Fluctuation theorems for discrete kinetic models of molecular motors

Motivated by discrete kinetic models for non-cooperative molecular motors on periodic tracks, we consider random walks (also not Markov) on quasi one dimensional (1d) lattices, obtained by gluing several copies of a fundamental graph in a linear fashion. We show that, for a suitable class of quasi 1d lattices, the large deviation rate function associated to the position of the walker satisfies a Gallavotti-Cohen symmetry for any choice of the dynamical parameters defining the stochastic walk. This class includes the linear model considered in \cite{LLM1}. We also derive fluctuation theorems for the time-integrated cycle currents and discuss how the matrix approach of \cite{LLM1} can be extended to derive the above Gallavotti-Cohen symmetry for any Markov random walk on $\mathbb{Z}$ with periodic jump rates. Finally, we review in the present context some large deviation results of \cite{FS1} and give some specific examples with explicit computations.Comment: Modified Appendix B, added figure 13, minor modifications. 27 pages, 16 figure

Discrete kinetic models for molecular motors: asymptotic velocity and gaussian fluctuations

We consider random walks on quasi one dimensional lattices, as introduced in \cite{FS}. This mathematical setting covers a large class of discrete kinetic models for non-cooperative molecular motors on periodic tracks. We derive general formulas for the asymptotic velocity and diffusion coefficient, and we show how to reduce their computation to suitable linear systems of the same degree of a single fundamental cell, with possible linear chain removals. We apply the above results to special families of kinetic models, also catching some errors in the biophysics literature.Comment: 32 pages, 5 figures. modified comments concerning ref. [12] after private communications of the author (A.B. Kolomeisky

An Extended action for the effective field theory of dark energy: a stability analysis and a complete guide to the mapping at the basis of EFTCAMB

We present a generalization of the effective field theory (EFT) formalism for dark energy and modified gravity models to include operators with higher order spatial derivatives. This allows the extension of the EFT framework to a wider class of gravity theories such as Horava gravity. We present the corresponding extended action, both in the EFT and the Arnowitt-Deser-Misner (ADM) formalism, and proceed to work out a convenient mapping between the two, providing a self contained and general procedure to translate a given model of gravity into the EFT language at the basis of the Einstein-Boltzmann solver EFTCAMB. Putting this mapping at work, we illustrate, for several interesting models of dark energy and modified gravity, how to express them in the ADM notation and then map them into the EFT formalism. We also provide for the first time, the full mapping of GLPV models into the EFT framework. We next perform a thorough analysis of the physical stability of the generalized EFT action, in absence of matter components. We work out viability conditions that correspond to the absence of ghosts and modes that propagate with a negative speed of sound in the scalar and tensor sector, as well as the absence of tachyonic modes in the scalar sector. Finally, we extend and generalize the phenomenological basis in terms of $\alpha$-functions introduced to parametrize Horndeski models, to cover all theories with higher order spatial derivatives included in our extended action. We elaborate on the impact of the additional functions on physical quantities, such as the kinetic term and the speeds of propagation for scalar and tensor modes.Comment: 36 pages, matches published version, typos correcte

Reconstruction of the Dark Energy equation of state from latest data: the impact of theoretical priors

We reconstruct the Equation of State of Dark Energy (EoS) from current data using a non-parametric approach where, rather than assuming a specific time evolution of this function, we bin it in time. We treat the transition between the bins with two different methods, i.e. a smoothed step function and a Gaussian Process reconstruction, investigating whether or not the two approaches lead to compatible results. Additionally, we include in the reconstruction procedure a correlation between the values of the EoS at different times in the form of a theoretical prior that takes into account a set of viability and stability requirements that one can impose on models alternative to $\Lambda$CDM. In such case, we necessarily specialize to broad, but specific classes of alternative models, i.e. Quintessence and Horndeski gravity. We use data coming from CMB, Supernovae and BAO surveys. We find an overall agreement between the different reconstruction methods used; with both approaches, we find a time dependence of the mean of the reconstruction, with different trends depending on the class of model studied. The constant EoS predicted by the $\Lambda$CDM model falls anyway within the $1\sigma$ bounds of our analysis.Comment: 17 pages, 5 figures. Prepared for submission to JCA

A practical approach to cosmological perturbations in modified gravity

The next generation of large scale surveys will not only measure cosmological parameters within the framework of General Relativity, but will also allow for precision tests of the framework itself. At the order of linear perturbations, departures from the growth in the LCDM model can be quantified in terms of two functions of time and Fourier number k. We argue that in local theories of gravity, in the quasi-static approximation, these functions must be ratios of polynomials in k, with the numerator of one function being equal to the denominator of the other. Moreover, the polynomials are even and of second degree in practically all viable models considered today. This means that, without significant loss of generality, one can use data to constraint only five functions of a single variable, instead of two functions of two variables. Furthermore, since the five functions are expected to be slowly varying, one can fit them to data in a non-parametric way with the aid of an explicit smoothness prior. We discuss practical application of this parametrization to forecasts and fits.Comment: 9 pages, v2: matching the published versio

Scalar radiation from Chameleon-shielded regions

I study the profile of the Chameleon field around a radially pulsating mass. Focusing on the case in which the background (static) Chameleon profile exhibits a thin-shell, I add small perturbations to the source in the form of time-dependent radial pulsations. It is found that the Chameleon field inherits a time-dependence, there is a resultant scalar radiation from the region of the source and the metric outside the spherically symmetric mass is not static. This has several interesting and potentially testable consequences.Comment: 4 pages, 4 figures, slightly edited version matching the journal versio

Testing Hu-Sawicki f(R) gravity with the Effective Field Theory approach

We show how to fully map a specific model of modified gravity into the Einstein-Boltzmann solver EFTCAMB. This approach consists in few steps and allows to obtain the cosmological phenomenology of a model with minimal effort. We discuss all these steps, from the solution of the dynamical equations for the cosmological background of the model to the use of the mapping relations to cast the model into the effective field theory language and use the latter to solve for perturbations. We choose the Hu-Sawicki f(R) model of gravity as our working example. After solving the background and performing the mapping, we interface the algorithm with EFTCAMB and take advantage of the effective field theory framework to integrate the full dynamics of linear perturbations, returning all quantities needed to accurately compare the model with observations. We discuss some observational signatures of this model, focusing on the linear growth of cosmic structures. In particular we present the behavior of $f\sigma_8$ and $E_G$ that, unlike the $\Lambda$CDM scenario, are generally scale dependent in addition to redshift dependent. Finally, we study the observational implications of the model by comparing its cosmological predictions to the Planck 2015 data, including CMB lensing, the WiggleZ galaxy survey and the CFHTLenS weak lensing survey measurements. We find that while WiggleZ data favor a non-vanishing value of the Hu-Sawicki model parameter, $\log_{10}(-f^0_{R})$, and consequently a large value of $\sigma_8$, CFHTLenS drags the estimate of $\log_{10}(-f^0_{R})$ back to the $\Lambda$CDM limit.Comment: 13 pages, 8 figure