53993819
Probing Modified Gravity Theories with ISW and CMB Lensing
The imprint of the cross-correlation of the Integrated Sach s-Wolfe effect (ISW) and lensing of the cosmic microwave background (CMB) radiation has recently been detected in the bispectrum of temperature maps. In this paper, we use the optimised skew-spectrum as well as skew-spectra associated with Minkowski Functionals (MFs) to test the possibility of using this signal to detect deviations in the theory of gravity away from General Relativity (GR). We fi nd that the although both statistics can put constraints on modified gravity, the optimised skew- spectra are especially sensitive to the parameter B0 that denotes the the Compton wavelengthof the scalaron at the present epoch, and both can be used to put stringent constraints on any departure from GR, or pinpoint any systematics in the data. We investigate three modified gravity theories, namely: the Post-Parametrised Friedmanian (PPF) formalism; the Hu-Sawicki (HS) model; and the Bertschinger-Zukin (BZ) formalism. Employing a likelihood analysis for an experimental setup similar to ESA’s Planck mission, we find that, assuming GR to be the correct model, we expect the constraints from the first two skew-spectra, S (0) l andS (1) l , to be the same: B0 < 0.45 at 95% confidence level (CL), and B0 < 0.67 at 99% CL in the BZ model. The third skew-spectrum does not give any meaningful constraint. The performance of MFs can be improved by using Wiener-type filtering, but we fi nd that the optimal skew-spectrum is much more powerful, giving B0 < 0.071 at 95% CL and B0 < 0.15 at 99% CL, which is a factor of six improvement compared to constraints derived from MF, and essentially identical to what can be achieved using the full bispectrum.
15707844
Holography, UV/IR Relation, Causal Entropy Bound, and Dark Energy
The constraint on the total energy in a given spatial region is given from holography by the mass of a black hole that just fits in that region, which leads to an UV/IR relation: the maximal energy density in that region is propotional to M(p)(2)/L(2), wher M(p) is the Planck mass and L is the spatial scale of that region under consideration. Assuming that maximal black hole in the universe is formed through gravitational collapse of perturbations in the universe, then the "Jeans" scale of the perturbations gives a causal connection scale R(CC). For gravitational perturbations, R(CC)(-2) = Max ((H) over dot + 2H(2), -(H) over dot) for a flat universe. We study the cosmological dynamics of the corresponding vacuum energy density by choosing the causal connection scale as the IR cutoff in the UV/IR relation, in the cases of the vacuum energy density as an independently conserved energy component and an effective dynamical cosmological constant, respectively. It turns out that only the case with the choice R(CC)(-2) = (H) over dot + 2H(2), could be consistent with the current cosmological observations when the vacuum density appears as an independently conserved energy component. In this case, the model is called holographic Ricci scalar dark energy model in the literature.
119185851
Timelike vector field dynamics in the early universe
We study the dynamics of a timelike vector field when the background spacetime is in an accelerating phase in the early universe. With a timelike vector field, an inflationary phase is shown to be difficult to realize, so we investigate the evolution of a vector field within a scalar field-driven inflation model. Also, we calculate the power spectrum of the vector field without considering the metric perturbations. While the time component of the vector field perturbations provides a scale invariant spectrum when ζ = 0, where ζ is a nonminimal coupling parameter, both the longitudinal and the transverse perturbations give a scale invariant spectrum when ζ = 1/6 in the absence of the coupling terms. The deviation of the power spectrum due to the coupling terms is calculated by use of the Greens’ function.
118528998
Note on self-gravitating radiation in AdS spacetime
Recently Vaganov and Hammersley investigated independently the equilibrium self-gravitating radiation in higher (d >= 4)-dimensional, spherically symmetric anti-de Sitter space. It was found that in 4 = 11, the temperature, mass, and entropy of the self-gravitating configuration are monotonic functions of the central energy density, asymptoting to their maxima as the central density goes to infinity. In this paper we investigate the equilibrium self-gravitating radiation in higher-dimensional, plane-symmetric anti-de Sitter space. We find that there exist essential differences from the spherically syrnmetric case: In each dimension (d >= 4), there are maximal mass (density), maximal entropy (density), and maximal temperature configurations; they do not appear at the same central energy density; the oscillation behavior appearing in the spherically symmetric case does not happen in this case; and the mass (density), as a function of the central energy density, increases first and reaches its maximum at a certain central energy density and then decreases monotonically in 4 = 8, besides the maximum, the mass (density) of the equilibrium configuration has a minimum: the mass (density) first increases and reaches its maximum, then decreases to its minimum, and then increases to its asymptotic value monotonically. The reason causing the difference is discussed.
118657913
Constraining models of f(R) gravity with Planck and WiggleZ power spectrum data
In order to explain cosmic acceleration without invoking "dark" physics, we consider f(R) modified gravity models, which replace the standard Einstein-Hilbert action in General Relativity with a higher derivative theory. We use data from the WiggleZ Dark Energy survey to probe the formation of structure on large scales which can place tight constraints on these models. We combine the large-scale structure data with measurements of the cosmic microwave background from the Planck surveyor. After parameterizing the modification of the action using the Compton wavelength parameter B0, we constrain this parameter using ISiTGR, assuming an initial non-informative log prior probability distribution of this cross-over scale. We find that the addition of the WiggleZ power spectrum provides the tightest constraints to date on B0 by an order of magnitude, giving log10(B0) < -4.07 at 95% confidence limit. Finally, we test whether the effect of adding the lensing amplitude ALens and the sum of the neutrino mass ∑mν is able to reconcile current tensions present in these parameters, but find f(R) gravity an inadequate explanation.
118029650
Future CMB integrated-Sachs-Wolfe-lensing bispectrum constraints on modified gravity in the parametrized post-Friedmann formalism
We forecast the constraints on both Hu-Sawicki model and Bertschinger-Zukin model of modified gravity within the Parameterized Post-Friedmann (PPF) formalism for the Planck satellite experiment by performing the joint analysis of ISW-Lensing bispectrum and CMB power spectrum. We find that, even considering the temperature-temperature mode of CMB power spectrum only, Planck data are expected to reduce the error bars on the modified gravity parameter $B_0$ (related to the present value of Compton wavelength of the extra scalar degree of freedom) at least one order magnitude compared with WMAP. The spectrum-bispectrum joint analysis can further improve the results by a factor ranging from 1.14 to 5.32 depending on the specific modified gravity model. One of our main results is that the cross-correlation between ISW-Lensing bispectrum and power spectrum can be safely neglected when performing the joint analysis. For simplicity, we only investigate the likelihood of one parameter ({$B_0$}) and fix all other cosmological parameters to their best-fit values in WMAP7yr results.
119336533
The Classical and Commutative Limits of noncommutative Quantum Mechanics: A Superstar \bigstar Wigner-Moyal Equation
We are interested in the similarities and differences between the quantum-classical (Q-C) and the noncommutative-commutative (NC-Com) correspondences. As one useful platform to address this issue we derive the superstar Wigner-Moyal equation for noncommutative quantum mechanics (NCQM). A superstar $\bigstar$-product combines the usual phase space $\ast$ star and the noncommutative $\star$ star-product. Having dealt with subtleties of ordering present in this problem we show that the classical correspondent to the NC Hamiltonian has the same form as the original Hamiltonian, but with a non-commutativity parameter $\theta$-dependent, momentum-dependent shift in the coordinates. Using it to examine the classical and the commutative limits, we find that there exist qualitative differences between these two limits. Specifically, if $\theta \neq 0$ there is no classical limit. Classical limit exists only if $\theta \to 0$ at least as fast as $\hbar \to 0$, but this limit does not yield Newtonian mechanics, unless the limit of $\theta/\hbar$ vanishes as $\theta \to 0$. Another angle to address this issue is the existence of conserved currents and the Noether's theorem in the continuity equation, and the Ehrenfest theorem in the NCQM context.
123062000
Quantum effects in the early universe. I. Influence of trace anomalies on homogeneous, isotropic, classical geometries
The use of the effective-action method to calculate quantum effects in the early universe is described. An application is made to the calculation of the effect of one-loop contributions of conformally invariant matter fields on the evolution of homogeneous, isotropic, spatially flat classical geometries containing classical radiation.
204014568
Allowed Domains for Chiral-Symmetry- and Isospin-Breaking Parameters
In addition to the chiral-symmetry-breaking terms ${\ensuremath{\epsilon}}_{0}{\ensuremath{\sigma}}_{0}+{\ensuremath{\epsilon}}_{8}{\ensuremath{\sigma}}_{8}$ an isospin - breaking term ${\ensuremath{\epsilon}}_{3}{\ensuremath{\sigma}}_{3}$ is included in the study of the (3,\ifmmode\bar\else\textasciimacron\fi{}3)\ensuremath{\bigoplus}(\ifmmode\bar\else\textasciimacron\fi{}3,3) model. By assuming that the intermediate symmetry is either ${\mathrm{SU}}_{2}$\ensuremath{\bigotimes}${\mathrm{SU}}_{2}$ or ${\mathrm{SU}}_{3}$, allowed domains for the chiral-symmetry- and isospin-breaking parameters are derived. A $\ensuremath{\sigma}$-model Lagrangian is then constructed. The positivity condition for the masses reproduces the general features of the domain structure.
119214934
A Master Equation for Gravitational Decoherence: Probing the Textures of Spacetime
We give a first principles derivation of a master equation for the evolution of a quantum matter field in a linearly perturbed Minkowski spacetime, based solely on quantum field theory and general relativity. We make no additional assumptions nor introduce extra ingredients, as is often done in alternative quantum theories. When the quantum matter field is projected to a one-particle state, the master equation for a non-relativistic quantum particle in a weak gravitational field predicts decoherence in the energy basis, in contrast to most existing theories of gravitational decoherence. We point out the gauge nature of time and space reparameterizations in matter–gravity couplings, and warn that ‘intrinsic’ decoherence or alternative quantum theories invoking stochastic dynamics arising from temporal or spatial fluctuations violate this fundamental symmetry of classical general relativity. Interestingly we find that the decoherence rate depends on extra parameters other than the Planck scale, an important feature of gravitational decoherence. This is similar to the dependence of the decoherence rate of a quantum Brownian particle to the temperature and spectral density of the environment it interacts with. The corresponding features when gravity acts as an environment in decohering quantum objects are what we call the ‘textures’ of spacetime. We point out the marked difference between the case when gravity is represented as a background spacetime versus the case when gravity acts like a thermodynamic bath to quantum particles. This points to the possibility of using gravitational decoherence measurements to discern whether gravity is intrinsically elemental or emergent.
118622161
Stochastic Gravity: Theory and Applications
Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semi-classical gravity is based on the Einstein-Langevin equation, which has, in addition, sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operator-valued) stress-energy bitensor, which describes the fluctuations of quantum-matter fields in curved spacetimes. A new improved criterion for the validity of semiclassical gravity may also be formulated from the viewpoint of this theory. In the first part of this review we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to the correlation functions. The functional approach uses the Feynman-Vernon influence functional and the Schwinger-Keldysh closed-time-path effective action methods. In the second part, we describe three applications of stochastic gravity. First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic-gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, using the Einstein-Langevin equation, we discuss the backreaction of Hawking radiation and the behavior of metric fluctuations for both the quasi-equilibrium condition of a black-hole in a box and the fully nonequilibrium condition of an evaporating black hole spacetime. Finally, we briefly discuss the theoretical structure of stochastic gravity in relation to quantum gravity and point out directions for further developments and applications.