The cosmic coincidence in Brans-Dicke cosmologies

Among the suggested solutions to the cosmological constant problem, we find the idea of a dynamic vacuum, with an energy density decaying with the universe expansion. We investigate the possibility of a variation in the gravitational constant as well, induced, at the cosmological scale, by the vacuum decay. We consider an effective Brans-Dicke theory in the spatially flat FLRW spacetime, finding late time solutions characterized by a constant ratio between the matter and vacuum energy densities. By using the observed limits for the universe age, we fix the only free parameter of our solutions, obtaining a relative matter density in the range 0.25-0.4. In particular, for Ht = 1 we obtain a relative matter density equals to 1/3. This constitutes a possible explanation for another problem related to the cosmological term, the cosmic coincidence problem.Comment: This essay received an "honorable mention" in the 2005 Essay Competition of the Gravity Research Foundatio

From de Sitter to de Sitter: A non-singular inflationary universe driven by vacuum

A semi-classical analysis of vacuum energy in the expanding spacetime suggests that the cosmological term decays with time, with a concomitant matter production. For early times we find, in Planck units, $\Lambda \approx H^4$, where H is the Hubble parameter. The corresponding cosmological solution has no initial singularity, existing since an infinite past. During an infinitely long period we have a quasi-de Sitter, inflationary universe, with $H \approx 1$. However, at a given time, the expansion undertakes a phase transition, with H and $\Lambda$ decreasing to nearly zero in a few Planck times, producing a huge amount of radiation. On the other hand, the late-time scenario is similar to the standard model, with the radiation phase followed by a dust era, which tends asymptotically to a de Sitter universe, with vacuum dominating again.Comment: This essay received an "honorable mention" in the 2006 Essay Competition of the Gravity Research Foundatio

Birnbaum–Saunders autoregressive conditional duration models applied to high-frequency financial data

Modern financial markets now record the precise time of each stock trade, along with price and volume, with the aim of analysing the structure of the times between trading events—leading to a big data problem. In this paper, we propose and compare two Birnbaum–Saunders autoregressive conditional duration models specified in terms of time-varying conditional median and mean durations. These models provide a novel alternative to the existing autoregressive conditional duration models due to their flexibility and ease of estimation. Diagnostic tools are developed to allow goodness-of-fit assessment and to detect departures from assumptions, including the presence of outliers and influential cases. These diagnostic tools are based on the parameter estimates using residual analysis and the Cook distance for global influence, and different perturbation schemes for local influence. A thorough Monte Carlo study is presented to evaluate the performance of the maximum likelihood estimators, and the forecasting ability of the models is assessed using the traditional and density forecast evaluation techniques. The Monte Carlo study suggests that the parameter estimators are asymptotically unbiased, consistent and normally distributed. Finally, a full analysis of a real-world financial transaction data set, from the German DAX in 2016, is presented to illustrate the proposed approach and to compare the fitting and forecasting performances with existing models in the literature. One case related to the duration time is identified as potentially influential, but its removal does not change resulting inferences demonstrating the robustness of the proposed approach. Fitting and forecasting performances favor the proposed models and, in particular, the median-based approach gives additional protection against outliers, as expected

Stochastic thermodynamics of a quantum dot coupled to a finite-size reservoir

In nano-scale systems coupled to finite-size reservoirs, the reservoir temperature may fluctuate due to heat exchange between the system and the reservoirs. To date, a stochastic thermodynamic analysis of heat, work and entropy production in such systems is however missing. Here we fill this gap by analyzing a single-level quantum dot tunnel coupled to a finite-size electronic reservoir. The system dynamics is described by a Markovian master equation, depending on the fluctuating temperature of the reservoir. Based on a fluctuation theorem, we identify the appropriate entropy production that results in a thermodynamically consistent statistical description. We illustrate our results by analyzing the work production for a finite-size reservoir Szilard engine