamps'') redshifts more slowly than that of ordinary matter. Consequently, the age of the universe is larger than in conventional scenarios.Comment: 14 pages, 2 figures; based on a talk by SMC at Cosmo-97, September 1997, Ambleside, England. Important references adde

Toward solving the cosmological constant problem by embedding

The typical scalar field theory has a cosmological constant problem. We propose a generic mechanism by which this problem is avoided at tree level by embedding the theory into a larger theory. The metric and the scalar field coupling constants in the original theory do not need to be fine-tuned, while the extra scalar field parameters and the metric associated with the extended theory are fine-tuned dynamically. Hence, no fine-tuning of parameters in the full Lagrangian is needed for the vacuum energy in the new physical system to vanish at tree level. The cosmological constant problem can be solved if the method can be extended to quantum loops.Comment: published versio

New Scale Factor Measure

The computation of probabilities in an eternally inflating universe requires a regulator or "measure". The scale factor time measure truncates the universe when a congruence of timelike geodesics has expanded by a fixed volume factor. This definition breaks down if the generating congruence is contracting---a serious limitation that excludes from consideration gravitationally bound regions such as our own. Here we propose a closely related regulator which is well-defined in the entire spacetime. The New Scale Factor Cutoff restricts to events with scale factor below a given value. Since the scale factor vanishes at caustics and crunches, this cutoff always includes an infinite number of disconnected future regions. We show that this does not lead to divergences. The resulting measure combines desirable features of the old scale factor cutoff and of the light-cone time cutoff, while eliminating some of the disadvantages of each.Comment: 20 pages, 1 figure; v2: references adde

Light Deflection, Lensing, and Time Delays from Gravitational Potentials and Fermat's Principle in the Presence of a Cosmological Constant

The contribution of the cosmological constant to the deflection angle and the time delays are derived from the integration of the gravitational potential as well as from Fermat's Principle. The findings are in agreement with recent results using exact solutions to Einstein's equations and reproduce precisely the new $\Lambda$-term in the bending angle and the lens equation. The consequences on time delay expressions are explored. While it is known that $\Lambda$ contributes to the gravitational time delay, it is shown here that a new $\Lambda$-term appears in the geometrical time delay as well. Although these newly derived terms are perhaps small for current observations, they do not cancel out as previously claimed. Moreover, as shown before, at galaxy cluster scale, the $\Lambda$ contribution can be larger than the second-order term in the Einstein deflection angle for several cluster lens systems.Comment: 6 pages, 1 figure, matches version published in PR

Theoretic Limits on the Equation of State Parameter of Quintessence

The value of scalar field coupled to gravity should be less than the Planck scale in the consistent theory of quantum gravity. It provides a theoretic constraint on the equation of state parameter for the quintessence. In some cases our theoretic constraints are more stringent than the constraints from the present experiments.Comment: 4 pages, 2 figures; minor corrections and refs adde

Generalized Hurst exponent and multifractal function of original and translated texts mapped into frequency and length time series

A nonlinear dynamics approach can be used in order to quantify complexity in written texts. As a first step, a one-dimensional system is examined : two written texts by one author (Lewis Carroll) are considered, together with one translation, into an artificial language, i.e. Esperanto are mapped into time series. Their corresponding shuffled versions are used for obtaining a "base line". Two different one-dimensional time series are used here: (i) one based on word lengths (LTS), (ii) the other on word frequencies (FTS). It is shown that the generalized Hurst exponent $h(q)$ and the derived $f(\alpha)$ curves of the original and translated texts show marked differences. The original "texts" are far from giving a parabolic $f(\alpha)$ function, - in contrast to the shuffled texts. Moreover, the Esperanto text has more extreme values. This suggests cascade model-like, with multiscale time asymmetric features as finally written texts. A discussion of the difference and complementarity of mapping into a LTS or FTS is presented. The FTS $f(\alpha)$ curves are more opened than the LTS onesComment: preprint for PRE; 2 columns; 10 pages; 6 (multifigures); 3 Tables; 70 reference

Energy conditions bounds and their confrontation with supernovae data

The energy conditions play an important role in the understanding of several properties of the Universe, including the current accelerating expansion phase and the possible existence of the so-called phantom fields. We show that the integrated bounds provided by the energy conditions on cosmological observables such as the distance modulus $\mu(z)$ and the lookback time $t_L(z)$ are not sufficient (nor necessary) to ensure the local fulfillment of the energy conditions, making explicit the limitation of these bounds in the confrontation with observational data. We recast the energy conditions as bounds on the deceleration and normalized Hubble parameters, obtaining new bounds which are necessary and sufficient for the local fulfillment of the energy conditions. A statistical confrontation, with $1\sigma-3\sigma$ confidence levels, between our bounds and supernovae data from the gold and combined samples is made for the recent past. Our analyses indicate, with $3\sigma$ confidence levels, the fulfillment of both the weak energy condition (WEC) and dominant energy condition (DEC) for $z \leq 1$ and $z \lesssim 0.8$, respectively. In addition, they suggest a possible recent violation of the null energy condition (NEC) with $3\sigma$, i.e. a very recent phase of super-acceleration. Our analyses also show the possibility of violation of the strong energy condition (\textbf{SEC}) with $3\sigma$ in the recent past ($z \leq 1$), but interestingly the $q(z)$-best-fit curve crosses the SEC-fulfillment divider at $z \simeq 0.67$, which is a value very close to the beginning of the epoch of cosmic acceleration predicted by the standard concordance flat $\Lambda$CDM scenario.Comment: 7 pages, 3 figures. V2: Version to appear in Phys.Rev.D, analyses extended to 1sigma, 2sigma and 3sigma confidence levels, references added, minors change

Energy Conditions and Supernovae Observations

In general relativity, the energy conditions are invoked to restrict general energy-momentum tensors on physical grounds. We show that in the standard Friedmann-Lemaitre-Robertson-Walker approach to cosmological modelling where the equation of state of the cosmological fluid is unknown, the energy conditions provide model-independent bounds on the behavior of the distance modulus of cosmic sources as a function of the redshift. We use both the gold and the legacy samples of current type Ia supenovae to carry out a model-independent analysis of the energy conditions violation in the context of standard cosmology.Comment: 4 pages, 2 figures; v2: References added, misprints corrected, published in Phys.Rev.D in the present for