We examine bounds on adiabatic and isocurvature density fluctuations from $mu$-type spectral distortions of the cosmic microwave background (CMB). Studies of such distortion are complementary to CMB measurements of the spectral index and its running,
and will help to constrain these parameters on significantly smaller scales. We show that a detection on the order of $mu sim 10^{-7}$ would strongly be at odds with the standard cosmological model of a nearly scale-invariant spectrum of adiabatic perturbations. Further, we find that given the current CMB constraints on the isocurvature mode amplitude, a nearly scale-invariant isocurvature mode (common in many curvaton models) cannot produce significant $mu$-distortion. Finally, we show that future experiments will strongly constrain the amplitude of the isocurvature modes with a highly blue spectrum as predicted by certain axion models.
A new approach is given for the implementation of boundary conditions used in solving the Mukhanov-Sasaki equation in the context of inflation. The familiar quantization procedure is reviewed, along with a discussion of where one might expect deviati
ons from the standard approach to arise. The proposed method introduces a (model dependent) fitting function for the z/z and a/a terms in the Mukhanov-Sasaki equation for scalar and tensor modes, as well as imposes the boundary conditions at a finite conformal time. As an example, we employ a fitting function, and compute the spectral index, along with its running, for a specific inflationary model which possesses background equations that are analytically solvable. The observational upper bound on the tensor to scalar ratio is used to constrain the parameters of the boundary conditions in the tensor sector as well. An overview on the generalization of this method is also discussed.
We investigate the cosmological perturbations in f(T) gravity. Examining the pure gravitational perturbations in the scalar sector using a diagonal vierbien, we extract the corresponding dispersion relation, which provides a constraint on the f(T) an
satzes that lead to a theory free of instabilities. Additionally, upon inclusion of the matter perturbations, we derive the fully perturbed equations of motion, and we study the growth of matter overdensities. We show that f(T) gravity with f(T) constant coincides with General Relativity, both at the background as well as at the first-order perturbation level. Applying our formalism to the power-law model we find that on large subhorizon scales (O(100 Mpc) or larger), the evolution of matter overdensity will differ from LCDM cosmology. Finally, examining the linear perturbations of the vector and tensor sectors, we find that (for the standard choice of vierbein) f(T) gravity is free of massive gravitons.
The effect of quintessence perturbations on the ISW effect is studied for a mixed dynamical scalar field dark energy (DDE) and pressureless perfect fluid dark matter. A new and general methodology is developed to track the growth of the perturbations
, which uses only the equation of state (EoS) parameter $w_{rm DDE} (z) equiv p_{rm DDE}/rho_{rm DDE}$ of the scalar field DDE, and the initial values of the the relative entropy perturbation (between the matter and DDE) and the intrinsic entropy perturbation of the scalar field DDE as inputs. We also derive a relation between the rest frame sound speed $hat{c}_{s,{rm DDE}}^2$ of an arbitrary DDE component and its EoS $w_{rm DDE} (z)$. We show that the ISW signal differs from that expected in a $Lambda$CDM cosmology by as much as +20% to -80% for parameterizations of $w_{rm DDE}$ consistent with SNIa data, and about $pm$ 20% for parameterizations of $w_{rm DDE}$ consistent with SNIa+CMB+BAO data, at 95% confidence. Our results indicate that, at least in principle, the ISW effect can be used to phenomenologically distinguish a cosmological constant from DDE.
We consider models built on $AdS_5otimes S^5/Gamma$ orbifold compactifications of the type $IIB$ superstring, where $Gamma$ is the abelian group $Z_n$. An attractive three family $mathcal{N}=0$ SUSY model is found for $n=7$ that is a modified Pati--S
alam Model which reduced to the Standard Model after symmetry breaking.
We provide what we believe is the minimal three family ${cal N} = 1$ SUSY and conformal Pati-Salam Model from type IIB superstring theory. This $Z_3$ orbifolded AdS$otimes S^5$ model has long lived protons and has potential phenomenological consequences for LHC.
Dark matter candidates and proton decay in a class of models based on the AdS/CFT correspondence are discussed. We show that the present bound on the proton decay lifetime is inconsistent with ${cal N} = 1$ SUSY, and strongly constrains ${cal N} = 0$
non-SUSY, low scale trinification type unification of orbifolded AdS$otimes S^5$ models.
