Production of primordial gravitational waves in a simple class of running vacuum cosmologies
TL;DR: In this article, the problem of cosmological production of gravitational waves is discussed in the framework of an expanding, spatially homogeneous and isotropic FRW type Universe with time-evolving vacuum energy density.
Abstract: The problem of cosmological production of gravitational waves is discussed in the framework of an expanding, spatially homogeneous and isotropic FRW type Universe with time-evolving vacuum energy density. The gravitational wave equation is established and its modified time-dependent part is analytically resolved for different epochs in the case of a flat geometry. Unlike the standard $\Lambda$CDM cosmology (no interacting vacuum), we show that gravitational waves are produced in the radiation era even in the context of general relativity. We also show that for all values of the free parameter, the high frequency modes are damped out even faster than in the standard cosmology both in the radiation and matter-vacuum dominated epoch. The formation of the stochastic background of gravitons and the remnant power spectrum generated at different cosmological eras are also explicitly evaluated. It is argued that measurements of the CMB polarization (B-modes) and its comparison with the rigid $\Lambda$CDM model plus the inflationary paradigm may become a crucial test for dynamical dark energy models in the near future.
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TL;DR: In this paper, the authors examined the running vacuum model with the cosmological constant and found that the best fitted value was a value slightly smaller than that in the original Lambda$CDM model.
Abstract: We examine the running vacuum model with $\Lambda (H) = 3
u H^2 + \Lambda_0$, where $
u$ is the model parameter and $\Lambda_0$ is the cosmological constant. From the data of the cosmic microwave background radiation, weak lensing and baryon acoustic oscillation along with the time dependent Hubble parameter $H(z)$ and weighted linear growth $f (z)\sigma_8(z)$ measurements, we find that $
u=(1.37^{+0.72}_{-0.95})\times 10^{-4}$ with the best fitted $\chi^2$ value slightly smaller than that in the $\Lambda$CDM model.
18 citations
TL;DR: In this paper, the authors investigated the evolution of the universe in the running vacuum model (RVM) with the cosmological constant being a function of the Hubble parameter and derived the evolution equation for the dark energy perturbation.
Abstract: We investigate the matter density perturbation $\delta_m$ and power spectrum $P(k)$ in the running vacuum model (RVM) with the cosmological constant being a function of the Hubble parameter, given by $\Lambda = \Lambda_0 + 6 \sigma H H_0+ 3
u H^2$, in which the linear and quadratic terms of $H$ would originate from the QCD vacuum condensation and cosmological renormalization group, respectively. Taking the dark energy perturbation into consideration, we derive the evolution equation for $\delta_m$ and find a specific scale $d_{cr}=2 \pi/k_{cr}$, which divides the evolution of the universe into the sub and super-interaction regimes, corresponding to $k \ll k_{cr}$ and $k \gg k_{cr}$, respectively. For the former, the evolution of $\delta_m$ has the same behavior as that in the $\Lambda$CDM model, while for the latter, the growth of $\delta_m$ is frozen (greatly enhanced) when $
u + \sigma >(<)0$ due to the couplings between radiation, matter and dark energy. It is clear that the observational data rule out the cases with $
u<0$ and $
u + \sigma <0$, while the allowed window for the model parameters is extremely narrow with $
u, |\sigma| \lesssim \mathcal{O}(10^{-7})$.
12 citations
TL;DR: In this paper, the authors investigated the cosmological production of gravitational waves in a nonsingular flat cosmology powered by a running vacuum energy density described by ρ Λ ≡ ρ ǫ (H ), a phenomenological expression potentially linked with the renormalization group approach in quantum field theory in curved spacetimes.
12 citations
TL;DR: In this article, a special running vacuum model (RVM) was proposed for the cosmological data, which has non-analytic background solutions for the energy densities of matter and radiation.
Abstract: We study a special running vacuum model (RVM) with $\Lambda = 3 \alpha H^2+3\beta H_0^4 H^{-2}+\Lambda_0$, where $\alpha$, $\beta$ and $\Lambda_0$ are the model parameters and $H$ is the Hubble one. This RVM has non-analytic background solutions for the energy densities of matter and radiation, which can only be evaluated numerically. From the analysis of the CMB power spectrum and baryon acoustic oscillation along with the prior of $\alpha>0$ to avoid having a negative dark energy density, we find that $\alpha<2.83\times 10^{-4}$ and $\beta=(-0.2^{+3.9}_{-4.5})\times 10^{-4}$ (95$\%$ C.L.). We show that the RVM fits the cosmological data comparably to the $\Lambda$CDM. In addition, we relate the fluctuation amplitude $\sigma_8$ to the neutrino mass sum $\Sigma m_
u$.
11 citations
TL;DR: In this paper, the authors derived the linear scalar perturbations for two running scenarios, modeling its cosmic evolution and identifying their different imprints on the cosmic microwave background anisotropies and the matter power spectrum.
Abstract: In cosmology, phenomenologically motivated expressions for running vacuum are commonly parametrized as linear functions $\Lambda(H^2)$ or $\Lambda(R)$. Such kind of models assume an equation of state for vacuum given by $\,\overline P_\Lambda=-\,\overline\rho_\Lambda$, relating their background pressure $\,\overline P_\Lambda$ and mean energy density $\,\overline\rho_\Lambda\equiv\Lambda/8\pi G$. This equation of state requires that the dynamic for vacuum is due to the energy exchange with the material species. Most of the approaches to background level consider only the energy exchange between vacuum and the transient dominant material component of the universe. We extend such models assuming the running vacuum as the sum of independent contributions $\,\overline\rho_{\Lambda} =\sum_i\,\overline\rho_{\Lambda i}$, associated with (and interacting with) each of the $i$ material species. We derive the linear scalar perturbations for two running scenarios, modeling its cosmic evolution and identifying their different imprints on the cosmic microwave background anisotropies and the matter power spectrum. In the $\Lambda(H^2)$ scenario the running vacuum are coupled with all the material species in the universe, whereas the $\Lambda(R)$ description only leads to coupling between vacuum and the non-relativistic matter components; which produces different imprints of the two models on the matter power spectrum. A comparison with the Planck 2015 data was made in order to constrain the free parameters of the models. In the case of the $\Lambda(H^2)$ model, it was found that $\Omega_\Lambda=0.705\pm0.027$ and $H_0=69.6\pm2.9\, km\, Mpc^{-1}\, s^{-1}$, which diminish the tension with the low redshift expectations.
10 citations
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TL;DR: This is the first direct detection of gravitational waves and the first observation of a binary black hole merger, and these observations demonstrate the existence of binary stellar-mass black hole systems.
Abstract: On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of $1.0 \times 10^{-21}$. It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203 000 years, equivalent to a significance greater than 5.1 {\sigma}. The source lies at a luminosity distance of $410^{+160}_{-180}$ Mpc corresponding to a redshift $z = 0.09^{+0.03}_{-0.04}$. In the source frame, the initial black hole masses are $36^{+5}_{-4} M_\odot$ and $29^{+4}_{-4} M_\odot$, and the final black hole mass is $62^{+4}_{-4} M_\odot$, with $3.0^{+0.5}_{-0.5} M_\odot c^2$ radiated in gravitational waves. All uncertainties define 90% credible intervals.These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.
9,596 citations
01 Apr 1984
TL;DR: A comprehensive review of the subject of gravitational effects in quantum field theory can be found in this paper, where special emphasis is given to the Hawking black hole evaporation effect, and to particle creation processes in the early universe.
Abstract: This book presents a comprehensive review of the subject of gravitational effects in quantum field theory. Although the treatment is general, special emphasis is given to the Hawking black hole evaporation effect, and to particle creation processes in the early universe. The last decade has witnessed a phenomenal growth in this subject. This is the first attempt to collect and unify the vast literature that has contributed to this development. All the major technical results are presented, and the theory is developed carefully from first principles. Here is everything that students or researchers will need to embark upon calculations involving quantum effects of gravity at the so-called one-loop approximation level.
6,464 citations
TL;DR: In this article, five different approaches to the cosmological constant problem are described, and a brief review of the history of this problem is given. But none of the approaches are considered in this paper.
Abstract: Astronomical observations indicate that the cosmological constant is many orders of magnitude smaller than estimated in modern theories of elementary particles. After a brief review of the history of this problem, five different approaches to its solution are described.
6,248 citations
TL;DR: In this article, the authors review the observational evidence for the current accelerated expansion of the universe and present a number of dark energy models in addition to the conventional cosmological constant, paying particular attention to scalar field models such as quintessence, K-essence and tachyon.
Abstract: We review in detail a number of approaches that have been adopted to try and explain the remarkable observation of our accelerating universe. In particular we discuss the arguments for and recent progress made towards understanding the nature of dark energy. We review the observational evidence for the current accelerated expansion of the universe and present a number of dark energy models in addition to the conventional cosmological constant, paying particular attention to scalar field models such as quintessence, K-essence, tachyon, phantom and dilatonic models. The importance of cosmological scaling solutions is emphasized when studying the dynamical system of scalar fields including coupled dark energy. We study the evolution of cosmological perturbations allowing us to confront them with the observation of the Cosmic Microwave Background and Large Scale Structure and demonstrate how it is possible in principle to reconstruct the equation of state of dark energy by also using Supernovae Ia observational data. We also discuss in detail the nature of tracking solutions in cosmology, particle physics and braneworld models of dark energy, the nature of possible future singularities, the effect of higher order curvature terms to avoid a Big Rip singularity, and approaches to modifying gravity which leads to a late-time accelerated expansion without recourse to a new form of dark energy.
5,954 citations
TL;DR: A review of dark energy can be found in this paper, where the authors present the basic physics and astronomy of the subject, reviews the history of ideas, assesses the state of the observational evidence, and comments on recent developments in the search for a fundamental theory.
Abstract: Physics welcomes the idea that space contains energy whose gravitational effect approximates that of Einstein's cosmological constant, \ensuremath{\Lambda}; today the concept is termed dark energy or quintessence. Physics also suggests that dark energy could be dynamical, allowing for the arguably appealing picture of an evolving dark-energy density approaching its natural value, zero, and small now because the expanding universe is old. This would alleviate the classical problem of the curious energy scale of a millielectron volt associated with a constant \ensuremath{\Lambda}. Dark energy may have been detected by recent cosmological tests. These tests make a good scientific case for the context, in the relativistic Friedmann-Lema\^{\i}tre model, in which the gravitational inverse-square law is applied to the scales of cosmology. We have well-checked evidence that the mean mass density is not much more than one-quarter of the critical Einstein--de Sitter value. The case for detection of dark energy is not yet as convincing but still serious; we await more data, which may be derived from work in progress. Planned observations may detect the evolution of the dark-energy density; a positive result would be a considerable stimulus for attempts at understanding the microphysics of dark energy. This review presents the basic physics and astronomy of the subject, reviews the history of ideas, assesses the state of the observational evidence, and comments on recent developments in the search for a fundamental theory.
4,783 citations