Energy conditions bounds on f(T) gravity

In standard approach to cosmological modeling in the framework of general relativity, the energy conditions play an important role in the understanding of several properties of the Universe, including singularity theorems, the current accelerating expansion phase, and the possible existence of the so-called phantom fields. Recently, the $f(T)$ gravity has been invoked as an alternative approach for explaining the observed acceleration expansion of the Universe. If gravity is described by a $f(T)$ theory instead of general relativity, there are a number of issues that ought to be reexamined in the framework of $f(T)$ theories. In this work, to proceed further with the current investigation of the limits and potentialities of the $f(T)$ gravity theories, we derive and discuss the bounds imposed by the energy conditions on a general $f(T)$ functional form. The null and strong energy conditions in the framework of $f(T)$ gravity are derived from first principles, namely the purely geometric Raychaudhuri's equation along with the requirement that gravity is attractive. The weak and dominant energy conditions are then obtained in a direct approach via an effective energy-momentum tensor for $f(T)$ gravity. Although similar, the energy condition inequalities are different from those of general relativity (GR), but in the limit $f(T)=T$ the standard forms for the energy conditions in GR are recovered. As a concrete application of the derived energy conditions to locally homogeneous and isotropic $f(T)$ cosmology, we use the recent estimated value of the Hubble parameter to set bounds from the weak energy condition on the parameters of two specific families of $f(T)$ gravity theories.Comment: 8 pages.V2: Typos corrected, refs. added. V3:Version to appear in Phys. Rev. D (2012). New subsection, minor changes, references added, typos correcte

Detecting large extra dimensions with optomechanical levitated sensors

Numbers of tabletop experiments have made efforts to detect large extra dimensions for the range from solar system to submillimeter system, but the direct evidence is still lacking. Here we present a scheme to test the gravitational law in 4+2 dimensions at microns by using cavity optomechanical method. We have investigated the probe spectrum for coupled quantum levitated oscillators in optical cavities. The results show that the spectral splitting can be obtained once the large extra dimensions present. Compare to the previous experiment, the sensitivity can be improved by the using of a specific geometry and a shield mirror to control and suppress the effect of the Casimir background. The weak frequency splitting can be optically read by the pump-probe scheme. Thus we can detect the gravitational deviation in the bulk based ADD model via spectroscopy without the isoelectronic technique

Stability of Gorenstein flat categories with respect to a semidualizing module

In this paper, we first introduce $\mathcal {W}_F$-Gorenstein modules to establish the following Foxby equivalence: \xymatrix@C=80pt{\mathcal {G}(\mathcal {F})\cap \mathcal {A}_C(R) \ar@[r]^{C\otimes_R-} & \mathcal {G}(\mathcal {W}_F) \ar@[l]^{\textrm{Hom}_R(C,-)}} where $\mathcal {G}(\mathcal {F})$, $\mathcal {A}_C(R)$ and $\mathcal {G}(\mathcal {W}_F)$ denote the class of Gorenstein flat modules, the Auslander class and the class of $\mathcal {W}_F$-Gorenstein modules respectively. Then, we investigate two-degree $\mathcal {W}_F$-Gorenstein modules. An $R$-module $M$ is said to be two-degree $\mathcal {W}_F$-Gorenstein if there exists an exact sequence \mathbb{G}_\bullet=\indent ...\longrightarrow G_1\longrightarrow G_0\longrightarrow G^0\longrightarrow G^1\longrightarrow... in $\mathcal {G}(\mathcal {W}_F)$ such that $M \cong$ \im(G_0\rightarrow G^0) and that $\mathbb{G}_\bullet$ is Hom$_R(\mathcal {G}(\mathcal {W}_F),-)$ and $\mathcal {G}(\mathcal {W}_F)^+\otimes_R-$ exact. We show that two notions of the two-degree $\mathcal {W}_F$-Gorenstein and the $\mathcal {W}_F$-Gorenstein modules coincide when R is a commutative GF-closed ring.Comment: 18 page

The Effects of Housing Push Factors and Rent Expectations on Household Formation of Young Adults

Following a group of young adults aged 25–34 living with their parents in the American Housing Survey (AHS) data from 1985 through 1995, this paper investigates the effect of overcrowding and neighborhood satisfaction on household formation after controlling for local rental levels and their changes over time. Most of these except for local rent levels have not been tested before in models and hence this study enriches the knowledge on household formation and its consequent potential demand for rental and ownership housing units.