Bounce and cyclic cosmology in extended nonlinear massive gravity

We investigate non-singular bounce and cyclic cosmological evolutions in a universe governed by the extended nonlinear massive gravity, in which the graviton mass is promoted to a scalar-field potential. The extra freedom of the theory can lead to certain energy conditions violations and drive cyclicity with two different mechanisms: either with a suitably chosen scalar-field potential under a given Stuckelberg-scalar function, or with a suitably chosen Stuckelberg-scalar function under a given scalar-field potential. Our analysis shows that extended nonlinear massive gravity can alter significantly the evolution of the universe at both early and late times.Comment: 20 pages, 5 figures, version published at JCA

Cyclic cosmology from Lagrange-multiplier modified gravity

We investigate cyclic and singularity-free evolutions in a universe governed by Lagrange-multiplier modified gravity, either in scalar-field cosmology, as well as in $f(R)$ one. In the scalar case, cyclicity can be induced by a suitably reconstructed simple potential, and the matter content of the universe can be successfully incorporated. In the case of $f(R)$-gravity, cyclicity can be induced by a suitable reconstructed second function $f_2(R)$ of a very simple form, however the matter evolution cannot be analytically handled. Furthermore, we study the evolution of cosmological perturbations for the two scenarios. For the scalar case the system possesses no wavelike modes due to a dust-like sound speed, while for the $f(R)$ case there exist an oscillation mode of perturbations which indicates a dynamical degree of freedom. Both scenarios allow for stable parameter spaces of cosmological perturbations through the bouncing point.Comment: 8 pages, 3 figures, references added, accepted for publicatio

FPTAS for Weighted Fibonacci Gates and Its Applications

Fibonacci gate problems have severed as computation primitives to solve other problems by holographic algorithm and play an important role in the dichotomy of exact counting for Holant and CSP frameworks. We generalize them to weighted cases and allow each vertex function to have different parameters, which is a much boarder family and #P-hard for exactly counting. We design a fully polynomial-time approximation scheme (FPTAS) for this generalization by correlation decay technique. This is the first deterministic FPTAS for approximate counting in the general Holant framework without a degree bound. We also formally introduce holographic reduction in the study of approximate counting and these weighted Fibonacci gate problems serve as computation primitives for approximate counting. Under holographic reduction, we obtain FPTAS for other Holant problems and spin problems. One important application is developing an FPTAS for a large range of ferromagnetic two-state spin systems. This is the first deterministic FPTAS in the ferromagnetic range for two-state spin systems without a degree bound. Besides these algorithms, we also develop several new tools and techniques to establish the correlation decay property, which are applicable in other problems

Non-Gaussian Halo Bias Re-examined: Mass-dependent Amplitude from the Peak-Background Split and Thresholding

Recent results of N-body simulations have shown that current theoretical models are not able to correctly predict the amplitude of the scale-dependent halo bias induced by primordial non-Gaussianity, for models going beyond the simplest, local quadratic case. Motivated by these discrepancies, we carefully examine three theoretical approaches based on (1) the statistics of thresholded regions, (2) a peak-background split method based on separation of scales, and (3) a peak-background split method using the conditional mass function. We first demonstrate that the statistics of thresholded regions, which is shown to be equivalent at leading order to a local bias expansion, cannot explain the mass-dependent deviation between theory and N-body simulations. In the two formulations of the peak-background split on the other hand, we identify an important, but previously overlooked, correction to the non-Gaussian bias that strongly depends on halo mass. This new term is in general significant for any primordial non-Gaussianity going beyond the simplest local fNL model. In a separate paper, we compare these new theoretical predictions with N-body simulations, showing good agreement for all simulated types of non-Gaussianity.Comment: 26 pages, 3 figures (v2): minor changes from (v1). matches published versio