Searcharxiv⌕ Search

arXiv subjects

Anzhong Wang

Publications and source records attributed to Anzhong Wang.

At least 181 records · Page 10Linked to original sources
arXiv2014

Gravitational quantum effects on power spectra and spectral indices with higher-order corrections

The uniform asymptotic approximation method provides a powerful, systematically-improved, and error-controlled approach to construct accurate analytical approximate solutions of mode functions of perturbations of the Friedmann-Robertson-Walker universe, designed especially for the cases where the relativistic linear dispersion relation is modified after gravitational quantum effects are taken into account. These include models from string/M-Theory, loop quantum cosmology and Hořava-Lifshitz quantum gravity. In this paper, we extend our previous studies of the first-order approximations to high orders for the cases where the modified dispersion relation (linear or nonlinear) has only one-turning point (or zero). We obtain the general expressions for the power spectra and spectral indices of both scalar and tensor perturbations up to the third-order, at which the error bounds are $\lesssim 0.15\%$. As an application of these formulas, we calculate the power spectra and spectral indices in the slow-roll inflation with a nonlinear power-law dispersion relation. To check the consistency of our formulas, we further restrict ourselves to the relativistic case, and calculate the corresponding power spectra, spectral indices and runnings to the second-order. Then, we compare our results with the ones obtained by the Green function method, and show explicitly that the results obtained by these two different methods are consistent within the allowed errors.

astro-ph.CO↗
arXiv2014

Gravitational quantum effects in the light of BICEP2 results

Recently BICEP2 found that the vanishing of the tensor-to-scalar ratio $r$ is excluded at $7σ$ level, and its most likely value is $r=0.2^{+0.07}_{-0.05}$ at $1 σ$ level. This immediately causes a tension with the Planck constraint $r < 0.11$. In addition, it also implies that the inflaton (in single field slow-roll inflation) experienced a Planck excursion during inflation $Δϕ/M_{Pl} \geq {\cal{O}}(1)$, whereby the effective theory of inflation becomes questionable. In this brief report, we show that the inflationary paradigm is still robust, even after the quantum effects are taken into account. Moreover, these effects also help to relax the tension on the different values of $r$ given by BICEP2 and Planck.

astro-ph.CO↗
arXiv2014

Holographic Superconductors in Horava-Lifshitz Gravity

We consider holographic superconductors related to the Schwarzschild black hole in the low energy limit of Hořava-Lifshitz spacetime. The non-relativistic electromagnetic and scalar fields are introduced to construct a holographic superconductor model in Hořava-Lifshitz gravity and the results show that the $α_2$ term plays an important role, modifying the conductivity curve line by means of an attenuation the conductivity.

hep-th↗
arXiv2014

Lifshitz spacetimes, solitons, and generalized BTZ black holes in quantum gravity at a Lifshitz point

In this paper, we study static vacuum solutions of quantum gravity at a fixed Lifshitz point in (2+1) dimensions, and present all the diagonal solutions in closed forms in the infrared limit. The exact solutions represent spacetimes with very rich structures: they can represent generalized BTZ black holes, Lifshitz space-times or Lifshitz solitons, in which the spacetimes are free of any kind of space-time singularities, depending on the choices of the free parameters of the solutions. We also find several classes of exact static non-diagonal solutions, which represent similar space-time structures as those given in the diagonal case. The relevance of these solutions to the non-relativistic Lifshitz-type gauge/gravity duality is discussed.

hep-th↗
arXiv2014

Post-Newtonian approximations in the Hořava-Lifshitz gravity with extra U(1) symmetry

In this paper, we first propose a universal coupling between the gravity and matter in the framework of the Hořava-Lifshitz theory of gravity with an extra U(1) symmetry for both the projectable and non-projectable cases. Then, using this universal coupling we study the post-Newtonian approximations and obtain the parameterized post-Newtonian (PPN) parameters in terms of the coupling constants of the theory. Contrary to the previous works in which only two PPN parameters were calculated, we obtain {\it all} PPN parameters. We then, for the first time in either projectable or non-projectable case, find that all the solar system tests carried out so far are satisfied in a large region of the parameters space. In particular, the same results obtained in general relativity can be easily realized here. A remarkable feature is that the solar system tests impose no constraint on the parameter $λ$ appearing in the kinetic part of the action. As a result, the solar system tests, when combined with the condition for avoidance of strong coupling, do not lead to an upper bound on the energy scale $M_{*}$ that suppresses higher dimensional operators in the theory. This is in sharp contrast to other versions of the HL theory.

hep-ph↗
arXiv2013

Primordial Non-Gaussianity of Gravitational Waves in Hořava-Lifshitz Gravity

In this paper, we study 3-point correlation function of primordial gravitational waves generated in the de Sitter background in the framework of the general covariant Hořava-Lifshitz gravity with an arbitrary coupling constant $λ$. We find that, at cubic order, the interaction Hamiltonian receives contributions from four terms built of the 3-dimensional Ricci tensor $R_{ij}$ of the leaves $t = $ constant. In particular, the 3D Ricci scalar $R$ yields the same $k$-dependence as that in general relativity, but with different magnitude due to coupling with the $U(1)$ field $A$ and a UV history. Interestingly, the two terms $R_{ij}R^{ij}$ and $\left(\nabla^{i}R^{jk}\right)\left(\nabla_{i}R_{jk}\right)$ exhibit peaks at the squeezed limit. We show that this is due to the effects of the polarization tensors. The signal generated by the fourth term, $R^i_j R^j_k R^k_i$, favors the equilateral shape when spins of the three tensor fields are the same, but peaks in between the equilateral and squeezed limits when spins are mixed. The consistency with the recently-released Planck observations on non-Gaussianity is also discussed and is found that $\left(H/M_*\right)^2\left(H/M_{pl}\right) \le 10^{-8}$, where $M_{*}$ denotes the suppression energy of high-order operators, $M_{pl}$ the Planck mass, and $H$ the energy of inflation.

hep-th↗
arXiv2013

Effects of parity violation on non-gaussianity of primordial gravitational waves in Hořava-Lifshitz gravity

In this paper, we study the effects of parity violation on non-gaussianities of primordial gravitational waves in the framework of Hořava-Lifshitz theory of gravity, in which high-order spatial derivative operators, including the ones violating parity, generically appear. By calculating the three point function, we find that the leading-order contributions to the non-gaussianities come from the usual second-order derivative terms, which produce the same bispectrum as that found in general relativity. The contributions from high-order spatial n-th derivative terms are always suppressed by a factor $(H/M_*)^{n-2} \; (n \ge 3)$, where $H$ denotes the inflationary energy and $M_*$ the suppression mass scale of the high-order spatial derivative operators of the theory. Therefore, the next leading-order contributions come from the 3-dimensional gravitational Chern-Simons term. With some reasonable arguments, it is shown that this 3-dimensional operator is the only one that violates the parity and in the meantime has non-vanishing contributions to non-gaussianities.

hep-th↗
arXiv2013

Inflationary cosmology with nonlinear dispersion relations

We present a technique, {\em the uniform asymptotic approximation}, to construct accurate analytical solutions of the linear perturbations of inflation after quantum effects of the early universe are taken into account, for which the dispersion relations generically become nonlinear. We construct explicitly the error bounds associated with the approximations and then study them in detail. With the understanding of the errors and the proper choice of the Liouville transformations of the differential equations of the perturbations, we show that the analytical solutions describe the exact evolution of the linear perturbations extremely well even only in the first-order approximations. As an application of the approximate analytical solutions, we calculate the power spectra and indices of scalar and tensor perturbations in the slow-roll inflation, and find that the amplitudes of the power spectra get modified due to the quantum effects, while the power spectrum indices remain the same as in the linear case.

astro-ph.CO↗
arXiv2013

Stationary and slowly rotating spacetimes in Hořava-Lifshitz gravity

Stationary, axisymmetric and slowly rotating vacuum spacetimes in the Hořava-Lifshitz (HL) gravity are studied, and shown that, for any given spherical static vacuum solution of the HL theory (of any model, including the ones with an additional U(1) symmetry), there always exists a corresponding slowly rotating, stationary and axisymmetric vacuum solution, which reduces to the former, when the rotation is switched off. The rotation is universal and only implicitly depends on the models of the HL theory and their coupling constants through the spherical seed solution. As a result, all asymptotically flat slowly rotating vacuum solutions are asymptotically identical to the slowly rotating Kerr solution. This is in contrast to the claim of Barausse and Sotiriou, Phys. Rev. Lett. {\bf 109}, 181101 (2012), in which slowly rotating black holes were reported (incorrectly) not to exist in the infrared limit of the non-projectable HL theory.

hep-th↗
arXiv2013

Inflation in general covariant Hořava-Lifshitz gravity without projectability

In this paper, we study inflation in the general covariant Hořava-Lifshitz gravity without the projectability condition. We write down explicitly the equations of the linear scalar perturbations of the FRW universe for a single scalar field without specifying to any gauge. Applying these equations to a particular gauge, we are able to obtain a master equation of the perturbations, in contrast to all the other versions of the theory without the projectability condition. This is because in the current version of the theory it has the same degree of freedom of general relativity. To calculate the power spectrum and index, we first define the initial conditions as the ones that minimize the energy of the ground state. Then, we obtain the full solutions of the equation of motion, by using the WKB approximations. From these solutions, we calculate the power spectrum and spectrum index of the comoving curvature perturbations and find the corrections due to the high order spatial derivative terms of the theory to those standard results obtained in general relativity. Remarkably, partly of corrections are a direct consequence of the non-projectability condition. It is also shown that the perturbations are still of scale-invariance, and the results obtained in the general covariant Hořava-Lifshitz gravity without the projectability condition are consistent with all current cosmological observations.

hep-th↗
arXiv2013

Polarizing primordial gravitational waves by parity violation

We study primordial gravitational waves (PGWs) in the Horava-Lifshitz (HL) theory of quantum gravity, in which high-order spatial derivative operators, including the ones violating parity, generically appear in order for the theory to be power-counting renormalizable and ultraviolet (UV) complete. Because of both parity violation and non-adiabatic evolution of the modes due to a modified dispersion relationship, a large polarization of PGWs becomes possible, and it could be well within the range of detection of the BB, TB and EB power spectra of the forthcoming cosmic microwave background (CMB) observations.

astro-ph.CO↗
arXiv2013

Static post-Newtonian limits in non-projectable Hořava-Lifshitz gravity with an extra U(1) symmetry

In this paper, we study static post-Newtonian limits in non-projectable Hořava-Lifshitz gravity with an extra U(1) symmetry. After obtaining all static spherical solutions in the infrared, we apply them to the solar system tests, and obtain the Eddington-Robertson-Schiff parameters in terms of the coupling constants of the theory. These parameters are well consistent with observations for the physically viable coupling constants. In contrast to the projectable case, this consistence is achieved without taking the gauge field and Newtonian prepotential as part of the metric.

hep-th↗
arXiv2013

U(1) symmetry and elimination of spin-0 gravitons in Horava-Lifshitz gravity without the projectability condition

In this paper, we show that the spin-0 gravitons appearing in Horava-Lifshitz gravity without the projectability condition can be eliminated by extending the gauge symmetries of the foliation-preserving diffeomorphisms to include a local U(1) symmetry. As a result, the problems of stability, ghost, strong coupling, and different speeds in the gravitational sector are automatically resolved. In addition, with the detailed balance condition softly breaking, the number of independent coupling constants can be significantly reduced (from more than 70 down to 15), while the theory is still UV complete and possesses a healthy IR limit, whereby the prediction powers of the theory are considerably improved. The strong coupling problem in the matter sector can be cured by introducing an energy scale $M_{*}$, so that $M_{*} < Λ_ω$, where $M_{*}$ denotes the suppression energy of high order derivative terms, and $Λ_ω$ the would-be strong coupling energy scale.

hep-th↗
arXiv2013

Non-Gaussianity of a single scalar field in general covariant Hořava-Lifshitz gravity

In this paper, we study non-Gaussianity generated by a single scalar field in slow-roll inflation in the framework of the non-relativistic general covariant Hořava-Lifshitz theory of gravity with the projectability condition and an arbitrary coupling constant $λ$, where $λ$ characterizes the deviation of the theory from general relativity (GR) in the infrared. We find that the leading effect of self-interaction, in contrary to the case of minimal scenario of GR, is in general of the order $\hatα_{n} ε^{3/2}$, where $ε$ is a slow-roll parameter, and $\hatα_{n} (n = 3, 5)$ are the dimensionless coupling coefficients of the six-order operators of the Lifshitz scalar, and have no contributions to power spectra and indices of both scalar and tensor. The bispectrum, comparing with the standard one given in GR, is enhanced, and gives rise to a large value of the nonlinearity parameter $f_{\text{NL}}$.We study how the modified dispersion relation with high order moment terms affects the evaluation of the mode function and in turn the bispectrum, and show explicitly that the mode function takes various asymptotic forms during different periods of its evolution. In particular, we find that it is in general of superpositions of oscillatory functions, instead of plane waves like in the minimal scenario of GR. This results in a large enhancement of the folded shape in the bispectrum.

hep-th↗
arXiv2013

Solar system tests and interpretation of gauge field and Newtonian prepotential in general covariant Hořava-Lifshitz gravity

We study spherically symmetric, stationary vacuum configurations in general covariant theory (U(1) extension) of Hořava-Lifshitz gravity with the projectability condition and an arbitrary coupling constant $λ$, and obtain all the solutions in closed forms. If the gauge field $A$ and the Newtonian prepotential $φ$ do not directly couple to matter fields, the theory is inconsistent with solar system tests for $λ\not=1$, no matter how small $|λ-1|$ is. This is shown to be true also with the most general ansatz of spherical (but not necessarily stationary) configurations. Therefore, to be consistent with observations, one needs either to find a mechanism to restrict $λ$ precisely to $λ_{GR}=1$, or to consider $A$ and/or $φ$ as parts of the 4-dimensional metric on which matter fields propagate. In the latter, requiring that the line element be invariant not only under the foliation-preserving diffeomorphism but also under the local U(1) transformations, we propose the replacements, $N \rightarrow N - \upsilon(A - {\cal{A}})/c^2$ and $N^i \rightarrow N^i+N\nabla^{i}φ$, where $\upsilon$ is a dimensionless coupling constant to be constrained by observations, $N$ and $N^i$ are, respectively, the lapse function and shift vector, and ${\cal{A}} \equiv - \dotφ + N^i\nabla_{i}φ+ N(\nabla_{i}φ)^2/2$. With this prescription, we show explicitly that the aforementioned solutions are consistent with solar system tests for both $λ=1$ and $λ\not=1$, provided that $|\upsilon-1|<10^{-5}$. From this result, the physical and geometrical interpretations of the fields $A$ and $φ$ become clear. However, it still remains to be understood how to obtain such a prescription from the action principle.

hep-th↗
arXiv2012

On "No-go theorem for slowly rotating black holes in Hořava-Lifshitz gravity"

Slowly rotating black holes in the non-projectable Hořava-Lifshitz (HL) theory were studied recently in Phys. Rev. Lett. {\bf 109}, 181101 (2012), and claimed that they do not exist. In this Comment, we show that this is incorrect, and such solutions indeed exist in the IR limit of the non-projectable HL theory.

hep-th↗
arXiv2012

Inflation in general covariant theory of gravity

In this paper, we study inflation in the framework of the nonrelativistic general covariant theory of the Hořava-Lifshitz gravity with the projectability condition and an arbitrary coupling constant $λ$. We find that the Friedmann-Robterson-Walker (FRW) universe is necessarily flat in such a setup. We work out explicitly the linear perturbations of the flat FRW universe without specifying to a particular gauge, and find that the perturbations are different from those obtained in general relativity, because of the presence of the high-order spatial derivative terms. Applied the general formulas to a single scalar field, we show that in the sub-horizon regions, the metric and scalar field are tightly coupled and have the same oscillating frequencies. In the super-horizon regions, the perturbations become adiabatic, and the comoving curvature perturbation is constant. We also calculate the power spectra and indices of both the scalar and tensor perturbations, and express them explicitly in terms of the slow roll parameters and the coupling constants of the high-order spatial derivative terms. In particular, we find that the perturbations, of both scalar and tensor, are almost scale-invariant, and the spectrum indices are the same as those given in GR, but the ratio of the scalar and tensor power spectra depends on the high-order spatial derivative terms, and can be different from that of GR significantly.

gr-qc↗