اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدSecond-order effective energy-momentum tensor of gravitational scalar perturbations with perfect fluid
240
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We investigate the second-order gravitational scalar perturbations for a barotropic fluid. We derive the effective energy-momentum tensor described by the quadratic terms of the gravitational and the matter perturbations. We show that the second-order effective energy-momentum tensor is gauge dependent. We impose three gauge conditions (longitudinal, spatially-flat, and comoving gauges) for dust and radiation. The resulting energy-momentum tensor is described only by a gauge invariant variable, but the functional form depends on the gauge choice. In the matter-dominated epoch with dust-like fluid background, the second-order effective energy density and pressure of the perturbations evolve as 1/a^2 in all three gauge choices, like the curvature density of the Universe, but they do not provide the correct equation of state. The value of this parameter depends also on the gauge choice. In the radiation-dominated epoch, the perturbations in the short-wave limit behave in the same way as the radiation-like fluid in the longitudinal and the spatially-flat gauges. However, they behave in a different way in the comoving gauge. As a whole, we conclude that the second-order effective energy-momentum tensor of the scalar perturbation is strictly gauge dependent.
قيم البحث
اقرأ أيضاً
Loop quantum cosmology (LQC) provides promising resolutions to the trans-Planckian issue and initial singularity arising in the inflationary models of general relativity. In general, due to different quantization approaches, LQC involves two types of
quantum corrections, the holonomy and inverse-volume, to both of the cosmological background evolution and perturbations. In this paper, using {em the third-order uniform asymptotic approximations}, we derive explicitly the observational quantities of the slow-roll inflation in the framework of LQC with these quantum corrections. We calculate the power spectra, spectral indices, and running of the spectral indices for both scalar and tensor perturbations, whereby the tensor-to-scalar ratio is obtained. We expand all the observables at the time when the inflationary mode crosses the Hubble horizon. As the upper error bounds for the uniform asymptotic approximation at the third-order are $lesssim 0.15%$, these results represent the most accurate results obtained so far in the literature. It is also shown that with the inverse-volume corrections, both scalar and tensor spectra exhibit a deviation from the usual shape at large scales. Then, using the Planck, BAO and SN data we obtain new constraints on quantum gravitational effects from LQC corrections, and find that such effects could be within the detection of the forthcoming experiments.
We study the effective energy-momentum tensor (EMT) for cosmological perturbations and formulate the gravitational back-reaction problem in a gauge invariant manner. We analyze the explicit expressions for the EMT in the cases of scalar metric fluctu
ations and of gravitational waves and derive the resulting equations of state. The formalism is applied to investigate the back-reaction effects in chaotic inflation. We find that for long wavelength scalar and tensor perturbations, the effective energy density is negative and thus counteracts any pre-existing cosmological constant. For scalar perturbations during an epoch of inflation, the equation of state is de Sitter-like.
For a scalar field $phi$ coupled to cold dark matter (CDM), we provide a general framework for studying the background and perturbation dynamics on the isotropic cosmological background. The dark energy sector is described by a Horndeski Lagrangian w
ith the speed of gravitational waves equivalent to that of light, whereas CDM is dealt as a perfect fluid characterized by the number density $n_c$ and four-velocity $u_c^mu$. For a very general interacting Lagrangian $f(n_c, phi, X, Z)$, where $f$ depends on $n_c$, $phi$, $X=-partial^{mu} phi partial_{mu} phi/2$, and $Z=u_c^{mu} partial_{mu} phi$, we derive the full linear perturbation equations of motion without fixing any gauge conditions. To realize a vanishing CDM sound speed for the successful structure formation, the interacting function needs to be of the form $f=-f_1(phi, X, Z)n_c+f_2(phi, X, Z)$. Employing a quasi-static approximation for the modes deep inside the sound horizon, we obtain analytic formulas for the effective gravitational couplings of CDM and baryon density perturbations as well as gravitational and weak lensing potentials. We apply our general formulas to several interacting theories and show that, in many cases, the CDM gravitational coupling around the quasi de-Sitter background can be smaller than the Newton constant $G$ due to a momentum transfer induced by the $Z$-dependence in $f_2$.
In scalar-vector-tensor (SVT) theories with parity invariance, we perform a gauge-ready formulation of cosmological perturbations on the flat Friedmann-Lema^{i}tre-Robertson-Walker (FLRW) background by taking into account a matter perfect fluid. We d
erive the second-order action of scalar perturbations and resulting linear perturbation equations of motion without fixing any gauge conditions. Depending on physical problems at hand, most convenient gauges can be chosen to study the development of inhomogeneities in the presence of scalar and vector fields coupled to gravity. This versatile framework, which encompasses Horndeski and generalized Proca theories as special cases, is applicable to a wide variety of cosmological phenomena including nonsingular cosmology, inflation, and dark energy. By deriving conditions for the absence of ghost and Laplacian instabilities in several different gauges, we show that, unlike Horndeski theories, it is possible to evade no-go arguments for the absence of stable nonsingular bouncing/genesis solutions in both generalized Proca and SVT theories. We also apply our framework to the case in which scalar and vector fields are responsible for dark energy and find that the separation of observables relevant to the evolution of matter perturbations into tensor, vector, and scalar sectors is transparent in the unitary gauge. Unlike the flat gauge chosen in the literature, this result is convenient to confront SVT theories with observations associated with the cosmic growth history.
We study scalar perturbations induced by scalar perturbations through the non-linear interaction appearing at second order in perturbations. We derive analytic solutions of the induced scalar perturbations in a perfect fluid. In particular, we consid
er the perturbations in a radiation-dominated era and a matter-dominated era. With the analytic solutions, we also discuss the power spectra of the induced perturbations.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
